Introduction

Remote sensing technology has become an indispensable tool in modern agriculture, including precise monitoring and management of crop health, soil conditions, and environmental factors. One significant tool of remote sensing is hyperspectral images (HSIs), which can provide detailed spectral information across a wide range of wavelengths (Ashraf et al., 2023). However, handling massive hyperspectral data remains a challenge for traditional data acquisition and compression techniques (Zhang et al., 2014).

Effectively compressing plant HSIs while retaining the non-redundant information of the original HSIs is of great significance. The primary challenges in HSI compression include:

• Large Data Volume: HSIs consist of hundreds of spectral bands, resulting in large data volumes that are difficult to store and process efficiently.

• Irrelevant Background Information: HSIs often contain substantial amounts of background information that are not relevant to the target plant regions, wasting storage and computational resources.

Candes & Tao (2006) proposed compression sensing (CS) to acquire and compress signals simultaneously.Berger et al. (2010) noted that the high correlation of the signal itself helps to improve the compression ratio and the reconstruction quality of CS.

In recent years, deep learning, including federated learning (Kong et al., 2024), has emerged as a powerful tool for hyperspectral data analysis, offering significant improvements in accuracy and efficiency for tasks such as ROI extraction and spectral unmixing. These advancements have opened new avenues for enhancing the performance of hyperspectral compressive sensing algorithms. Methods based on regions of interest (ROI) improve reconstruction performance at low bit rates. More recent approaches leverage deep learning techniques to further refine ROI extraction, achieving higher accuracy in complex scenarios.

Different from ordinary 2D images, HSIs have high inter-spectral and intra-spatial correlation (Xu et al., 2018a). How to make full use of these characteristics of HSIs to improve the reconstruction performance has been a research hotspot in the field of hyperspectral compression sensing (HCS) research. The sparse and low-rank near-isometric linear embedding (SLRNILE) method, based on the John-Lindenstrauss lemma, was proposed to reduce the dimension and extract proper features for HSI classification (Sun et al., 2017).Kang & Lu (2009) proposed a video sequence grouping method based on distributed compressed sensing after studying the correlation of video sequences.Chen, Nasrabadi & Tran (2011) proposed a sparse method for target detection in HSIs.Wang et al. (2015) proposed a pixel-based distributed compression sensing algorithm.Wang et al. (2017) proposed a HCS method based on joint tensor Tucker decomposition and weighted total variation regularization. In this approach, a single HSI was regarded as a tensor with three modes (width, height and frequency band), and then the direct tensor modeling method was employed to identify the hidden spatial-spectral structure. The proposal and application of tensor compression algorithm is of great significance for better remain of structural information. However, the above researches can not make full use of high spectral-spatial correlation, and consider the characteristics of multiple arbitiary-shape ROIs of the HSIs and unuseful backgound information.

In our previous research, in order to figure out the optimal sparse representation method that can maximize the sparsity of the spectral data and the best measurement matrix that can preserve the non-redundant information of the original data under a certain compression rate, we have studied the compression performance of different sparse representation methods and measurement matrices for plant HSIs. The adaptive grouping distributed compression sensing (AGDCS) algorithm was proposed to compress and reconstruct the HSIs (Xu et al., 2017). In the aspect of reconstruction, a prediction-based spatial-spectral adaptive hyperspectral compressive sensing (PSSAHCS) algorithm was proposed (Xu et al., 2018b). And a new adaptive distributed compressive sensing method based on guided filter (ADCSGF) was proposed (Xu et al., 2020). We introduced the greedy compression sensing method, and used five greedy reconstruction algorithms to sample and reconstruct the spectral reflectance of plants under different sampling rates (Xu et al., 2018a;Xu et al., 2018b). We proposed a hyperspectral compressive sensing method based on multiple arbitrary-shape regions of interest (HCSMAROI) (Jia et al., 2021), which reconstructed HSIs pixel by pixel but did not consider the high interrelation in the spatial domain.

In this paper, we propose a novel Recursive Sub-Tensor Hyperspectral Compressive Sensing (RSTHCS) for plant leaves based on multiple arbitrary-shape regions of interest. RSTHCS fully takes into account high spatial and spectral correlation of arbitrary-shape plant leave HSIs. Within the RSTHCS framework, an iterative maximum inscribed rectangle algorithm is employed to extract all sub-tensors for multiple arbitrary-shape ROIs while discarding the background region. Subsequently, hyperspectral tensor compressive sensing is applied to compress and reconstruct each sub-tensor sequentially, leading to the reconstruction of the entire hyperspectral images of plant leaves. The proposed RSTHCS not only discards unuseful background information but also employs tensor hyperspectral compressive sensing to compress and reconstruct each sub-tensor sequentially.

Methods

The framework of the proposed method

Figures 1 and2 illustrate the framework and flow of the proposed RSTHCS method, respectively. The method can be summarized as follows:

• Input the plant leaf HSIs: The HSIs of plant leaves are input. The input HSI data has dimensions ofh × w × c, whereh andw represent the height and width of the image, andc is the number of spectral bands.

• Optimal band selection using SSDC: The Spatial Spectral Decorrelation Criterion (SSDC) is used to identify the optimal band with the highest Signal-to-Noise Ratio (SNR), which serves as the basis for mask image generation to isolate the leaf regions. The SNR for thez-th band is calculated as follows:(1)${\displaystyle \text{SNR}=20{log}_{10}\left(\frac{M_z}{{\sigma }^2}\right)}$whereM_z is the local mean of the image in thez-th band, andσ² is the noise variance.

• Binarization and mask image generation: The selected band undergoes binarization to create a mask image. The steps are as follows: The binary maskM can be used to show the leaf regions and background as follows:(2)${\displaystyle M\left(i,j\right)=\left\{\begin{array}{cc}1\hfill & \text{if}\left(i,j\right)\text{belongs to leaf region}\hfill \\ 0\hfill & \text{if}\left(i,j\right)\text{belongs to background}\hfill \end{array}\right.}$

  1. A thresholding process is applied to the grayscale image to separate leaf regions from the background.

  2. The binary image is labeled as 1 (white) for the leaf regions and 0 (black) for the background.

  3. The filling operation is used to fill the holes in the leaf regions and then removal operation to remove the disturbing noises.

• Extracting leaf regions: The mask image is applied to the original HSIs to extract the leaf regions.

• Sub-tensor extraction using recursive maximum inscribed rectangle algorithm: The recursive maximum inscribed rectangle algorithm is used to extract sub-tensors from the plant leaf region. The largest inscribed rectangle is identified within the leaf region, forming a sub-tensorT₁ that includes both spatial and spectral information. For each iteration, the sub-tensorT_k is defined by its spatial coordinates and spectral bands, with dimensionsh_k × w_k × c:(3)${\displaystyle T_k=I_{x_k:x_k+w_k,y_k:y_k+h_k,z_1:z_c}}$whereh_k andw_k are the height and width of thek-th sub-tensor, andz₁ toz_c represent the spectral bands.

