Digital Signal Processing Reference
In-Depth Information
Practical algorithms were provided, and their theoretical properties were analyzed
and discussed. We also dealt with other important aspects of sparsity-regularized
inverse problems and iterative thresholding. The goal was to have a clear picture
of the state of the art in the field and to outline open questions that we believe are
crucial to investigate in the future. Finally, we provided some guided numerical ex-
periments based on a MATLAB toolbox that we make available on the Web. This
is a complete library that implements the algorithms described in the chapter and
allows the reader to reproduce the tutorial examples shown in the chapter as well as
many others.
In the next two chapters, we will see in more detail how some linear inverse prob-
lems can be regularized with nonconvex sparsity penalties such as the
0
pseudo-
norm, on which we touched in this chapter. We will show that hard thresholding will
be at the heart of the iterative stagewise pursuit algorithms that will be proposed,
leading to very good results, if appropriately combined with a varying threshold
strategy.
