Adaptive compressed sensing for video acquisition

Abstract

In this paper, we propose an adaptive compressed sensing scheme that utilizes a support estimate to focus the measurements on the large valued coefficients of a compressible signal. We embed a "sparse-filtering" stage into the measurement matrix by weighting down the contribution of signal coefficients that are outside the support estimate. We present an application which can benefit from the proposed sampling scheme, namely, video compressive acquisition. We demonstrate that our proposed adaptive CS scheme results in a significant improvement in reconstruction quality compared with standard CS as well as adaptive recovery using weighted 1 minimization.

Optimized truncation model for adaptive compressive sensing acquisition of images

“…We observe that, * N k can be approximately obtained as (5) and the elements between * N k and N k may not be exactly reconstructed. And the number of these elements grows with the increase of N k , which degrades the reconstruction SER.…”

“…Generally, the l 2 norm is often much smaller than the l 1 norm for the "tail" part of a same compressible signal [5,6]. So the CS reconstruction error can be reduced by truncating the "tail" part for a compressible signal.…”

“…We compare the quality (PSNR and SSIM) of the reconstructed image of "Proposed ACS" to that of: 1) standard CS (denoted "Standard CS") and 2) the weighted adaptive CS in [5] (denoted "Reference [5]"). The images are first normalized to unit l 2 norm and then divided into 16×16 blocks (N=256).…”

“…3 shows that the recovered PSNR in dB for the 4 test images. It is shown that "Proposed ACS" achieves an average PSNR gain of 1.4dB (ǻSSIM=0.06) comparing to "Standard CS" and 0.7dB (ǻ66,0 0.02) comparing to "Reference [5]". We also test block size of 32×32, for which the gains are 1.4dB (ǻ66,0 0.08) and 0.7dB (ǻ66,0 0.03), respectively.…”

“…Once too many coefficients are truncated at a high sampling rate, the quality of the reconstructed signal may be degraded. Mansour et al [5] considered this problem by simply establishing a linear model to adapt the sampling rate for CS acquisition to reduce the noise folding effect. However, it does not optimize the relationship between "tail" part and the sampling rate, and the reconstruction algorithm in standard CS needs to be modified according to its solution, which complicates its practical implementation.…”