Bayesian Cramér-Rao Bound for Noisy Non-Blind and Blind Compressed Sensing

2010/05/24 by Hadi Zayyani, Zayyani, Hadi, Massoud Babaie‐Zadeh +3
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1005.4316

openalex publication_date 2010/05/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian Cramer-Rao bound for estimating the sparse coefficients while the measurement matrix elements are independent zero mean random variables. Simulation results show a large gap between the lower bound and the performance of the practical algorithms when the number of measurements are low.

Citations

• Fundamentals of Statistical Signal Processing: Estimation Theory
• Atomic Decomposition by Basis Pursuit
• A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed ℓ ⁰ Norm

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• Blind Compressed Sensing
• Bayesian hypothesis testing for one bit compressed sensing with sensing matrix perturbation
• A probabilistic and RIPless theory of compressed sensing
• A signal recovery algorithm for sparse matrix based compressed sensing
• Robust Bayesian Compressed sensing