Simple Linear Models for Image Deblurring
What is the image deblurring problem? How to build some simple linear models for image deblurring?
Image deblurring is fundamental in making pictures sharp and useful. In the image deblurring, we aim at recovering the original and sharp image by using a certain mathematical model of blurring process. Unfortunately, it seems to be no hope to recover the original image exactly! Today, we introduce some simple linear models for solving the image deblurring problem. The content of this story refers to the following book:
Per Christian Hansen, James G. Nagy, Dianne P. O’Leary (2006). Deblurring Images: Matrix, Spectra, and Filtering. SIAM.
Blurred Picture and Its Representation
When we take some photos, it is common that blur occurs during an exposure as the camera moves. Below shows the comparison between sharp image (ideal one) and blurred image (bad one). If we define the sharp image as X of size m-by-n and blurred image as B of same size, then the goal is to develop efficient and reliable algorithms for recovering as much information as possible from the given blurred image.
