• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.6
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• pp.2748-2766
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• 2016

Compared with traditional patch-based sparse representation, recent studies have concluded that group-based sparse representation (GSR) can simultaneously enforce the intrinsic local sparsity and nonlocal self-similarity of images within a unified framework. This article investigates an accelerated split Bregman method (SBM) that is based on GSR which exploits image compressive sensing (CS). The computational efficiency of accelerated SBM for the measurement matrix of a partial Fourier matrix can be further improved by the introduction of a fast Fourier transform (FFT) to derive the enhanced algorithm. In addition, we provide convergence analysis for the proposed method. Experimental results demonstrate that accelerated SBM is potentially faster than some existing image CS reconstruction methods.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.135-173
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• 2023

The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3338-3355
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• 2018

Images acquired by Large Aperture Static Imaging Spectrometer (LASIS) exhibit obvious interference stripes, which are vertical and stationary due to the special imaging principle of interference hyperspectral image (IHI) data. As the special characteristics above will seriously affect the intrinsic structure and sparsity of IHI, decomposition of IHI has drawn considerable attentions of many scientists and lots of efforts have been made. Although some decomposition methods for interference hyperspectral data have been proposed to solve the above problem of interference stripes, too many times of iteration are necessary to get an optimal solution, which will severely affect the efficiency of application. A novel algorithm for decomposition of interference hyperspectral images based on split Bregman iteration is proposed in this paper, compared with other decomposition methods, numerical experiments have proved that the proposed method will be much more efficient and can reduce the times of iteration significantly.

• Journal of Information Processing Systems
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• v.14 no.6
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• pp.1405-1419
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• 2018

An image fusion method is proposed on the basis of depth model segmentation to overcome the shortcomings of noise interference and artifacts caused by infrared and visible image fusion. Firstly, the deep Boltzmann machine is used to perform the priori learning of infrared and visible target and background contour, and the depth segmentation model of the contour is constructed. The Split Bregman iterative algorithm is employed to gain the optimal energy segmentation of infrared and visible image contours. Then, the nonsubsampled contourlet transform (NSCT) transform is taken to decompose the source image, and the corresponding rules are used to integrate the coefficients in the light of the segmented background contour. Finally, the NSCT inverse transform is used to reconstruct the fused image. The simulation results of MATLAB indicates that the proposed algorithm can obtain the fusion result of both target and background contours effectively, with a high contrast and noise suppression in subjective evaluation as well as great merits in objective quantitative indicators.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.519-532
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• 2020

In this paper, we first propose a new total variation-based regularization model for image restoration. We next propose a fixed-point-like method for solving the new image restoration model, and then we provide convergence analysis for the fixed-point-like method. To evaluate the feasibility and efficiency of the fixed-point-like method for the new proposed total variation-based regularization model, we provide numerical experiments for several test problems.

• IEIE Transactions on Smart Processing and Computing
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• v.3 no.1
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• pp.19-27
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• 2014

Compressive sensing is an emerging sampling technique which enables sampling a signal at a much lower rate than the Nyquist rate. In this paper, we propose a novel framework based on Kronecker compressive sensing that provides multi-resolution image reconstruction capability. By exploiting the relationship of the sensing matrices between low and high resolution images, the proposed method can reconstruct both high and low resolution images from a single measurement vector. Furthermore, post-processing using BM3D improves its recovery performance. The experimental results showed that the proposed scheme provides significant gains over the conventional framework with respect to the objective and subjective qualities.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.11
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• pp.3479-3492
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• 2022

Longitudinal quantification of brain changes due to development, aging or disease plays an important role in the filed of personalized-medicine applications. However, due to the temporal variability in shape and different imaging equipment and parameters, estimating anatomical changes in longitudinal studies is significantly challenging. In this paper, a longitudinal Magnetic Resonance(MR) brain image segmentation algorithm proposed by combining intensity information and anisotropic smoothness term which contain a spatial smoothness constraint and longitudinal consistent constraint into a variational framework. The minimization of the proposed energy functional is strictly and effectively derived from a fast optimization algorithm. A large number of experimental results show that the proposed method can guarantee segmentation accuracy and longitudinal consistency in both simulated and real longitudinal MR brain images for analysis of anatomical changes over time.

• Journal of the Optical Society of Korea
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• v.20 no.6
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• pp.752-761
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• 2016

Hyperspectral images are often contaminated with stripe noise, which severely degrades the imaging quality and the precision of the subsequent processing. In this paper, a variational model is proposed by employing spectral-spatial adaptive unidirectional variation and a sparse representation. Unlike traditional methods, we exploit the spectral correction and remove stripes in different bands and different regions adaptively, instead of selecting parameters band by band. The regularization strength adapts to the spectrally varying stripe intensities and the spatially varying texture information. Spectral correlation is exploited via dictionary learning in the sparse representation framework to prevent spectral distortion. Moreover, the minimization problem, which contains two unsmooth and inseparable $l_1$-norm terms, is optimized by the split Bregman approach. Experimental results, on datasets from several imaging systems, demonstrate that the proposed method can remove stripe noise effectively and adaptively, as well as preserve original detail information.