Regularization Schemes

In Nagy and O'Leary (2003a), regularization is used to make the least-squares deblurring problem less sensitive to the noise. Figures  and show the result of using the identity operator for regularization. This is comparable to the results presented in Nagy and O'Leary (2003b). We go a step further by using regularization to impose a priori information on the solution of the problem. We exploit the fact that letters should be homogeneous for intervals (piecewise constant) with abrupt discontinuities between them.

 

comp_damp
Figure 2 A) Original image, B) Deblurred image using LS with damped regularization.

 

comp_damp_graph
Figure 3 Comparison between Figures A and B; A) Slice y=229 and B) Slice x=229.

 

• First order derivative regularization
• Gradient magnitude and Laplacian regularization
• Gradient magnitude and smooth regularization