A Scaled and Adaptive FISTA Algorithm for Signal-Dependent Sparse Image Super-Resolution Problems

Lazzaretti, Marta; Rebegoldi, Simone; Calatroni, Luca; Estatico, Claudio

doi:10.1007/978-3-030-75549-2_20

Cited by 3 publications

(4 citation statements)

References 17 publications

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“…In particular, we will apply our algorithm to the regularization proposed in [16], named CEL0, as an approximation of the ℓ 0 norm for image super resolution in microscopy. We will show that this functional can be set in the form (5), and we will present the results of a numerical experience in this framework, comparing our proposed algorithm to other iteratively reweighted methods presented in the literature for this specific application [16,17,28].…”

Section: Contributionmentioning

confidence: 99%

“…Unlike other standard results available in the literature, our result holds at the exact proximal-gradient point ŷ(k,0) , of which we have no knowledge if τ > 0, rather than at the point ỹ(k,0) that is actually computed in the algorithm. This is because such an upper bound is unlikely to hold at an inexact point computed according to (28), as discussed in [36, section 3.2]. Indeed, even if it is possible to obtain an upper bound for the distance between the exact point ŷ(k,0) and its approximation ỹ(k,0) (see inequality (16) in lemma 5), a similar relation between the subgradients at ŷ(k,0) and those at ỹ(k,0) can not be proved.…”

Section: Assumption 2 (I)mentioning

confidence: 99%

“…)) must be approximated by a point ỹ(k,i) satisfying inequality (28). Such a point can be computed by applying an iterative optimization method to the dual of problem (71), until the primal-dual gap satisfies a suitable, easy to check condition [9, section 3.1].…”

Section: Image Deblurring and Denoising Using Nonconvex Edge Preservi...mentioning

confidence: 99%

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On an iteratively reweighted linesearch based algorithm for nonconvex composite optimization

et al. 2023

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In this paper we propose a new algorithm for solving a class of nonsmooth nonconvex problems, which is obtained by combining the iteratively reweighted scheme with a finite number of forward–backward iterations based on a linesearch procedure. The new method overcomes some limitations of linesearch forward–backward methods, since it can be applied also to minimize functions containing terms that are both nonsmooth and nonconvex. Moreover, the combined scheme can take advantage of acceleration techniques consisting in suitable selection rules for the algorithm parameters. We develop theconvergence analysis of the new method within the framework of the Kurdyka-Lojasiewicz property. Finally, we present the results of a numerical experience on microscopy image super resolution, showing that the performances of our method are comparable or superior to those of other algorithms designed for this specific application.

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Section: Contributionmentioning

confidence: 99%

Section: Assumption 2 (I)mentioning

confidence: 99%

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On an iteratively reweighted linesearch based algorithm for nonconvex composite optimization

et al. 2023

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“…The "soft threshold" is utilized as the gradient of the objective function and the "gradient descent" is employed to obtain the best value. Researchers have raised numerous improved FISTAs, such as AFISTA, [14] which fastens the FISTA by a continuation strategy, and S-FISTA [15], which uses a scaling technique for gradient proximal step. EFISTA [16], monotonic FISTA [17], restart FISTA [18,19] and backtracking strategy [20] are also available.…”

Section: Introductionmentioning

confidence: 99%

A Faster and More Accurate Iterative Threshold Algorithm for Signal Reconstruction in Compressed Sensing

Wei

Mao

Dai

et al. 2022

Sensors

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Fast iterative soft threshold algorithm (FISTA) is one of the algorithms for the reconstruction part of compressed sensing (CS). However, FISTA cannot meet the increasing demands for accuracy and efficiency in the signal reconstruction. Thus, an improved algorithm (FIPITA, fast iterative parametric improved threshold algorithm) based on mended threshold function, restart adjustment mechanism and parameter adjustment is proposed. The three parameters used to generate the gradient in the FISTA are carefully selected by assessing the impact of them on the performance of the algorithm. The developed threshold function is used to replace the soft threshold function to reduce the reconstruction error and a restart mechanism is added at the end of each iteration to speed up the algorithm. The simulation experiment is carried out on one-dimensional signal and the FISTA, RadaFISTA and RestartFISTA are used as the comparison objects, with the result that in one case, for example, the residual rate of FIPITA is about 6.35% lower than those three and the number of iterations required to achieve the minimum error is also about 102 less than that of FISTA.

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Parameter-Free FISTA by Adaptive Restart and Backtracking

Aujol,

Calatroni,

Dossal

et al. 2024

SIAM J. Optim.

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A Scaled and Adaptive FISTA Algorithm for Signal-Dependent Sparse Image Super-Resolution Problems

Cited by 3 publications

References 17 publications

On an iteratively reweighted linesearch based algorithm for nonconvex composite optimization

On an iteratively reweighted linesearch based algorithm for nonconvex composite optimization

A Faster and More Accurate Iterative Threshold Algorithm for Signal Reconstruction in Compressed Sensing

Parameter-Free FISTA by Adaptive Restart and Backtracking

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