IEEE Transactions on Information Theory
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Morphological Component Analysis: An Adaptive Thresholding Strategy
IEEE Transactions on Image Processing
Majorization–Minimization Algorithms for Wavelet-Based Image Restoration
IEEE Transactions on Image Processing
Image Restoration Using Space-Variant Gaussian Scale Mixtures in Overcomplete Pyramids
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
Two dimensional K-SVD for the analysis sparse dictionary
PCM'12 Proceedings of the 13th Pacific-Rim conference on Advances in Multimedia Information Processing
On MAP and MMSE estimators for the co-sparse analysis model
Digital Signal Processing
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Sparse optimization in overcomplete frames has been widely applied in recent years to ill-conditioned inverse problems. In particular, analysis-based sparse optimization consists of achieving a certain trade-off between fidelity to the observation and sparsity in a given linear representation, typically measured by some lp quasinorm. Whereas most popular choice for p is 1 (convex optimization case), there is an increasing evidence on both the computational feasibility and higher performance potential of non-convex approaches (0 ≤ p p = 0 case is especial, because analysis coefficients of typical images obtained using typical pyramidal frames are not strictly sparse, but rather compressible. Here we model the analysis coefficients as a strictly sparse vector plus a Gaussian correction term. This statistical formulation allows for an elegant iterated marginal optimization. We also show that it provides state-of-the-art performance, in a least-squares error sense, in standard deconvolution tests.