Adaptive Compressed Sensing Using Intra-Scale Variable Density Sampling

Abstract

Adaptive sensing has the potential to achieve near optimal performance by using current measurements to design subsequential sensing vectors. Existing adaptive sensing methods are usually based on recursive bisection or known structures of certain sparse representations. They suffer from either wasting extra measurements for detecting large coefficients, or missing these coefficients because of violations of these structures. In this paper, intra-scale variable density sampling (InVDS) is presented to capture the heterogeneous property of coefficients. First, Latin hypercube sampling with good uniformity is employed to find areas containing large coefficients. Then, the neighborhoods of $K$ largest coefficients are measured according to the block-sparsity or clustering property. Finally, the denoising-based approximate message passing algorithm is introduced to enhance the performance of image reconstruction. The probability that our sampling method fails to obtain large coefficients is analyzed. The superiority of InVDS is validated by numerical experiments with wavelet, discrete cosine, and Hadamard transforms.