Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Iterative Identification and Restoration of Images (The International Series in Engineering and Computer Science)
Multichannel blind separation and deconvolution of images for document analysis
IEEE Transactions on Image Processing
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This paper studies the application of preconditioned conjugate gradient methods in high-resolution color image reconstruction problems. The high-resolution color images are reconstructed from multiple undersampled, shifted, degraded color frames with subpixel displacements. The resulting degradation matrices are spatially variant. To capture the changes of reflectivity across color channels, the weighted H1 regularization functional is used in the Tikhonov regularization. The Neumann boundary condition is also employed to reduce the boundary artifacts. The preconditioners are derived by taking the cosine transform approximation of the degradation matrices. Numerical examples are given to illustrate the fast convergence of the preconditioned conjugate gradient method.