Discrete Inverse Problems

Discrete Inverse Problems: Insight and Algorithms

This new book is published by SIAM in the series Fundamentals of Algorithms. It has 8 chapters, 46 exercises, and 213 pages. It is currently number 17 on SIAM's bestseller list.

The book uses the software from Regularization Tools.

Misprints as of March 27, 2011:

Page 24, line 9 from bottom (displayed equation): x_j should be t_j
Page 27, last line: "we have no information"
Page 31, line 5: "note that"
Page 99, Eq. (5.13): subscript k should be λ
Page 137, after Eq. (7.5): g_-n+1 should be h_-n+1

Suggestion for a Short Course

Lecture 1: Discrete Inverse Problems overheads + overheads

Chapter 1
Chapter 2: sections 2.1, 2.2, 2.3
Chapter 3: sections 3.1.1, 3.2.1, 3.3, 3.5
Exercises: 2.2, 2.4, 3.4, 3.5, 3.6

Lecture 2: Regularization Methods overheads

Chapter 4: sections 4.1, 4.2, 4.3, 4.4, 4.7
Exercises: 4.1, 4.5, 4.6, 4.7

Lecture 3: Regularization Paramters overheads

Chapter 5: sections 5.1, 5.2, 5.3, 5.4, 5.5, 5.6
Exercises: 4.2, 5.1, 5.2

Lecture 4: Solving "Real" Problems overheads

Chapter 7: sections 7.1, 7.2, 7.3, 7.4, 7.10
Exercises: 7.2, 7.3 (TSVD and Tikhonov only), 7.4

Lecture 5: Iterative Regularization overheads

Chapter 6: sections 6.1, 6.2, 6.3
Chapter 7: section 7.7
Exercises: 6.2, 6.3, 6.5, 7.3 (iterative methods), 7.8

Additional Material for a Longer Course

Lecture 6: Image Deblurring (currently no overheads)

Chapter 7: sections 7.5, 7.6
Exercises: 7.5, 7.6, 7.7

Lecture 8: Beyond the 2-Norm overheads

Chapter 8: sections 8.1, 8.2, 8.6
Exercises: 8.1, 8.3, 8.4