Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Digital Coding of Waveforms: Principles and Applications to Speech and Video
Digital Coding of Waveforms: Principles and Applications to Speech and Video
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
Compressed sensing performance bounds under Poisson noise
IEEE Transactions on Signal Processing
Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Scalar quantization error analysis for image subband coding usingQMFs
IEEE Transactions on Signal Processing
Least squares quantization in PCM
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine
IEEE Transactions on Information Theory
The Noise-Sensitivity Phase Transition in Compressed Sensing
IEEE Transactions on Information Theory
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Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and introduce a simple technique for improving compressed sensing reconstruction from such measurements. The technique is based on a linear model of the correlation of additive noise with the signal. The modification of the reconstruction algorithm based on this model is very simple and has negligible additional computational cost compared to standard reconstruction algorithms, but is not known in existing literature. The proposed technique reduces reconstruction error considerably in the case of linearly correlated measurements and noise. Numerical experiments confirm the efficacy of the technique. The technique is demonstrated with application to low-rate quantization of compressed measurements, which is known to introduce correlated noise, and improvements in reconstruction error compared to ordinary Basis Pursuit De-Noising of up to approximately 7dB are observed for 1bit/sample quantization. Furthermore, the proposed method is compared to Binary Iterative Hard Thresholding which it is demonstrated to outperform in terms of reconstruction error for sparse signals with a number of non-zero coefficients greater than approximately 1/10th of the number of compressed measurements.