Compressed sensing of image signals with threshold processing

The basic principle of compressed sensing (CS) theory is that if a signal is sparse, CS promises to deliver a full recovery of this signal with high probability from far fewer measurements than the original signal. Unfortunately, image signals usually are not sparse. When an image is transformed into other domain, such as DWT or DCf domain, the transform coefficients can be compressible but still do not satisfy the criteria of sparsity, and hence it is near impossible to be precisely recovered employing general CS algorithms without change. In this paper, we propose a compressed sensing method based on threshold processing. As image reconstruction error of CS is nearly inevitable, we purposely discard certain small transform coefficients based on threshold processing. This way, the sparsity of image transform coefficients is intentionally increased. While intuitively threshold processing will introduce error, it can, at the same time, improve the CS reconstructing efficiency because of increased sparsity. We show that there exists an optimal threshold that achieves the highest reconstruction accuracy owing to increased sparsity in spite of induced errors owing to threshold processing. We present an adaptive genetic algorithm to locate this optimal point whose effectiveness is supported by experimental results. (C) 2016 Elsevier GmbH. All rights reserved.