Fast Correlation Computation Method for Matching Pursuit Algorithms in Compressed Sensing

There have been many matching pursuit algorithms (MPAs) which handle the sparse signal recovery problem a.k.a. compressed sensing (CS). In the MPAs, the correlation computation step has a dominant computational complexity. In this letter, we propose a new fast correlation computation method when we use some classes of partial unitary matrices as the sensing matrix. Those partial unitary matrices include partial Fourier matrices and partial Hadamard matrices which are popular sensing matrices. The proposed correlation computation method can be applied to almost all MPAs without causing any degradation of their recovery performance. And, for most practical parameters, the proposed method can reduce the computational complexity of the MPAs substantially

Deterministic Compressed Sensing Matrices from Additive Character Sequences

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

Deterministic Construction of Partial Fourier Compressed Sensing Matrices Via Cyclic Difference Sets

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically constructed via cyclic difference sets (CDS). Precisely, the matrix is constructed by $K$ rows of the $N\times N$ inverse discrete Fourier transform (IDFT) matrix, where each row index is from a $(N, K, \lambda)$ cyclic difference set. The restricted isometry property (RIP) is statistically studied for the deterministic matrix to guarantee the recovery of sparse signals. A computationally efficient reconstruction algorithm is then proposed from the structure of the matrix. Numerical results show that the reconstruction algorithm presents competitive recovery performance with allowable computational complexity.Comment: This paper has been withdrawn by the author due to crucial error