The Cosparse Analysis Model and Algorithms

Abstract

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments.

Submitted (2011)

References in corpus (1)

• Coherence-Based Performance Guarantees for Estimating a Sparse Vector Under Random Noise

Cited by in corpus (41)

• Sparse Regularization via Convex Analysis
• A Survey of Sound Source Localization with Deep Learning Methods
• AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing
• PURIFY: a new approach to radio-interferometric imaging
• Content-aware Scalable Deep Compressed Sensing
• Greedy-Like Algorithms for the Cosparse Analysis Model
• Smoothing and Decomposition for Analysis Sparse Recovery
• Constrained Overcomplete Analysis Operator Learning for Cosparse Signal Modelling
• Fundamental performance limits for ideal decoders in high-dimensional linear inverse problems
• ${\ell }^1$-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed?
• Sparse Signal Recovery via Generalized Entropy Functions Minimization
• Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized x-ray CT
• One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations
• Image Fusion With Cosparse Analysis Operator
• Compressed Sensing with 1D Total Variation: Breaking Sample Complexity Barriers via Non-Uniform Recovery
• Analysis Dictionary Learning based Classification: Structure for Robustness
• Asymptotic Analysis of Inpainting via Universal Shearlet Systems
• NMF with Sparse Regularizations in Transformed Domains
• Coded Acquisition of High Frame Rate Video
• Sparse image reconstruction on the sphere: analysis and synthesis
• Robust analysis ${\ell }_1$-recovery from Gaussian measurements and total variation minimization
• Living near the edge: A lower-bound on the phase transition of total variation minimization
• Sample Complexity of Total Variation Minimization
• On the Error in Phase Transition Computations for Compressed Sensing
• Learning Co-Sparse Analysis Operators with Separable Structures
• Frame-based Sparse Analysis and Synthesis Signal Representations and Parseval K-SVD
• Revisiting Synthesis Model of Sparse Audio Declipper
• Discriminative Nonlinear Analysis Operator Learning: When Cosparse Model Meets Image Classification
• Efficient Least Residual Greedy Algorithms for Sparse Recovery
• Estimation with Low-Rank Time-Frequency Synthesis Models
• Generalizing CoSaMP to Signals from a Union of Low Dimensional Linear Subspaces
• NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems
• Dictionary Learning with Equiprobable Matching Pursuit
• DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds
• Spark Deficient Gabor Frame Provides a Novel Analysis Operator for Compressed Sensing
• Improved Recovery of Analysis Sparse Vectors in Presence of Prior Information
• Scampi: a robust approximate message-passing framework for compressive imaging
• Generalization analysis of an unfolding network for analysis-based Compressed Sensing
• Oracle inequalities for square root analysis estimators with application to total variation penalties
• Analysis vs Synthesis with Structure - An Investigation of Union of Subspace Models on Graphs
• Star DGT: a Robust Gabor Transform for Speech Denoising