This paper studies a problem of image restoration that observed images are contaminated by Gaussian and impulse noise. Existing methods for this problem in the literature are based on minimizing an objective functional having the l(1) fidelity term and the Mumford-Shah regularizer. We present an algorithm on this problem by minimizing a new objective functional. The proposed functional has a content-dependent fidelity term which assimilates the strength of fidelity terms measured by the l(1) and l(2) norms. The regularizer in the functional is formed by the l(1) norm of tight framelet coefficients of the underlying image. The selected tight framelet filters are able to extract geometric features of images. We then propose an iterative framelet-based approximation/sparsity deblurring algorithm (IFASDA) for the proposed functional. Parameters in IFASDA are adaptively varying at each iteration and are determined automatically. In this sense, IFASDA is a parameter-free algorithm. This advantage makes the algorithm more attractive and practical. The effectiveness of IFASDA is experimentally illustrated on problems of image deblurring with Gaussian and impulse noise. Improvements in both PSNR and visual quality of IFASDA over a typical existing method are demonstrated. In addition, Fast_IFASDA, an accelerated algorithm of IFASDA, is also developed.

In this paper, we propose an image inpainting optimization model whose objective function is a smoothed l(1) norm of the weighted nondecimated discrete cosine transform (DCT) coefficients of the underlying image. By identifying the objective function of the proposed model as a sum of a differentiable term and a nondifferentiable term, we present a basic algorithm inspired by Beck and Teboulle's recent work on the model. Based on this basic algorithm, we propose an automatic way to determine the weights involved in the model and update them in each iteration. The DCT as an orthogonal transform is used in various applications. We view the rows of a DCT matrix as the filters associated with a multiresolution analysis. Nondecimated wavelet transforms with these filters are explored in order to analyze the images to be inpainted. Our numerical experiments verify that under the proposed framework, the filters from a DCT matrix demonstrate promise for the task of image inpainting.

Supplementary data are available at Bioinformatics online.

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Evidences increasingly indicate the involvement of long non-coding RNAs (lncRNAs) in various biological processes. As the mutations and abnormalities of lncRNAs are closely related to the progression of complex diseases, the identification of lncRNA-disease associations has become an important step toward the understanding and treatment of diseases. Since only a limited number of lncRNA-disease associations have been validated, an increasing number of computational approaches have been developed for predicting potential lncRNA-disease associations. However, how to predict potential associations precisely through computational approaches remains challenging. In this study, we propose a novel two-side sparse self-representation (TSSR) algorithm for lncRNA-disease association prediction. By learning the self-representations of lncRNAs and diseases from known lncRNA-disease associations adaptively, and leveraging the information provided by known lncRNA-disease associations and the intra-associations among lncRNAs and diseases derived from other existing databases, our model could effectively utilize the estimated representations of lncRNAs and diseases to predict potential lncRNA-disease associations. The experiment results on three real data sets demonstrate that our TSSR outperforms other competing methods significantly. Moreover, to further evaluate the effectiveness of TSSR in predicting potential lncRNAs-disease associations, case studies of Melanoma, Glioblastoma, and Glioma are carried out in this paper. The results demonstrate that TSSR can effectively identify some candidate lncRNAs associated with these three diseases.