Image Processing

Figure 4.8: Removing the blur caused by uniform linear motion.

4.4Techniques for Constrained Restoration

In constrained restoration, some different techniques are used.

4.4.1Constrained Restoration

The solution to eq. (4.20) can also be considered from the least square sense, which is to minimize the function of ${\Vert \mathbf{Q}\widehat{\mathbf{f}}\Vert }^2,$ where Q is a linear operator on f, subject to the constraint $\Vert g-\mathbf{H}\widehat{f}\Vert ={\Vert n\Vert }^2.$ This problem can be solved by using the method of Lagrange multipliers. Denote l as the Lagrange multiplier (a constant) and the criterion function can be written as

$L\left(\widehat{\mathbf{f}}\right){\Vert \mathbf{Q}\widehat{f}\Vert }^2+l({\Vert g-H\widehat{f}\Vert }^{}$