• Updating the mask image and threshold check: Once a sub-tensor is extracted, the corresponding region in the mask is set to 0, removing the region from further processing. If the maximum width or height of the sub-tensor is less than a predefined threshold (Th), the process moves to step (i). This threshold ensures that only significant regions are processed. SeeSub Tensor Compressive Sensing subsection for details

• Tensor compression using tucker decomposition: Each extracted sub-tensor undergoes Tucker decomposition to compress the data while retaining the most significant features:(4)${\displaystyle T_k\approx A{\times }_{1}U{\times }_{2}V{\times }_{3}W}$whereA is the core tensor, andU,V, andW are the factor matrices along each mode (spatial and spectral dimensions). Tucker decomposition reduces the dimensionality and compresses the sub-tensor efficiently.

• Sub-tensor reconstruction: After compression, each sub-tensor is reconstructed using the Tucker components:(5)${\displaystyle {\hat{T}}_k=A{\times }_{1}U{\times }_{2}V{\times }_{3}W}$This step is iterated from step (e) to continuously extract and process new sub-tensors until all significant regions are reconstructed.

• Processing small regions with sparse compressive sensing: For regions where the maximum width or height of the sub-tensor is less than Th, SSCS (Zhang et al., 2016) is applied to compress and reconstruct the remaining small regions. This ensures that even minor details are effectively processed.

• Combining reconstructed sub-tensors: After all sub-tensors have been reconstructed, they are combined to form the final hyperspectral image of the leaf region. The complete reconstruction$\hat{T}$ is obtained by combined by all reconstructed sub-tensors:(6)${\displaystyle \hat{T}=\sum _{k=1}^n{\hat{T}}_k}$wheren is the total number of sub-tensors. The final reconstructed hyperspectral data retains the original dimensionsh × w × c.

SSDC

SSDC takes advantage of the significant correlation between spatial domain and spectral domain of HSIs (Gao et al., 2013). The selection of the optimal spectral band is a crucial step in the proposed RSTHCS method, as it ensures that the most informative spectral data is used for subsequent processing. The SSDC leverages the high correlation between adjacent spectral bands to estimate the noise variance and compute the SNR for each band. We perform multiple linear regression using the bands adjacent to z (i.e., (z − 1) − th,z − th and (z + 1) − th) bands to solve the regression parameters and get the fitting image. The calculation principle is as follows (Xu et al., 2020):(7)${\displaystyle {\tilde{f}}_{x,y,z}=a{f}_{x,y,z-1}+b{f}_{x,y,z+1}+d{f}_{p,z}+d}$(8)${\displaystyle f_{p,z}=\left\{\begin{array}{cc}{f}_{x-1,y,z}\hfill & ,x>1\hfill \\ f_{x,y-1,z}\hfill & ,x=1,y>1\hfill \\ 0\hfill & ,x=1,y=1\hfill \end{array}\right.}$wheref is the original value of the image,$\tilde{f}$ is the gray value of the image calculated by the linear regression coefficients a, b, c and d.f_p,z is given byEq. (8). Make a difference to remove the correlation as shown inEq. (9):(9)${\displaystyle r_{x,y,z}=f_{x,y,z}-{\tilde{f}}_{x,y,z}}$wherer_x,y,z is residual betweenf_x,y,z and${\tilde{f}}_{x,y,z}$.(10)${\displaystyle {\sigma }^2=\frac{1}{h\times w-5}\sum _{x=1}^h\sum _{y=1}^w{r}_{x,y}^2}$whereσ² is the noise variance.(11)${\displaystyle M_z=\frac{1}{h\times w}\sum _{x=1}^h\sum _{y=1}^w{f}_{x,y,z}}$whereM_z is the local mean of the image inz − th band. Then SNR of this band is calculated byEq. (12).(12)${\displaystyle SNR=20lg\frac{M_z}{{\sigma }^2}.}$Finally, the band with the highest SNR is selected as the optimal band, which is then used for further processing. This step is critical as it ensures that only the most optimal spectral data is used in the sequence steps, thereby enhancing the accuracy and efficiency of the compressive sensing process.

In our experiments, it is found that the optimal wavelengths of tea leaf HSIs and soybean ones are 600 nm and 680 nm, respectively. Therefore, these bands were chosen as the baseline for subsequent mask image generation, data compression sampling, and reconstruction operations.Figure 3 is the SSDC-wavelength curve for the soybean data as an example.

Sub tensor compressive sensing

After obtaining the mask image through SSDC, the initial maximum inscribed rectangle of the leaf region can be determined. This rectangle is then utilized to extract the sub-tensor of plant leaf HSIs. The first sub-tensor can be decomposed using the following tensor factorization. Subsequently, the mask image is updated by infilling its maximum inscribed rectangle with dark background. The iteration process continues until the long side of the maximum inscribed rectangle is less than the threshold Th. The smaller the threshold, the more complete the reconstructed leaf ROI. When the threshold is less than 3, the extracted regions cannot be used for tensor operations. So we set the threshold to 3.Figure 4 shows the recursive updated process of the maximum inscribed rectangle of the mask image.

Each sub-tensor T can be decomposed using the Tucker decomposition as follows: as shown inFig. 5, the result of the Tucker decomposition of sub-tensorT₁ is a third-order core sub-tensorA with lower rank and the corresponding factor matricesU,V andW. These three factor matrices in their respective directions serve as bases for sub-tensorT₁. The core sub-tensorA is the set of coefficients that combine these base vectors to reconstruct the original sub-tensorT₁, effectively capturing the majority of data characteristics inherent in the original sub-tensorT₁.

Tensor reconstruction aims to approximate the original tensor using factor matrices and the core tensor. Specifically, the Tucker decomposition decomposes the sub-tensorT₁ intoU,V andW, which represent the factor matrices and the coefficientA, which represents the core sub-tensor. Each element in the core tensor can be considered as the weight of the cross product between corresponding column vectors in the factor matrices (Kolda & Bader, 2009). The reconstructed sub-tensor can be obtained by:(13)${\displaystyle \widehat{T_1}\approx A{\times }_{1}U{\times }_{2}V{\times }_{3}W=\sum _{p=1}^P\sum _{q=1}^Q\sum _{r=1}^R{a}_{pqr}{u}_p\circ v_q\circ w_r}$where$\widehat{T_1}\in {\mathbb{R}}^{I\times J\times K}$,U ∈ ℝ^I×P,V ∈ ℝ^J×Q andW ∈ ℝ^K×R are the factor matrices (which are usually orthogonal) and can be regarded as the principal components in each mode. The tensorA ∈ ℝ^P×Q×R is referred to the core tensor where its entries indicate the level of interaction between different components (Gao et al., 2013). The symbol ∘ represents cross product operation.

