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A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
We propose, analyze and test an alternating minimization algorithm for recovering images from blurry and noisy observa- tions with total variation (TV) regularization. This algorithm arises from a new half-quadratic model ...
Practical Compressive Sensing with Toeplitz and Circulant Matrices
Compressive sensing encodes a signal into a relatively small number of incoherent linear measurements. In theory, the optimal incoherence is achieved by completely random measurement matrices. However, such matrices are ...
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration
We generalize the alternating minimization algorithm recently proposed in  to effciently solve a general, edge-preserving, variational model for recovering multichannel images degraded by within- and cross-channel ...
Alternating Direction Algorithms for L1-Problems in Compressive Sensing
In this paper, we propose and study the use of alternating direction algorithms for several L1-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, ...
A Fast TVL1-L2 Minimization Algorithm for Signal Reconstruction from Partial Fourier Data
Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In this paper, ...