Quantization and Compressive Sensing

DOI10.1007/978-3-319-16042-9_7zbMath1333.94016arXiv1405.1194OpenAlexW1961240022MaRDI QIDQ3460834

Laurent Jacques, Rayan Saab, Felix Krahmer, Petros T. Boufounos

Publication date: 8 January 2016

Published in: Compressed Sensing and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.1194

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (8)

Quantization of compressive samples with stable and robust recovery ⋮ Sigma Delta Quantization for Images ⋮ A unified approach to uniform signal recovery from nonlinear observations ⋮ An Introduction to Compressed Sensing ⋮ Quantized Compressed Sensing: A Survey ⋮ On recovery guarantees for one-bit compressed sensing on manifolds ⋮ On the \(\ell^\infty\)-norms of the singular vectors of arbitrary powers of a difference matrix with applications to sigma-delta quantization ⋮ Memoryless scalar quantization for random frames

Uses Software

• PDCO
• UNLocBoX

Cites Work

• Unnamed Item
• Error bounds for consistent reconstruction: random polytopes and coverage processes
• Near-optimal encoding for sigma-delta quantization of finite frame expansions
• Democracy in action: quantization, saturation, and compressive sensing
• Lower bounds for the error decay incurred by coarse quantization schemes
• Iterative hard thresholding for compressed sensing
• Hanson-Wright inequality and sub-Gaussian concentration
• Second-order sigma-delta (\(\Sigma \Delta\)) quantization of finite frame expansions
• Alternative dual frames for digital-to-analog conversion in sigma-delta quantization
• Frame paths and error bounds for sigma-delta quantization
• Quantization noise shaping on arbitrary frame expansions
• The restricted isometry property and its implications for compressed sensing
• Sobolev duals in frame theory and Sigma-Delta quantization
• A simple proof of the restricted isometry property for random matrices
• Entropy numbers of diagonal operators between symmetric Banach spaces
• Approximating a bandlimited function using very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order
• Sobolev duals for random frames and \(\varSigma \varDelta \) quantization of compressed sensing measurements
• Dimension reduction by random hyperplane tessellations
• Smooth frame-path termination for higher order sigma-delta quantization
• One-bit compressed sensing with non-Gaussian measurements
• One-Bit Compressed Sensing by Linear Programming
• Proximal Splitting Methods in Signal Processing
• Suprema of Chaos Processes and the Restricted Isometry Property
• A Quantized Johnson–Lindenstrauss Lemma: The Finding of Buffon’s Needle
• Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors
• Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach
• An optimal family of exponentially accurate one-bit Sigma-Delta quantization schemes
• New and Improved Johnson–Lindenstrauss Embeddings via the Restricted Isometry Property
• Extensions of Lipschitz mappings into a Hilbert space
• Restricted isometry properties and nonconvex compressive sensing
• On sparse reconstruction from Fourier and Gaussian measurements
• Sigma-delta (/spl Sigma//spl Delta/) quantization and finite frames
• Oversampled Sigma-Delta Modulation
• Atomic Decomposition by Basis Pursuit
• Quantized overcomplete expansions in IR/sup N/: analysis, synthesis, and algorithms
• One-bit sigma-delta quantization with exponential accuracy
• Trust, But Verify: Fast and Accurate Signal Recovery From 1-Bit Compressive Measurements
• Regime Change: Bit-Depth Versus Measurement-Rate in Compressive Sensing
• The Pros and Cons of Compressive Sensing for Wideband Signal Acquisition: Noise Folding versus Dynamic Range
• Message-Passing De-Quantization With Applications to Compressed Sensing
• The pros and cons of democracy
• Quantization
• Least squares quantization in PCM
• Lower bound on the mean-squared error in oversampled quantization of periodic signals using vector quantization analysis
• Quantization and Finite Frames
• Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing
• One-bit compressive sensing of dictionary-sparse signals
• Universal Rate-Efficient Scalar Quantization
• Root-Exponential Accuracy for Coarse Quantization of Finite Frame Expansions
• Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine
• Probability Inequalities for Sums of Bounded Random Variables
• Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-Rank Matrices
• Stabilizing Nonuniformly Quantized Compressed Sensing With Scalar Companders
• Stable signal recovery from incomplete and inaccurate measurements
• A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables
• A lower estimate for entropy numbers

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