Similarly, the remaining sub-tensors of the HSIs can be reconstructed from$\widehat{T_1}$. According to the position of summarizing all sub-tensor reconstructed results, so a complete reconstructed result$\hat{T}$ can be obtained as follows:(14)${\displaystyle \hat{T}=\sum _{i=1}^n\widehat{T_i}}$wheren refers to the number of sub-tensor of plant leaf HSIs. It is important to note that the edges of the leaves are serrated in the reconstructed sub-tensors.

For each leaf tensor, the reconstruction process can be carried out as follows:

(1) The Kronecker measurement matrix is constructed and the leaf tensor is compressed. Let the compression ratios for the three dimensions of the subtensor ber₁,r₂ andr₂, respectively. Let the height, width, and number of bands of the subtensor beh′,w′ andb′, respectively. After compressive sampling, the values of three dimensionsm₁,m₂ andm₃ can be obtained fromEqs. (15),(16) and(17), respectively.(15)${\displaystyle m_1=r_1\times h^{\prime }\left(0<r_1\le 1\right).}$(16)${\displaystyle m_2=r_2\times w^{\prime }\left(0<r_2\le 1\right).}$(17)${\displaystyle m_3=r_3\times b^{\prime }\left(0<r_3\le 1\right).}$In the experiment, after specifying the total sampling ratem, the sampling rates are distributed among the three dimensionsr₁,r₂ andr₂. The Kronecker measurement matrix is then constructed based onEq. (18).(18)${\displaystyle \varphi ={\varphi }_3\otimes {\varphi }_2\otimes {\varphi }_1.}$InEq. (18),ϕ₁ ∈ ℝ^m₁×h′,ϕ₂ ∈ ℝ^m₂×w′,ϕ₁ ∈ ℝ^m₃×b′ are mutually independent random Gaussian measurement matrices. The matrixϕ represents the Kronecker-structured measurement matrix. Sampling is performed to obtain the measurement valuesY ∈ ℝ^m₁m₂m₃.

(2) To construct the Kronecker sparse basis Ψ and the Kronecker sensing matrix Θ , the construction of Ψ can be obtained fromEq. (19)(19)${\displaystyle \Psi ={\Psi }_3\otimes {\Psi }_2\otimes {\Psi }_1.}$In this equation, Ψ₁ ∈ ℝ^h′×h′, Ψ₂ ∈ ℝ^w′×w′, Ψ₃ ∈ ℝ^b′×b′ are mutually independent DCT (Discrete Cosine Transform) sparse bases. The matrix Ψ ∈ ℝ^{h′w′b′×h′w′b′} has a Kronecker structure. The construction of Θ can be obtained fromEq. (20)(20)${\displaystyle \Theta ={\Theta }_3\otimes {\Theta }_2\otimes {\Theta }_1.}$In this equation, Θ ∈ ℝ^{m₁m₂m₃×h′w′b′} has a Kronecker structure. Θ₁, Θ₂ and Θ₃ can be obtained fromEqs. (21),(22) and(23), respectively.(21)${\displaystyle {\Theta }_1={\varphi }_1\times {\Psi }_1.}$(22)${\displaystyle {\Theta }_2={\varphi }_2\times {\Psi }_2.}$(23)${\displaystyle {\Theta }_3={\varphi }_3\times {\Psi }_3.}$

(3) According to tensor compressive sampling theory, the sparse subtensor coefficients$\hat{S}$ can be obtained. The reconstruction algorithm employs the Subtensor Orthogonal Matching Pursuit (SOMP) algorithm. According toEq. (24), the approximate value of the original subtensor$\hat{X}$ can be obtained from$\hat{S}$(24)${\displaystyle \hat{X}=\Psi \hat{S}.}$After obtaining the reconstructed approximate solution for each subtensor, combine them according to their positions in each subregion to obtain the reconstructed result for the entire hyperspectral data of the leaf region.

Experimental Results

In the experiment, two types of plant leaf HSIs are selected: tea leaves and soybean leaves, which contain two sets of data respectively. The HSIs of tea leaves in our previous research are used in this paper (Xu et al., 2017). The first set (#1) of tea leaves HSIs covers wavelengths from 445 nm to 914 nm, with a total of 369 bands. And the second set (#2) of tea leaves HSIs spans wavelengths ranging from 430 nm to 900 nm, with a total of 374 bands. The images of 661 nm, 553 nm and 445 nm from tea leaves data are selected as the red, green and blue channels to construct the false color composite RGB images as shown inFigs. 6A and6B.

In the soybean HSIs experiments, a hyperspectral imaging system, ImSpector V10E (SPECIM, Finland) covering the spectral wavelengths of 400–1,000 nm, was employed. The system comprises a CCD camera (DL-604M, Andor, Ireland), an imaging spectrograph, a lens, a light sources provided by 150W quartz tungsten halogen lamp (2900-ER, Illumination, USA). The system is equipped with software (Isuzu Optics Corp, Taiwan) for the computer operating the spectral image system. The spectral resolution is 0.65 nm and the resolution of CCD array detector in the camera is 1,344 ×1,024. The system is driven by electronically controlled displacement platform (IRCP0076, Isuzu Optics Corp, Taiwan) to scan the samples line by line. Two HSIs of soybean leaves cover wavelengths from 445 nm to 850 nm, with a total of 518 bands. The image of 666 nm, 558 nm and 476 nm from soybean leaves data are selected as the red, green and blue channels to construct the false color composite RGB images as shown inFigs. 6C and6D.

The experiments are performed in comparison with other methods, including Block Compressive Sensing (BCS), HCSMAROI, and Tensor Compressive Sensing (TCS). The evaluation criterion includes visual quality, PSNR, reconstructed time, and reconstructed spectra, spectral angle mapper (SAM) and spectral indices. The software platform employed is MATLAB R2018b, and the hardware platform is a Lenovo notebook computer equipped with an Intel i7 CPU clocked at 2.8 GHz with 8 GB of memory.

Reconstruction performance of tea leaf HSIs

Experimental results in the spatial domain

Figure 7 illustrates the experimental results for #1 HSIs of tea leaves using BCS, HCSMAROI, TCS and RSTHCS at the sampling rates 2%, 6%, 10%, 14%, 18% and 22%. HCSMAROI, TCS and RSTHCS preserve more spatial correlation to achieve superior reconstructed performances compared with BCS. Notably, RSTHCS allocates all the sampling rates to tea leaf ROIs and achieves better subjective quality for reconstructed tea leaf regions than BCS and TCS algorithms, particularly at low sampling rates.

