Question: Regularized least squares image deblurring. This exercise is on the image deblurring problem in 15.3.3 of the textbook. The purpose is to develop a fast
Regularized least squares image deblurring. This exercise is on the image deblurring problem in 15.3.3 of the textbook. The purpose is to develop a fast method for solving the regularized least-squares problem on page 321: minimize kAx yk 2 + (kDvxk 2 + kDhxk 2 ). (27) Notation. A black-and-white image of size nn is represented as an nn matrix X with Xij the intensity of pixel i, j, or as an n 2 -vector x. We use column-major order when converting a matrix X to a vector x: x = X1:n,1 X1:n,2 . . . X1:n,n . In MATLAB the conversion can be done by the command x = X(:) or, equivalently, x = reshape(X, n^2, 1). To convert an n 2 -vector x to an n n matrix X we use X = reshape(x, n, n). In (27), the vectors x and y have length n 2 . The vector y is given and represents an observed, noisy and blurred image Y of size n n. The variable x is the reconstructed n n image X in vector form. The following notation will be used to express the matrices A, Dv, Dh in (27)
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