Unequal-Compressed Sensing Based on the Characteristics of Wavelet Coefficients

Abstract

Compressed sensing (CS) has drawn quite an amount of attentions as a joint sampling and compression approach. Its theory shows that if a signal is sparse or compressible in a certain transform domain, it can be decoded from much fewer measurements than suggested by the Nyquist sampling theory. In this paper, we propose an unequal-compressed sensing algorithm which combines the compressed sensing theory with the characteristics of the wavelet coefficients. First, the original signal is decomposed by the multi-scale discrete wavelet transform (DWT) to make it sparse. Secondly, we retain the low frequency coefficients; meanwhile, one of the high frequency sub-band coefficients is measured by random Gaussian matrix. Thirdly, the sparse Bayesian learning (SBL) algorithm is used to reconstruct the high frequency sub-band coefficients. What’s more, other high frequency sub-band coefficients can be recovered according to the high frequency sub-band coefficients and the characteristics of wavelet coefficients. Finally, we use the inverse discrete wavelet transform (IDWT) to reconstruct the original signal. Compared with the original CS algorithms, the proposed algorithm has better reconstructed image quality in the same compression ratio. More importantly, the proposed method has better stability for low compression ratio.