A very nice educational tool is presented in this paper that illustrates how to deal with ill-conditioned inverse problems using singular value decomposition (SVD), with application to an image deblurring problem. The reader is gradually introduced to this tool via a series of assignments to Tikhonov regularization, with manual choices of the values of the Tikhonov regularization parameter. Then another approach, the truncated SVD approach, is introduced by throwing out all singular values greater than some value. Use of Kronecker products for the matrix representing the blurring operation is introduced. Both methods are applied as tools to reconstruct the true original image from a blurred noisy image, an application of image processing.

Computational students and educators will find this a useful tool for this important, but difficult topic. The material requires a student to be well trained in linear algebra at the level of the Golub and Van Loan book [1]. Behind the sample MATLAB code, much work has been invested, providing the reader with code that is easy to test. It would have been difficult for a beginner to develop and code all the tools without difficulty. I intend to use this nice example in my class.