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Spectral signals often suffer from the common problems of band overlap and random Gaussian noise. To address these problems, we propose a sparsity regularization-based model that deconvolutes the degraded spectral signals. Sparsity regularization is achieved by fitting the probability density function of the gradient of the signal, and then, the iteratively reweighted least-squares method is used to solve the minimization problem. Results from experiments using real spectral signals showed that this algorithm separates the overlapping peaks and effectively suppresses the noise. The deconvoluted spectral signals will promote the practical application of infrared spectral analysis in the fields of target recognition, material identification, and chemometrics analysis. [ABSTRACT FROM AUTHOR]

Image restoration is an ill-posed problem that requires regularization to solve. Many existing regularization terms in the literature are the convex function. However, nonconvex nonsmooth regularization has advantages over convex regularization for restoring images, but its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, an adaptive nonconvex nonsmooth regularization is proposed for image restoration by using the spatial information indicator. Moreover, an efficient numerical algorithm for solving the resulting minimization problem is provided by applying the variable splitting and the penalty techniques. Finally, its advantages are shown in deblurring edges and restoring fines of image simultaneously in experiments. [ABSTRACT FROM AUTHOR]

Total variation (TV) has been used as a popular and effective image prior model in regularization-based image restoration, because of its ability to preserve edges. However, as the total variation model favors a piecewise constant solution, the processing results in the flat regions of the image are poor, and the amplitude of the edges will be underestimated; the underlying cause of the problem is that the model is based on derivation which only considers the local feature of the image. In this paper, we first propose an adaptive non-local total variation image blind restoration algorithm for deblurring a single image via a non-local total variation operator, which exploits the correlation in the image, and then an extended split Bregman iteration is proposed to address the joint minimization problem. Second, the maximum average absolute difference (MAAD) method is employed to estimate the blur support and initialize the blur kernel. Extensive experiments demonstrate that the proposed approach produces results superior to most methods in both visual image quality and quantitative measures. [ABSTRACT FROM AUTHOR]