As shown inTable 2,Figs. 8A and8B, the mean PSNRs of reconstructed images using four different algorithms on two HSIs of tea leaves are all improved with the increasing of the sampling rates. Notably, TCS and RSTHCS can achieve better reconstruction performance than that of BCS and HCSMAROI. And RSTHCS can achieve the highest mean PSNRs at all sampling rates. In #1 HSIs of tea leaves, the mean PSNR value of RSTHCS is 1.23 dB and 29.946 dB higher than that of TCS and BCS at the sampling rate of 2%, respectively. In #2 HSIs of tea leaves, the mean PSNR value of RSTHCS is 1.23 dB and 29.432 dB higher than that of TCS and BCS at the sampling rate of 2%, respectively. These results shows that RSTHCS can achieve quite good reconstructed performance in the spatial domain.

Table 2:

Comparison of mean PSNR/dB of the HSIs of tea leaves for different algorithms.

	Algorithms	Sampling rates
		2%	6%	10%	14%	18%	22%
#1 HSIs of tea leaves	BCS	11.721	29.823	33.826	35.156	35.875	36.332
	HCSMAROI	24.412	34.029	35.790	36.576	37.013	37.312
	TCS	40.441	41.941	43.240	44.387	45.034	45.793
	RSTHCS	41.667	43.095	44.650	46.192	48.112	50.818
#2 HSIs of tea leaves	BCS	12.067	29.046	32.988	34.393	35.172	35.661
	HCSMAROI	24.040	33.443	35.184	35.945	36.370	36.646
	TCS	40.269	41.398	43.104	44.873	46.130	46.986
	RSTHCS	41.499	43.510	45.191	46.819	48.822	51.744

DOI:10.7717/peerjcs.2410/table-2

As shown inTable 3, the results of two HSIs of tea leaves indicate that the reconstructed time of four algorithms increase with higher sampling rate. Notably, the reconstructed time of TCS and RSTHCS are lower than that of BCS and HCSMAROI at sampling rates from 2% to 22%. It means that TCS and RSTHCS outperformed the traditional BCS algorithm in terms of reconstruction efficiency. In #1 HSIs of tea leaves, at the sampling rate of 2%, the reconstructed time of RSTHCS is 2131s shorter than that of BCS and only 27s longer than that of TCS. In #2 HSIs of tea leaves, at the sampling rate of 2%, the reconstructed time for RSTHCS is 2692s shorter than that for BCS and only 10s slightly longer than that of TCS.

Table 3:

Comparison of reconstructed Time/s of the HSIs of tea leaves with different algorithms.

	Algorithms	Sampling rates
		2%	6%	10%	14%	18%	22%
#1 HSIs of tea leaves	BCS	2,284	2,601	2,758	3,151	3,456	3,509
	HCSMAROI	1,071	1,379	1,599	1,840	2,071	2,307
	TCS	126	133	138	158	189	249
	RSTHCS	153	165	216	218	225	262
#2 HSIs of tea leaves	BCS	2,880	3,066	3,399	3,565	3,865	4,197
	HCSMAROI	1,291	1,639	1,882	2,162	2,451	2,750
	TCS	178	184	208	218	251	253
	RSTHCS	188	214	253	277	300	357

DOI:10.7717/peerjcs.2410/table-3

Experimental results in the spectral domain

Spectral analysis of plant HSIs plays a crucial role in monitoring plant growth, disease and insect pest detection and the inversion of physiological parameters.Figures 9A–9F show the average reconstructed spectra of the multiple arbitrary-shape ROIs of BCS, HCSMAROI, TCS and RSTHCS for #1 HSIs of tea leaves at different sampling rates from 2% to 22%. It is evident that the reconstructed spectra of RSTHCS are closer to the ground truth than that of BCS, HCSMAROI and TCS at various sampling rates. Particularly, at low sampling rates, the reconstructed spectra of RSTHCS is closer to the ground truth than those of the other algorithms.Table 4 shows the SAM of different algorithms for HSIs of the first and second tea leaves at different sampling rates. The proposed RSTHCS can achieve significantly smaller SAM values than those of the other algorithms for these two tea leaf HSIs at different sampling rates. The proposed RSTHCS can obtain better spectral reconstruction performance than that of the other algorithms for HSIs of tea leaves.

Table 5 provides error comparisons for spectral indices, including DD, TVI, LCI and mND680, of different algorithms for two HSIs of tea leaves at different sampling rates. In #1 HSIs of tea leaves, for spectral indices of DD and TVI at different sampling rates, the errors of RSTHCS are relatively lower than those of the other algorithms. For spectral indices LCI and mND680 at different sampling rates, although the errors of RSTHCS are not always the smallest, they are reduced to the order of 10⁻⁴ or 10⁻⁵. In #2 HSIs of tea leaves, for spectral indices of DD, TVI, LCI and mND680 at different sampling rates, the errors of RSTHCS are generally lower than those of the other algorithms.

Figure 10 shows the variation trends of four spectral indices errors of two HSIs of tea leaves with the increasing of sampling rates. It can be seen fromTable 4 that the spectral index errors of BCS and HCSMAROI are larger, while the differences of errors of spectral indices between TCS and RSTHCS are small. In order to better observe the differences between four algorithms, two coordinate axes with different scales. The left axis depicts the spectral indices errors of BCS and HCSMAROI, while the right axis illustrates the spectral index error of TCS and RSTHCS.

Table 4:

Comparison of SAM of the HSIs of tea leaves with different algorithms.

	Algorithms	Sampling rates
		2%	6%	10%	14%	18%	22%
#1 HSIs of tea leaves	BCS	1.400 × 101	1.543	5.588 × 10−1	3.668 × 10−1	2.947 × 10−1	2.599 × 10−1
	HCSMAROI	3.296	5.065 × 10−1	3.928 × 10−1	3.616 × 10−1	3.445 × 10−1	3.331 × 10−1
	TCS	1.089 × 10−2	9.585 × 10−3	7.146 × 10−3	7.045 × 10−2	6.127 × 10−3	5.971 × 10−3
	RSTHCS	6.07 × 10−4	3.423 × 10−4	2.578 × 10−4	2.217 × 10−4	1.981 × 10−4	1.656 × 10−4
#2 HSIs of tea leaves	BCS	1.390 × 101	1.868	7.161 × 10−1	4.563 × 10−1	3.548 × 10−1	3.046 × 10−1
	HCSMAROI	4.077	5.943 × 10−1	4.370 × 10−1	3.938 × 10−1	3.706 × 10−1	3.557 × 10−1
	TCS	1.283 × 10−2	1.244 × 10−3	1.237 × 10−3	1.002 × 10−2	8.826 × 10−3	8.412 × 10−3
	RSTHCS	1.105 × 10−3	5.004 × 10−4	3.968 × 10−4	3.384 × 10−4	2.874 × 10−4	2.513 × 10−4

DOI:10.7717/peerjcs.2410/table-4

Table 5:

Error comparisons of spectral indices of different algorithms of the HSIs of tea leaves.

