Appendix B. Ill-Posed Problems in Image and Video Processing
Many image/video-processing problems are ill-posed whose analysis and solution requires a strong mathematical foundation and proper image/video/motion modeling. This appendix aims to summarize fundamental modeling approaches in modern image and video processing, and provide the foundation for sparse image representations, to help put some well-known regularization methods for solving ill-posed image- and video-processing problems on a common framework.
B.1 Image Representations
B.1.1 Deterministic Framework – Function/Vector Spaces
We can represent a discrete image s(n1, n2) by an N × N matrix of pixels or by an N2 × 1 vector s = [s1 s2 ... sN2]T by mapping pixels (n1, n2) into a ...
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