Here we study the extreme visual recovery problem, in which over 90 of pixel values in a given image are missing. Existing low rank-based algorithms are only effective for recovering data with at most 90 missing values. Thus, we exploit visual data's smoothness property to help solve this challenging extreme visual recovery problem. Based on the Discrete Cosine Transformation (DCT), we propose a novel DCT norm that involves all pixels and produces smooth estimations in any view. Our theoretical analysis shows that the total variation (TV) norm, which only achieves local smoothness, is a special case of the proposed DCT norm. We also develop a new visual recovery algorithm by minimizing the DCT and nuclear norms to achieve a more visually pleasing estimation. Experimental results on a benchmark image dataset demonstrate that the proposed approach is superior to state-of-the-art methods in terms of peak signal-to-noise ratio and structural similarity.
An ADMM-like optimization scheme @cite_12 can be adopted to solve Fcn.. However, the traditional TV norm only can guarantee an estimation presenting a locally smooth visualization, when in reality a natural image should be smoothed at every scale. In the next section, we propose a multi-scale DCT norm in the frequency domain.
@cite_12
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Abstract In this paper, we consider the problem of multi-class image classification when the classes behaviour has a low rank structure. That is, classes can be embedded into a low dimensional space. Traditional multi-class classification algorithms usually use nuclear norm to approximate the rank of the weight matrix. Considering the limited ability of the nuclear norm for the accurate approximation, we propose a new scalable large scale multi-class classification algorithm by using the recently proposed truncated nuclear norm as a better surrogate of the rank operator of matrices along with multinomial logisitic loss. To solve the non-convex and non-smooth optimization problem, we further develop an efficient iterative procedure. In each iteration, by lifting the non-smooth convex subproblem into an infinite dimensional l 1 norm regularized problem, a simple and efficient accelerated coordinate descent algorithm is applied to find the optimal solution. We conduct a series of evaluations on several public large scale image datasets, where the experimental results show the encouraging improvement of classification accuracy of the proposed algorithm in comparison with the state-of-the-art multi-class classification algorithms.