	Spectral index	Algorithms	Sampling rates
			2%	6%	10%	14%	18%	22%
	DD	BCS	3.16 × 10−1	2.64 × 10−1	1.10 × 10−1	7.25 × 10−2	5.65 × 10−2	4.84 × 10-2
		HCSMAROI	4.69 × 10−1	7.72 × 10−2	4.62 × 10−2	3.68 × 10−2	3.19 × 10−2	2.73 × 10-2
		TCS	1.89 × 10−3	1.66 × 10−3	8.78 × 10−4	7.32 × 10−4	8.24 × 10−5	7.39 × 10-5
		RSTHCS	4.00 × 10−5	8.02 × 10−6	6.19 × 10−6	3.04 10−7	7.52 × 10−6	3.53 × 10-6
#1 HSIs of tea leaves	TVI	BCS	5.39 × 10−2	4.95 × 10−2	2.28 × 10−3	4.82 × 10−3	4.94 × 10−3	5.23 × 10-3
		HCSMAROI	1.81 × 10−1	5.13 × 10−3	5.12 × 10−3	5.04 × 10−3	4.47 × 10−3	4.15 × 10-3
		TCS	2.38 × 10−4	2.12 × 10−5	9.19 × 10−5	9.66 × 10−6	1.75 × 10−4	1.62 × 10-4
		RSTHCS	1.35 × 10−5	5.66 × 10−6	2.58 × 10−7	1.09 × 10−6	4.79 × 10−6	3.42 × 10-6
	LCI	BCS	4.93 × 10−2	3.59 × 10−2	2.53 × 10−3	3.81 × 10−3	6.56 × 10−3	7.83 × 10-3
		HCSMAROI	1.06 × 10−1	3.55 × 10−3	8.32 × 10−3	9.45 × 10−3	9.65 × 10−3	9.46 × 10-3
		TCS	2.88 × 10−4	9.71 × 10−5	4.34 × 10−5	3.17 × 10−5	8.49 × 10−6	7.69 × 10-6
		RSTHCS	8.38 × 10−5	7.40 × 10−5	3.22 × 10−5	1.24 × 10−5	2.42 × 10−5	2.79 × 10-5
	mND680	BCS	2.58 × 10−2	1.10 × 10−2	2.80 × 10−3	3.82 × 10−3	3.54 × 10−3	3.63 × 10-3
		HCSMAROI	1.82 × 10−1	1.67 × 10−2	1.16 × 10−2	1.17 × 10−2	1.12 × 10−2	1.07 × 10-2
		TCS	5.84 × 10−4	2.60 × 10−5	2.40 × 10−5	6.04 × 10−6	3.99 × 10−5	3.81 × 10-5
		RSTHCS	4.24 × 10−4	1.76 × 10−4	1.31 × 10−4	1.10 × 10−4	9.50 × 10−5	8.22 × 10-5
	DD	BCS	9.56 × 10−1	3.88 × 10−1	1.54 × 10−1	9.42 × 10−2	7.10 × 10−2	5.70 × 10-2
		HCSMAROI	4.56 × 10−1	2.59 × 10−2	5.65 × 10−3	3.64 × 10−4	2.86 × 10−3	3.77 × 10-3
		TCS	1.83 × 10−3	1.79 × 10−3	1.77 × 10−3	1.18 × 10−3	8.02 × 10−4	1.09 × 10-3
		RSTHCS	1.35 × 10−4	4.44 × 10−5	2.75 × 10−5	2.73 × 10−5	3.02 × 10−5	1.73 × 10-5
#2 HSIs of tea leaves	TVI	BCS	8.52 × 10−1	3.96 × 10−2	1.83 × 10−3	4.96 × 10−3	5.07 × 10−3	5.25 × 10-3
		HCSMAROI	5.00 × 10−2	1.92 × 10−2	1.35 × 10−2	1.11 × 10−2	9.49 × 10−3	8.49 × 10-3
		TCS	4.01 × 10−4	4.35 × 10−4	4.43 × 10−4	1.76 × 10−4	9.91 × 10−5	7.59 × 10-5
		RSTHCS	8.58 × 10−6	1.75 × 10−5	1.55 × 10−5	1.08 × 10−5	4.52 × 10−6	5.26 × 10-6
	LCI	BCS	6.33 × 10−2	5.98 × 10−2	1.06 × 10−2	1.71 × 10−3	1.56 × 10−3	3.69 × 10-3
		HCSMAROI	9.62 × 10−2	8.74 × 10−3	7.16 × 10−3	6.46 × 10−3	5.85 × 10−3	5.55 × 10-3
		TCS	1.34 × 10−4	1.36 × 10−4	1.57 × 10−4	1.15 × 10−4	1.05 × 10−4	1.19 × 10-4
		RSTHCS	7.91 × 10−5	5.24 × 10−5	2.08 × 10−5	3.03 × 10−5	4.53 × 10−5	4.76 × 10-5
	mND680	BCS	8.96 × 10−2	5.65 × 10−2	3.09 × 10−3	5.90 × 10−4	6.72 × 10−4	9.64 × 10-4
		HCSMAROI	9.36 × 10−2	2.66 × 10−2	9.28 × 10−3	3.78 × 10−3	1.37 × 10−3	3.14 × 10-4
		TCS	1.11 × 10−2	1.65 × 10−3	5.96 × 10−3	8.06 × 10−4	5.12 × 10−5	2.12 × 10-4
		RSTHCS	2.57 × 10−3	1.90 × 10−4	1.45 × 10−4	1.10 × 10−4	8.62 × 10−5	7.43 × 10-5

DOI:10.7717/peerjcs.2410/table-5

Reconstruction performance of soybean leaf HSIs

Experimental results in the spatial domain

Figure 11 illustrates the experimental results for #1 HSIs of soybean leaves of BCS, HCSMAROI, TCS and RSTHCS at the sampling rates of 2%, 6%, 10%, 14%, 18% and 22%. Compared to BCS and HCSMAROI, the reconstruction performance of TCS and RSTHCS is significantly better, and the HSIs can be well reconstructed even at low sampling rate. Particularly in RSTHCS, its inscribed characteristic eliminates interference from irrelevant background, ensuring all the sampling data come from the leaf region, thereby greatly improves sampling quality. Furthermore, the sub-tensor reconstructed algorithm considers the spatial spectra structure of the soybean leaves, further enhancing the quality of leaf reconstruction.

