In this paper we are interested in the differential inclusion 0 is an element of x (t) + b/tx(t) + partial derivative F(x(t)) in a finite-dimensional Hilbert space R-d, where F is a proper, convex, lower semicontinuou...
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In this paper we are interested in the differential inclusion 0 is an element of x (t) + b/tx(t) + partial derivative F(x(t)) in a finite-dimensional Hilbert space R-d, where F is a proper, convex, lower semicontinuous function. The motivation of this study is that the differential inclusion models the fista algorithm as considered in [A. Chambolle and C. Dossal, J. Optim. Theory Appl., 166 (2015), pp. 968{982]. In particular, we investigate the different asymptotic properties of solutions for this inclusion for b > 0. We show that the convergence rate of F (x (t)) towards the minimum of F is of order of O (t(-2b/3)) when 0 < b < 3, while for b > 3 this order is of o(t(-2)) and the solution-trajectory converges to a minimizer of F. These results generalize the ones obtained in the differential setting (where F is differentiable) in [H. Attouch, Z. Chbani, J. Peypouquet, and P. Redont, Math. Program., 2016, pp. 1{53], [H. Attouch, Z. Chbani, and H. Riahi, arXiv:1706.05671, 2017], [J. Aujol and C. Dossal, Optimal Rate of Convergence of an ODE Associated to the Fast Gradient Descent Schemes for b > 0, 2017], and [W. Su, S. Boyd, and E. J. Candes, J. Mach. Learn. Res., 17 (2016), pp. 1-43]. In addition, we show that the order of the convergence rate O (t(-2b/3)) of F (x(t)) towards the minimum is optimal, in the case of low friction b < 3, by making a particular choice of F.
An improved fast iterative shrinkage thresholding algorithm (Ifista) for image deblurring is proposed. The Ifista algorithm uses a positive definite weighting matrix in the gradient function of the minimization proble...
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An improved fast iterative shrinkage thresholding algorithm (Ifista) for image deblurring is proposed. The Ifista algorithm uses a positive definite weighting matrix in the gradient function of the minimization problem of the known fast iterative shrinkage thresholding (fista) image restoration algorithm. A convergence analysis of the Ifista algorithm shows that due to the weighting matrix, the Ifista algorithm has an improved convergence rate and improved restoration capability of the unknown image over that of the fista algorithm. The weighting matrix is predetermined and fixed, and hence, like the fista algorithm, the Ifista algorithm requires only one matrix vector product operation in each iteration. As a result, the computational burden per iteration of the Ifista algorithm remains the same as in the fista algorithm. Numerical examples are presented that demonstrate the improved performance of the Ifista algorithm over that of the fista and iterative shrinkage thresholding (ISTA) algorithms in terms of the convergence speed and the peak signal-to-noise ratio.
Underwater image enhancement, especially in color restoration and detail reconstruction, remains a significant challenge. Current models focus on improving accuracy and learning efficiency through neural network desig...
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Underwater image enhancement, especially in color restoration and detail reconstruction, remains a significant challenge. Current models focus on improving accuracy and learning efficiency through neural network design, often neglecting traditional optimization algorithms' benefits. We propose FAIN-UIE, a novel approach for color and fine-texture recovery in underwater imagery. It leverages insights from the Fast Iterative Shrink-Threshold algorithm (fista) to approximate image degradation, enhancing network fitting speed. FAIN-UIE integrates the residual degradation module (RDM) and momentum calculation module (MC) for gradient descent and momentum simulation, addressing feature fusion losses with the Feature Merge Block (FMB). By integrating multi-scale information and inter-stage pathways, our method effectively maps multi-stage image features, advancing color and fine-texture restoration. Experimental results validate its robust performance, positioning FAIN-UIE as a competitive solution for practical underwater imaging applications.
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