Deep learning has been used to image compressive sensing (CS) for enhanced reconstruction performance. However, most existing deep learning methods train different models for different subsampling ratios, which brings additional hardware burden. In t
his paper, we develop a general framework named scalable deep compressive sensing (SDCS) for the scalable sampling and reconstruction (SSR) of all existing end-to-end-trained models. In the proposed way, images are measured and initialized linearly. Two sampling masks are introduced to flexibly control the subsampling ratios used in sampling and reconstruction, respectively. To make the reconstruction model adapt to any subsampling ratio, a training strategy dubbed scalable training is developed. In scalable training, the model is trained with the sampling matrix and the initialization matrix at various subsampling ratios by integrating different sampling matrix masks. Experimental results show that models with SDCS can achieve SSR without changing their structure while maintaining good performance, and SDCS outperforms other SSR methods.
In this paper we are concerned with the asymptotic analysis of nonbinary spatially-coupled low-density parity-check (SC-LDPC) ensembles defined over GL$left(2^{m}right)$ (the general linear group of degree $m$ over GF$left(2right)$). Our purpose is t
o prove threshold saturation when the transmission takes place on the binary erasure channel (BEC). To this end, we establish the duality rule for entropy for nonbinary variable-node (VN) and check-node (CN) convolutional operators to accommodate the nonbinary density evolution (DE) analysis. Based on this, we construct the explicit forms of the potential functions for uncoupled and coupled DE recursions. In addition, we show that these functions exhibit similar monotonicity properties as those for binary LDPC and SC-LDPC ensembles over general binary memoryless symmetric (BMS) channels. This leads to the threshold saturation theorem and its converse for nonbinary SC-LDPC ensembles on the BEC, following the proof technique developed by S. Kumar et al.
Most compressive sensing (CS) reconstruction methods can be divided into two categories, i.e. model-based methods and classical deep network methods. By unfolding the iterative optimization algorithm for model-based methods onto networks, deep unfold
ing methods have the good interpretation of model-based methods and the high speed of classical deep network methods. In this paper, to solve the visual image CS problem, we propose a deep unfolding model dubbed AMP-Net. Rather than learning regularization terms, it is established by unfolding the iterative denoising process of the well-known approximate message passing algorithm. Furthermore, AMP-Net integrates deblocking modules in order to eliminate the blocking artifacts that usually appear in CS of visual images. In addition, the sampling matrix is jointly trained with other network parameters to enhance the reconstruction performance. Experimental results show that the proposed AMP-Net has better reconstruction accuracy than other state-of-the-art methods with high reconstruction speed and a small number of network parameters.