As shown inFigs. 8C,8D andTable 6 for two HSIs of soybean leaves, the reconstructed mean PSNRs of TCS and RSTHCS surpass those of BCS and HCSMAROI at sampling rates from 2% to 22%. The mean PSNRs of reconstructed images for all four different algorithms are all improved with the increasing sampling rate, with RSTHCS consistently achieving the highest mean PSNRs at all rates. In #1 HSIs of soybean leaves, at the low sampling rate of 2%, the mean PSNR value of RSTHCS is 0.271dB and 26.991dB higher than that of TCS and BCS, respectively. In #2 HSIs of soybean leaves, at the low sampling rate of 2%, the mean PSNR value of RSTHCS is 0.309 dB and 26.532 dB higher than TCS and BCS, respectively. Thus, RSTHCS consistenly achieves significantly highest reconstruction mean PSNR in the spatial domain.

The proposed RSTHCS method is optimized in several aspects to enhance reconstruction performance and computational efficiency. Specifically, RSTHCS divides the plant leaf regions into multiple sub-tensors using the recursive maximum inscribed rectangle algorithm, effectively reducing the computational burden. Each sub-tensor is compressed and reconstructed using Tucker decomposition, with a computational complexity ofO(n³), wheren is the dimension of the sub-tensor. Therefore, the overall computational complexity of the RSTHCS method can be expressed asO(k × n³), wherek is the number of sub-tensors.

In contrast, traditional methods such as BCS and HCSMAROI need to process the entire HSIs, with a computational complexity ofO(N³), whereN is the dimension of the hyperspectral image. RSTHCS only processes the plant leaf regions, in most cases,k × n³ <  < N³, resulting in a lower computational complexity.

As shown inTable 7, the results of two HSIs of soybean leaves show that the reconstructed time for all four algorithms increases with higher sampling rate. Notably, the reconstructed time for BCS and HCSMAROI algorithm are significantly higher than those of TCS and RSTHCS. This indicates that the tensor algorithm, particularly RSTHCS, outperforms the traditional BCS algorithm in the HSIs reconstruction efficiency. RSTHCS achieves the shortest reconstruction time at all sampling rates. In #1 HSIs of soybean leaves, at the low sampling rate of 2%, the reconstructed time for RSTHCS is 332s and 14,801s shorter than TCS and BCS, respectively. In #2 HSIs of soybean leaves, at the same low sampling rate of 2%, the reconstructed time of RSTHCS is 1,025s and 17,148s shorter than TCS and BCS at the low sampling rate of 2%.

Experimental results in the spectral domain

Figures 9G–9L show the average reconstructed spectra of the multiple arbitrary-shape ROIs of BCS, HCSMMAROI, TCS and RSTHCS of #1HSIs of soybean leaves at different sampling rates from 2% to 22%. When the sampling rate is more than 10%, the reconstructed spectra of four algorithms are all close to the original spectra. The results highlight that the reconstructed spectra of RSTHCS is consistently closer to the original spectra than those of the others at all sampling rates. Especially, even at sampling rate of 2%, RSTHCS exhibits prominent reconstructed performance.

Table 8 shows the SAM of different algorithms for the HSIs of the first and second soybean leaves at different sampling rates. The proposed RSTHCS can achieve significantly smaller SAM values than those of the other algorithms for these two tea leaf HSIs and different sampling rates. The proposed RSTHCS can obtain better spectral reconstruction performance than that of the other algorithms for HSIs of soybean leaves.

Table 9 gives error comparisons of spectral indices of DD, TVI, LCI and mND680 of four algorithms at different sampling rates.Figures 10I–10P illustrate the trends in the variation errors for these four spectral indices with the increase of the sampling rate. For four spectral indices at different sampling rates, errors of RSTHCS are relatively lower than those of the other algorithms. At the sampling rate of 22%, RSTHCS has especially obvious advantage. And the spectral index error of BCS shows the largest error values at different rates.

Table 6:

Comparison of mean PSNRs/dB of the HSIs of soybean leaves with different algorithms.

	Algorithms	Sampling rates
		2%	6%	10%	14%	18%	22%
#1 HSIs of soybean leaves	BCS	13.245	31.278	33.597	34.845	35.561	36.044
	HCSMAROI	27.119	38.982	40.930	41.847	42.366	42.710
	TCS	39.965	41.184	42.413	43.411	44.122	44.847
	RSTHCS	40.236	41.601	42.608	43.576	44.329	45.300
#2 HSIs of soybean leaves	BCS	12.793	30.155	32.510	33.769	34.511	35.001
	HCSMAROI	25.918	37.822	39.840	40.786	41.320	41.669
	TCS	39.196	40.444	41.771	42.691	43.443	44.191
	RSTHCS	39.505	40.888	41.899	42.913	43.567	44.587

DOI:10.7717/peerjcs.2410/table-6

Table 7:

Comparison of reconstructed Time/s of the HSIs of soybean leaves with different algorithms.

	Algorithms	Sampling rates
		2%	6%	10%	14%	18%	22%
#1 HSIs of soybean leaves	BCS	15,710	18,340	20,535	22,127	25,692	27,814
	HCSMAROI	9,924	12,879	13,735	15,785	17,349	19,889
	TCS	1,241	1,451	1,482	1,777	1,967	2,122
	RSTHCS	909	995	1,132	1,293	1,482	1,900
#2 HSIs of soybean leaves	BCS	18,105	20,921	22,267	23,837	24,326	31,050
	HCSMAROI	10,975	14,065	14,351	16,171	18,525	21,016
	TCS	1,982	2,092	2,127	2,183	2,227	2,329
	RSTHCS	959	1,148	1,248	1,467	1,549	1,700

DOI:10.7717/peerjcs.2410/table-7

Table 8:

Comparison of SAM of the HSIs of soybean leaves with different algorithms.

