Regularized Generalized Inverse Accelerating Linearized Alternating Minimization Algorithm for Frame-Based Poissonian Image Deblurring

A Characterization of Multi-Wavelet Dual Frames in Sobolev Spaces

“…In view of the great design freedom and the e cient application in practice, such as image restoration, signal de-noising, the numerical solution of operator equations, wavelet, and multi-wavelet frames have been extensively investigated by many researchers (see [1][2][3][4][5][6][7][8] for details). In particular, many of these applications show that it is highly desirable to have a wavelet frame for Sobolev spaces [9][10][11][12][13][14][15].…”

“…In particular, many of these applications show that it is highly desirable to have a wavelet frame for Sobolev spaces [9][10][11][12][13][14][15]. Recently, Han and Shen in [10,11] generalized the MEP of Ron and Shen [16] from 2 R to Sobolev spaces pairs R , − R for the construction of wavelet dual frames; the vanishing moment and smoothness requirements of two systems were separated completely from each other. Consequently, the construction of wavelet dual frames in Sobolev spaces is much easier.…”

Nonhomogeneous Wavelet Dual Frames and Extension Principles in Reducing Subspaces

“…In view of the great design freedom and the potential applications in signal processing and many other fields, wavelet frames have been extensively investigated by many researchers (see [1][2][3][4][5][6][7][8][9] for details). In particular, the homogeneous wavelet dual frames (or called affine dual frames) in L 2 (R d ) were original characterized by Han [10] and then characterized by Bownik [11], some of their variations can be found in [12][13][14].…”

Fixed point algorithm based on adapted metric method for convex minimization problem with application to image deblurring

“…Although the split-Bregman framework has been shown to be very useful, a sub-minimization problem of solving the system of linear or nonlinear equations is included in each iteration and may time-consuming sometimes. Very recently, alternating direction minimization methods based on the linearized technique [17,18] have been widely investigated to overcome this and further improve the efficiency. Another class of methods is the primal-dual algorithms.…”