O'Reilly logo

Image Reconstruction by Gengsheng Lawrence Zeng

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

NewObjectiveFunction(X)=OldObjectiveFunction(X)+β||X| | 2 ,

where β is a user specified controlling parameter. Using the squared norm of the gradient ||X| | 2 as a penalty term can be generalized as using an “energy” function U(X) as penalty term. The energy function U(X) is defined as

U(X)= i,j w ij V( x j x j ),

where the summation is over a neighborhood (clique), and V is a convex function, which may or may not be quadratic (see Figure 6.19). If V is a quadratic function, this energy function encourages smoothness and penalizes jumps. If the function V increases more slowly than a quadratic function (say, V increases linearly), then it can preserve edges and smooth out the noise. How does the algorithm ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required