Adaptive gradient-based block compressive sensing with sparsity for noisy images

This paper develops a novel adaptive gradient-based block compressive sensing (AGbBCS_SP) methodology for noisy image compression and reconstruction. The AGbBCS_SP approach splits an image into blocks by maximizing their sparsity, and reconstructs images by solving a convex optimization problem. In block compressive sensing, the commonly used square block shapes cannot always produce the best results. The main contribution of our paper is to provide an adaptive method for block shape selection, improving noisy image reconstruction performance. The proposed algorithm can adaptively achieve better results by using the sparsity of pixels to adaptively select block shape. Experimental results with different image sets demonstrate that our AGbBCS_SP method is able to achieve better performance, in terms of peak signal to noise ratio (PSNR) and computational cost, than several classical algorithms

Compressive Imaging via Approximate Message Passing with Image Denoising

We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose compressive imaging algorithms that employ the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising at each iteration; in order for AMP to reconstruct the original input signal well, a good denoiser must be used. We apply two wavelet based image denoisers within AMP. The first denoiser is the "amplitude-scaleinvariant Bayes estimator" (ABE), and the second is an adaptive Wiener filter; we call our AMP based algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results show that both AMP-ABE and AMP-Wiener significantly improve over the state of the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener offers lower mean square error (MSE) than existing compressive imaging algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise as well as the adaptive Wiener filter.Comment: 15 pages; 2 tables; 7 figures; to appear in IEEE Trans. Signal Proces