Year: 2010
Type: preprint
Abstract: Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive character sequences. The Weil bound is then used to show that the matrix has asymptotically optimal coherence for $N=K^2$, and to present a sufficient condition on the sparsity level for unique sparse recovery. Also, the restricted isometry property (RIP) is statistically studied for the deterministic matrix. Using additive character sequences with small alphabets, the compressed sensing matrix can be efficiently implemented by linear feedback shift registers. Numerical results show that the deterministic compressed sensing matrix guarantees reliable matching pursuit recovery performance for both noiseless and noisy measurements.
Source: arXiv (Cornell University)
Author: Yu, Nam Yul
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1639246335