On the Role of Total Variation in Compressed Sensing

DOI10.1137/140978569zbMath1381.94038arXiv1407.5339OpenAlexW2107034604MaRDI QIDQ5250010

Clarice Poon

Publication date: 15 May 2015

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.5339

zbMATH Keywords

total variation minimizationcompressed sensing

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Sampling theory in information and communication theory (94A20)

Related Items

WARPd: A Linearly Convergent First-Order Primal-Dual Algorithm for Inverse Problems with Approximate Sharpness Conditions ⋮ Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames ⋮ Compressive Sensing with Redundant Dictionaries and Structured Measurements ⋮ Stable Image Reconstruction Using Transformed Total Variation Minimization ⋮ Short Communication: Localized Adversarial Artifacts for Compressed Sensing MRI ⋮ \(\boldsymbol{L_1-\beta L_q}\) Minimization for Signal and Image Recovery ⋮ Enhanced total variation minimization for stable image reconstruction ⋮ Do log factors matter? On optimal wavelet approximation and the foundations of compressed sensing ⋮ BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING ⋮ Geometric properties of solutions to the total variation denoising problem ⋮ NESTANets: stable, accurate and efficient neural networks for analysis-sparse inverse problems ⋮ Compressive time-of-flight 3D imaging using block-structured sensing matrices ⋮ Reconstruction Methods in THz Single-Pixel Imaging ⋮ Hyperbolic Wavelet Frames and Multiresolution in the Weighted Bergman Spaces ⋮ Compressed Sensing Photoacoustic Tomography Reduces to Compressed Sensing for Undersampled Fourier Measurements ⋮ Improved Recovery Guarantees and Sampling Strategies for TV Minimization in Compressive Imaging

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A mathematical introduction to compressive sensing
• Super-resolution from noisy data
• A consistent and stable approach to generalized sampling
• User-friendly tail bounds for sums of random matrices
• Parameter estimation for exponential sums by approximate prony method
• RIPless compressed sensing from anisotropic measurements
• Stable Image Reconstruction Using Total Variation Minimization
• BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING
• The Split Bregman Method for L1-Regularized Problems
• On sparse reconstruction from Fourier and Gaussian measurements
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• Nonlinear approximation and the space BV[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]
• Stable and Robust Sampling Strategies for Compressive Imaging
• A Probabilistic and RIPless Theory of Compressed Sensing
• Recovering Low-Rank Matrices From Few Coefficients in Any Basis
• Compressed Sensing Off the Grid
• Near-Optimal Compressed Sensing Guarantees for Total Variation Minimization
• Towards a Mathematical Theory of Super‐resolution