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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]

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]

Passive millimeter-wave (PMMW) images often suffer common problems of noise and blurring. A new method is proposed to estimate the instrument response function (IRF) and desired image simultaneously. The proposed variational model integrates the adaptive weight data term, image smooth term, and IRF smooth term. The major novelty of this work is that Huber–Markov regularization is adopted for PMMW image restoration, which can preserve structural details as well as suppress noise effectively. The IRF is parametrically formulated as a Gaussian-shaped function based on experimental measurements through the utilized PMMW imaging system. The alternation minimization iterative method is applied to achieve the IRF width and desired image. Comparative experimental results with some real PMMW images reveal that the proposed approach can effectively suppress noise, reduce ringing artifacts, and improve the spatial resolution. [ABSTRACT FROM AUTHOR]

Raman spectral interpretation often suffers common problems of band overlapping and random noise. Spectral deconvolution and feature-parameter extraction are both classical problems, which are known to be difficult and have attracted major research efforts. This paper shows that the two problems are tightly coupled and can be successfully solved together. Mutual support of Raman spectral deconvolution and feature-extraction processes within a joint variational framework are theoretically motivated and validated by successful experimental results. The main idea is to recover latent spectrum and extract spectral feature parameters from slit-distorted Raman spectrum simultaneously. Moreover, a robust adaptive Tikhonov regularization function is suggested to distinguish the flat, noise, and points, which can suppress noise effectively as well as preserve details. To evaluate the performance of the proposed method, quantitative and qualitative analyses were carried out by visual inspection and quality indexes of the simulated and real Raman spectra. [ABSTRACT FROM PUBLISHER]

Deconvolution has become one of the most used methods for improving spectral resolution. Deconvolution is an ill-posed problem, especially when the point spread function (PSF) is unknown. Non-blind deconvolution methods use a predefined PSF, but in practice the PSF is not known exactly. Blind deconvolution methods estimate the PSF and spectrum simultaneously from the observed spectra, which become even more difficult in the presence of strong noise. In this paper, we present a semi-blind deconvolution method to improve the spectral resolution that does not assume a known PSF but models it as a parametric function in combination with the a priori knowledge about the characteristics of the instrumental response. First, we construct the energy functional, including Tikhonov regularization terms for both the spectrum and the parametric PSF. Moreover, an adaptive weighting term is devised in terms of the magnitude of the first derivative of spectral data to adjust the Tikhonov regularization for the spectrum. Then we minimize the energy functional to obtain the spectrum and the parameters of the PSF. We also discuss how to select the regularization parameters. Comparative results with other deconvolution methods on simulated degraded spectra, as well as on experimental infrared spectra, are presented. [ABSTRACT FROM AUTHOR]