	Algorithms	Sampling rates
		2%	6%	10%	14%	18%	22%
#1 HSIs of soybean leaves	BCS	1.136 × 101	9.573 × 10−1	5.379 × 10−1	4.010 × 10−1	3.298 × 10−1	2.832 × 10-1
	HCSMAROI	4.785 × 100	5.954 × 10−1	3.832 × 10−1	2.989 × 10−1	2.527 × 10−1	2.527 × 10-1
	TCS	1.479 × 10−3	1.174 × 10−3	3.628 × 10−4	3.123 × 10−4	3.053 × 10−4	3.051 × 10-4
	RSTHCS	3.332 × 10−4	2.109 × 10−4	1.484 × 10−4	1.311 × 10−4	1.189 × 10−4	1.101 × 10-4
#2 HSIs of soybean leaves	BCS	1.102 × 101	1.036 × 100	5.684 × 10−1	4.100 × 10−1	3.278 × 10−1	2.775 × 10-1
	HCSMAROI	5.210 × 100	6.307 × 10−1	3.868 × 10−1	2.929 × 10−1	2.448 × 10−1	2.152 × 10-1
	TCS	7.886 × 10−4	4.755 × 10−4	3.284 × 10−4	2.233 × 10−4	2.158 × 10−4	2.095 × 10−4
	RSTHCS	5.837 × 10−4	2.866 × 10−4	1.100 × 10−4	8.950 × 10−5	7.827 × 10−5	6.812 × 10−5

DOI:10.7717/peerjcs.2410/table-8

Table 9:

Error comparisons of spectral indices of different algorithms of the HSIs of soybean leaves.

	Spectral index	Algorithms	Sampling rates
			2%	6%	10%	14%	18%	22%
	DD	BCS	9.58 × 10−1	1.01 × 10−1	5.18 × 10−2	3.45 × 10−2	2.62 × 10−2	2.12 × 10−2
		HCSMAROI	5.46 × 10−1	5.97 × 10−2	3.06 × 10−2	2.17 × 10−2	1.74 × 10−2	1.47 × 10−2
		TCS	4.140 × 10−5	1.67 × 10−5	3.77 × 10−6	2.78 × 10−5	3.12 × 10−5	3.39 × 10−5
		RSTHCS	3.72 × 10−5	3.83 × 10−5	2.70 × 10−5	2.48 × 10−5	2.26 × 10−5	2.00 × 10−5
#1 HSIs of soybean leaves	TVI	BCS	6.69 × 10−2	8.16 × 10−3	6.97 × 10−3	2.90 × 10−3	4.83 × 10−4	1.02 × 10−3
		HCSMAROI	2.21 × 10−1	8.03 × 10−3	2.09 × 10−3	6.57 × 10−4	2.02 × 10−3	2.73 × 10−3
		TCS	1.94 × 10−5	1.51 × 10−5	1.22 × 10−5	7.99 × 10−6	7.18 × 10−6	6.67 × 10−6
		RSTHCS	8.97 × 10−6	5.82 × 10−6	4.36 × 10−6	3.49 × 10−6	3.85 × 10−6	3.13 × 10−6
	LCI	BCS	1.80 × 10−1	1.69 × 10−2	2.43 × 10−2	2.10 × 10−2	1.79 × 10−2	1.56 × 10−2
		HCSMAROI	1.93 × 10−1	1.82 × 10−2	1.46 × 10−2	1.10 × 10−2	8.77 × 10−3	7.41 × 10−3
		TCS	9.06 × 10−5	1.13 × 10−4	1.05 × 10−4	1.02 × 10−4	9.69 × 10−5	9.24 × 10−5
		RSTHCS	1.08 × 10−4	1.05 × 10−4	9.65 × 10−5	7.49 × 10−5	4.33 × 10−5	3.03 × 10−6
	mND680	BCS	4.52 × 10−2	8.62 × 10−3	1.33 × 10−2	1.04 × 10−2	8.10 × 10−3	6.31 × 10−3
		HCSMAROI	2.26 × 10−1	1.64 × 10−2	1.84 × 10−2	6.93 × 10−3	4.79 × 10−3	3.04 × 10−3
		TCS	3.91 × 10−4	2.57 × 10−4	7.23 × 10−4	6.48 × 10−4	5.27 × 10−4	4.84 × 10−4
		RSTHCS	1.33 × 10−4	1.31 × 10−4	1.32 × 10−4	5.87 × 10−5	6.13 × 10−5	5.63 × 10−5
	DD	BCS	9.30 × 10−1	3.53 × 10−2	3.20 × 10−2	2.53 × 10−2	1.93 × 10−2	1.59 × 10−2
		HCSMAROI	5.00 × 10−1	3.36 × 10−2	2.21 × 10−2	1.52 × 10−2	1.22 × 10−2	1.07 × 10−2
		TCS	7.86 × 10−5	1.10 × 10−4	6.47 × 10−5	3.23 × 10−5	3.11 × 10−5	2.95 × 10-5
		RSTHCS	8.15 × 10−5	5.06 × 10−5	7.99 × 10−6	1.36 × 10−6	1.97 × 10−6	5.70 × 10−6
#2 HSIs of soybean leaves	TVI	BCS	6.74 × 10−1	7.42 × 10−3	7.10 × 10−3	2.11 × 10−3	9.65 × 10−4	2.60 × 10−3
		HCSMAROI	2.63 × 10−1	8.44 × 10−3	1.13 × 10−3	2.24 × 10−3	3.75 × 10−3	4.33 × 10−3
		TCS	3.57 × 10−6	1.32 × 10−6	4.36 × 10−6	2.40 × 10−6	2.10 × 10−6	1.70 × 10−6
		RSTHCS	1.97 × 10−6	1.70 × 10−6	1.40 × 10−6	8.33 × 10−7	6.71 × 10−7	5.19 × 10−7
	LCI	BCS	2.48 × 10−2	1.90 × 10−2	2.26 × 10−2	1.81 × 10−2	1.43 × 10−2	1.19 × 10−2
		HCSMAROI	2.01 × 10−1	1.74 × 10−2	1.19 × 10−2	7.73 × 10−3	5.60 × 10−3	4.35 × 10−3
		TCS	8.45 × 10−5	1.04 × 10−4	1.12 × 10−4	9.86 × 10−5	9.59 × 10−5	9.26 × 10−5
		RSTHCS	6.85 × 10−5	7.67 × 10−5	7.89 × 10−5	2.67 × 10−5	6.28 × 10−7	8.65 × 10−6
	mND680	BCS	1.97 × 10−2	1.85 × 10−2	2.15 × 10−3	4.23 × 10−3	3.74 × 10−3	2.55 × 10−3
		HCSMAROI	2.15 × 10−1	7.63 × 10−3	4.09 × 10−3	3.31 × 10−3	1.30 × 10−3	2.38 × 10−4
		TCS	3.37 × 10−4	1.07 × 10−3	5.44 × 10−4	3.20 × 10−3	1.82 × 10−3	1.23 × 10−3
		RSTHCS	4.21 × 10−4	1.49 × 10−4	1.01 × 10−4	8.69 × 10−5	7.86 × 10−5	7.21 × 10−5

DOI:10.7717/peerjcs.2410/table-9

Discussion

In this paper, we have compared the proposed RSTHCS with BCS, HCSMAROI, and TCS. BCS and TCS compress and reconstruct the whole rectangular leaf regions, which include parts of the background regions. HCSMAROI, a representative method of our previous works, extracts multiple arbitrary shape regions of interest (ROI), and then compresses and reconstructs each region. The key difference between HCSMAROI and the proposed RSTHCS lies in the compression and reconstruction strategy for each arbitrary-shape ROI. TCS is introduced in the recursive sub-tensor hyperspectral compressive sensing for each arbitrary-shape ROI.

