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Based on the observation that a matrix X consisted of non-local highly-correlated patches is of low rank, many image restoration methods use low-rank regularization to exploit correlation between image contents, so that the uncertainty of the unknown image signal can be reduced. To tackle the problem that the underlying cost function to pursue minimal rank is hard to solve, an effective way is to employ smooth non-convex surrogate log |XXT| for the rank penalty. Essentially, such technique only considers to utilize correlation within image patches. In this paper, we propose to jointly exploit both intra- and inter-patch correlation of the input image, so as to further reduce the uncertainty of the signal, and thus improve the prediction of the latent image. The corresponding two surrogates are integrated to incorporate both intra- and inter-patch correlation. To solve the optimization problem, we use iterative alternating direction technique to divide the problem into two subproblems, each of which is solved via an empirical Bayesian procedure built upon variational approximation. Experimental results show that the proposed approach outperforms several state-of-the-art methods in terms of PSNR and perceptual quality.

In wireless visual communication systems, it is crucial to effectively utilize channel power and bandwidth in the pursue of optimal performance, and it is worthwhile to adapt the transmission scheme to human vision system (HVS) so as to achieve perceptually appealing results. Inspired by observations that visual quality of an image is closely related to the gradient data, this paper proposes to convey visual information by random projection measurements of image gradients in an analog framework. Since HVS is more sensitive to luminance variations of image contents, which are contained in the gradient data, the proposed scheme achieves better perceptual quality than conventional analog uncoded schemes like SoftCast. Besides, the gradient transform removes the low and medium frequency components of the image hence substantially reduces the power of the signal transmitted in the analog channel, thus evidently improves the power-distortion performance of the system. Furthermore, by applying random projection to the gradients, the number of transmitted data can be adjusted according to bandwidth conditions. Another contribution of this paper is to develop an effective optimization scheme for the compressive gradient based reconstruction problem. Experimental results validate the effectiveness of the proposed transmission and reconstruction scheme under different channel signal-to-noise ratio and bandwidth conditions.

This paper combines an adaptive reconstruction based approach and a learning based technique into an effective scheme for single image super-resolution. Unlike conventional schemes that adopt pre-trained dictionaries to tell the relationship between high-resolution (HR) image and the low-resolution (LR) observation, the proposed method attempts to learn the joint distribution of highly-correlated patch couples from the input image itself instead of an external dataset, so that the learnt models are specially tailored for the current patches and thus can better fit the image data of interest. To be specific, we first apply spatially adaptive gradient sparsity regularization in the reconstruction of the HR image using the contour information, and then utilize the generated HR output to guide the joint distribution learning to infer the relationship between the highly-correlated HR and LR patches. In this way, we simultaneously exploit the inter-scale correlation as well as the local and non-local correlation of the image contents. Empirical results show that the performance of the proposed method is highly competitive with state-of-the-art schemes in terms of peak signal-to-noise ratio (PSNR) and perceptual quality.