A novel Adaptive weighted Kronecker Compressive Sensing

TL;DR

This paper introduces an adaptive weighted Kronecker compressive sensing method for multidimensional signal reconstruction, utilizing a cube-based sampling scheme that adapts to block sparsity and leverages perceptual weighting for improved efficiency.

Contribution

The paper proposes a novel cube-based sampling and reconstruction approach with adaptive sampling allocation and perceptual weighting, enhancing multidimensional signal recovery.

Findings

Competitive with state-of-the-art methods

Efficient in low measurement scenarios

Parallelizable reconstruction process

Abstract

Recently, multidimensional signal reconstruction using a low number of measurements is of great interest. Therefore, an effective sampling scheme which should acquire the most information of signal using a low number of measurements is required. In this paper, we study a novel cube-based method for sampling and reconstruction of multidimensional signals. First, inspired by the block-based compressive sensing (BCS), we divide a group of pictures (GoP) in a video sequence into cubes. By this way, we can easily store the measurement matrix and also easily can generate the sparsifying basis. The reconstruction process also can be done in parallel. Second, along with the Kronecker structure of the sampling matrix, we design a weight matrix based on the human visuality system, i.e. perceptually. We will also benefit from different weighted $\ell_1$-minimization methods for reconstruction. Furthermore, conventional methods for BCS consider an equal number of samples for all blocks. However, the sparsity order of blocks in natural images could be different and, therefore, a various number of samples could be required for their reconstruction. Motivated by this point, we will adaptively allocate the samples for each cube in a video sequence. Our aim is to show that our simple linear sampling approach can be competitive with the other state-of-the-art methods.