Multi-Resolution Kronecker Compressive Sensing

Abstract

Compressive sensing is an emerging sampling technique which enables sampling a signal at a much lower rate than the Nyquist rate. In this paper, we propose a novel framework based on Kronecker compressive sensing that provides multi-resolution image reconstruction capability. By exploiting the relationship of the sensing matrices between low and high resolution images, the proposed method can reconstruct both high and low resolution images from a single measurement vector. Furthermore, post-processing using BM3D improves its recovery performance. The experimental results showed that the proposed scheme provides significant gains over the conventional framework with respect to the objective and subjective qualities.

A Novel Measurement Matrix Optimization Approach for Hyperspectral Unmixing

“…Design of measurement matrix is a research hotspot in CS, and measurement matrix optimization has become an inevitable trend to construct a new measurement matrix system. In recent years, scholars have yielded many optimization methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to design measurement matrix to reduce the minimum coherence of Gram matrix. These are typically fallen into three categories: iterative thresholding method [3][4][5][6][7][8][9][10][11][12][13][14], gradient iteration process [15][16][17][18][19], and Tensor product [20][21][22].…”

Multi-resolution compressed sensing reconstruction via approximate message passing

“…In [18], a CS-based two-layer scalable image coding is proposed, where the encoder employs two measurement matrices with different sizes, and inter-layer prediction is used to reduce the bit rate. In [19], the authors extended the Kronecker CS [22] to MR measurements, such that the sensing is performed on the LR image, and the goal is to recover the HR signal from LR measurements. In [20], a multiscale framework is proposed for CS of videos.…”

“…1) Target LR image: The target LR images are different when different downsampling matrices are used. For the transform-domain approach, the target LR image X d is represented by Eq (19)…”