In the spatial domain, subjective reconstruction quality and PSNR values at different sampling rates are used to evaluate the reconstruction performance of different algorithms for tea and soybean leaf HSIs. RSTHCS consistently achieves the best performance. This superior performance can be attributed to the following reasons:

1. Efficient Handling of Large Data Volumes: RSTHCS divides the hyperspectral data into smaller sub-tensors, which can reduce the computational burden and allow for more precise reconstruction of each sub-tensor. This segmentation ensures that each ROI is independently optimized, leading to higher overall PSNR values.

2. Preservation of Spectral-Spatial Correlation: By maintaining the spectral-spatial structure within each sub-tensor during compression and reconstruction, RSTHCS achieves higher fidelity reconstructions compared to other techniques.

In the spectral domain, average reconstructed spectra, SAM, and spectral indices are introduced to compare the reconstructed performance. At low sampling rates, the reconstructed spectra of RSTHCS are closer to the original spectra compared to BCS, HCSMAROI, and TCS. RSTHCS can achieve significantly smaller SAM values at different sampling rates. For the spectral indices such as DD, TVI, LCI, and mND680, RSTHCS almost achieves the least reconstructed error. The reasons for these results include:

1. Reduction of Irrelevant Background Information: By focusing on multiple arbitrary-shape ROIs and discarding irrelevant background information, RSTHCS enhances the efficiency and effectiveness of the compression process. This strategy ensures that the spectral characteristics of the leaf regions are preserved more accurately.

2. Adaptability to Complex Shapes and Structures: The method’s ability to handle and accurately reconstruct arbitrary-shape ROIs ensures that the spectral characteristics of the leaf regions are preserved more accurately.

Additionally, the reconstructed time is used to compare the time consumption of different methods. For soybean HSIs with relatively large sizes, the proposed RSTHCS requires significantly less time than the other algorithms. Even for tea HSIs with relatively small sizes, RSTHCS still exhibits relatively low reconstruction time. This is because RSTHCS only compresses and reconstructs the multiple arbitrary shape ROIs of plant leaf HSIs, which discards the background information and thus saves storage space and computational resources.

TCS makes full use of the high spectral-spatial correlation of HSIs and can achieve better reconstruction performance than BCS and HCSMAROI. RSTHCS not only compresses and reconstructs multiple arbitrary shape ROIs of plant leaf HSIs but also discards the background information. RSTHCS does not need to compress the background region anymore. RSTHCS uses TCS to compress and reconstruct each sub-tensor of multiple arbitrary shape ROIs of plant leaf HSIs. In other words, RSTHCS can make full use of the advantages of TCS and save the storage space of the background region effectively. Therefore, RSTHCS can achieve better reconstruction performance than BCS, HCSMAROI, and TCS.

The compression ratio is defined as the ratio of the image area to the total areas covered by the leaves. Compared with soybean leaves, the area of tea leaves occupies a smaller part of the whole image area, so compression ratios of tea leaves are larger than those of soybean leaves. During the data reconstruction sampling, more tea samples were obtained per leaf area. Therefore, at the same sampling rate, the reconstructed mean PSNR values of tea leaves are higher than those of soybean leaves, and the reconstruction quality is also higher.

The areas of soybean leaves are larger than those of tea leaves and the HSIs of soybean leaves contain a greater number of bands. Specifically, two HSIs of tea leaves contain 369 and 374 bands, respectively, while HSIs of soybean leaves include 518 bands. Therefore, compared with the HSIs of tea leaves, the HSIs of soybean leaves provide more abundant data and require longer reconstructed time.

The proposed RSTHCS method offers several advantages over traditional techniques. It efficiently handles large data volumes by dividing the hyperspectral data into smaller sub-tensors, thereby reducing the computational burden and enabling efficient processing of large datasets. This method preserves the spectral-spatial correlation within each sub-tensor during compression and reconstruction, resulting in higher fidelity reconstructions compared to other techniques. Additionally, RSTHCS focuses on multiple arbitrary-shape ROIs, which can effectively discard irrelevant background information and enhance the efficiency and effectiveness of the compression process. Its adaptability to complex shapes and structures is crucial for applications involving irregularly shape plant leaves, providing a significant advantage over traditional methods. Experimental results demonstrate that RSTHCS achieves superior image reconstruction quality at low sampling rates, which can achieve more precise data retention and lower reconstruction errors.

However, the RSTHCS method also has its limitations. While it reduces the computational burden by dividing data into sub-tensors, the overall computational complexity can still be high for very large datasets. Future work will focus on optimizing the algorithm and exploring parallel and distributed computing techniques to improve efficiency. The effectiveness of RSTHCS relies on the accurate extraction of ROIs. In complex scenes, the initial extraction process might introduce errors that can affect overall performance. Further research is needed to refine ROI extraction methods. Additionally, although RSTHCS performs well with plant leaves, its applicability to other types of HSIs and different application scenarios requires further investigation and validation.

Conclusion

The previous research can not compress and reconstruct multiple arbitrary-shape ROIs of plant leaves quite effectively in high spatial and spectral correlation at low bit rate while discarding the unuseful background. There are high inter-spectral and inter-spatial correlations for plant leaf HSIs. Based on the experimental results of two types of plant leaf HSIs, compared with BCS, HCSMAROI and TCS, RSTHCS can achieve better reconstruction performances in both spectral and spatial domains. At low sampling rates, the mean PSNR of the reconstructed image of RSTHCS is better than that of the other algorithms. The reconstructed spectra of RSTHCS are also closer to the original spectra compared to the other algorithms. The proposed RSTHCS can achieve significantly smaller SAM values than those of the other algorithms. Furthermore, RSTHCS maintains spectral indices such as DD, TVI, LCI and mND680 with relatively lower errors than the other methods. Therefore, the proposed RSTHCS exhibits significant potential for applications in the field of plant leaf HSIs.

The main shortcomings is that the proposed RSTHCS is not fit for the complex scenarios, in which it is difficult to extract the ROIs accurately. In the future research, we will introduce more effective segment methods to extract the ROIs accurately in the relatively complex scenarios and use the proposed RSTHCS in the agriculture applications.