TIMESTAMPS
The term 'denoising' originated in the 1980s to describe wavelet transform based algorithms for the removal of noise from signals. More recently, use of the term has overflown well outside of its original context, to refer to the reduction or removal of noise from signals, whether transform- based or not. The problem permeates just about all branches of science and engineering involving some form of inference on a phenomenon of interest, based on noisy or incomplete observations. Correspondingly, the present state and history of this area are very rich (and no attempt will be made to do them justice in the tutorial).
After giving a bird's eye tour of current research trends in denoising, we will zoom in on some of our own recent research in these areas, including transform based and discrete denoising. Particular emphasis will be put on information theoretic and universality aspects. We will also describe ways in which many of the tools and techniques developed for denoising can be harnessed for other problems, including compression, channel coding, joint source channel coding, and compressed sensing. Theoretical, algorithmic, and experimental aspects will be covered.