arXiv subjects

Federica Porta

Publications and source records attributed to Federica Porta.

9 recordsLinked to original sources

arXiv2026

A Line--Search--Based Stochastic Gradient Method for 3D Computed Tomography

We introduce FB-LISA, a forward-backward (FB) generalization of a recently proposed line-search-based stochastic gradient algorithm to address the imaging problem of volumetric reconstruction in Computed Tomography, a substantially high demanding problem, which involves orders of magnitude of data, a high computational burden for forward and backprojection, and memory requirements that push current GPU architectures to their limits. Our formulation employs stochastic mini-batches composed of full 2D projections, preserving the physical structure of the acquisition process while enabling significant speed-ups during early iterations. The resulting method demonstrates how concepts traditionally associated with deep learning can be repurposed to accelerate large-scale inverse problems, without relying on training data or learned priors.

math.NA↗

arXiv2026

Plug-and-Play blind super-resolution of real MRI images for improved multiple sclerosis diagnosis

Magnetic resonance imaging (MRI) is central to the diagnosis of multiple sclerosis, where the identification of biomarkers such as the central vein sign benefits from high-resolution images. However, most clinical brain MRI scans are performed using 1.5 T scanners, which provide lower sensitivity compared to higher-field systems. We propose a blind super-resolution framework to enhance real 1.5 T MRI images acquired in clinical settings, where only post-processed data are available and the degradation model is not fully known. The problem is formulated as a non-convex blind inverse problem involving the joint estimation of the high-resolution image and the blur kernel. Image regularization is handled through a Plug-and-Play strategy based on a pretrained denoiser, while suitable constraints are imposed on the blur kernel. To solve the resulting model, we design a heterogeneous alternating block-coordinate method in which the two variables are updated using different types of algorithms. Convergence properties are rigorously established. Experiments on FLAIR and SWI sequences acquired at 1.5 T show improved structural definition and enhanced visibility of clinically relevant features, with visual comparison against 3 T images.

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arXiv2026

Block-coordinate Plug-And-Play Methods with Armijo-like line-search for Image Restoration

In this paper, we develop a class of block-coordinate forward-backward methods for solving non-convex and non-separable composite optimization problems, and specialize them to imaging inverse problems within the Plug-and-Play (PnP) framework based on Gradient Step (GS) denoisers. The block-coordinate strategy is designed to reduce the high memory consumption associated with the computation of GS denoisers, whose implementation typically requires storing large computational graphs. The proposed methods allow for the joint use of inertial acceleration, variable metric strategies, inexact proximal computations, and adaptive steplength selection via an appropriate line-search procedure. Under mild assumptions on the objective function, we establish a sublinear convergence rate and the stationarity of the limit points. Moreover, convergence of the entire sequence of the iterates is guaranteed under a Kurdyka-{\L}ojasiewicz assumption. Numerical experiments on ill-posed imaging problems, including deblurring and super-resolution, demonstrate that the proposed PnP approach achieves state-of-the-art reconstruction quality while substantially reducing GPU memory requirements, making it particularly suitable for large-scale and resource-constrained imaging applications.

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arXiv2021

Combining Weighted Total Variation and Deep Image Prior for natural and medical image restoration via ADMM

In the last decades, unsupervised deep learning based methods have caught researchers attention, since in many real applications, such as medical imaging, collecting a great amount of training examples is not always feasible. Moreover, the construction of a good training set is time consuming and hard because the selected data have to be enough representative for the task. In this paper, we focus on the Deep Image Prior (DIP) framework and we propose to combine it with a space-variant Total Variation regularizer with an automatic estimation of the local regularization parameters. Differently from other existing approaches, we solve the arising minimization problem via the flexible Alternating Direction Method of Multipliers (ADMM). Furthermore, we provide a specific implementation also for the standard isotropic Total Variation. The promising performances of the proposed approach, in terms of PSNR and SSIM values, are addressed through several experiments on simulated as well as real natural and medical corrupted images.

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arXiv2016

On the convergence of a linesearch based proximal-gradient method for nonconvex optimization

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a critical point if the objective function satisfies the Kurdyka-Lojasiewicz property at each point of its domain, under the assumption that a limit point exists. The proposed method is applied to a wide collection of image processing problems and our numerical tests show that our algorithm results to be flexible, robust and competitive when compared to recently proposed approaches able to address the optimization problems arising in the considered applications.

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arXiv2015

A variable metric forward--backward method with extrapolation

Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the last decade. In this paper we focus on the convex case and, inspired by recent approaches for accelerating first-order iterative schemes, we develop a scaled inertial forward-backward algorithm which is based on a metric changing at each iteration and on a suitable extrapolation step. Unlike standard forward-backward methods with extrapolation, our scheme is able to handle functions whose domain is not the entire space. Both {an ${\mathcal O}(1/k^2)$ convergence rate estimate on the objective function values and the convergence of the sequence of the iterates} are proved. Numerical experiments on several {test problems arising from image processing, compressed sensing and statistical inference} show the {effectiveness} of the proposed method in comparison to well performing {state-of-the-art} algorithms.

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arXiv2015

Variable metric inexact line-search based methods for nonsmooth optimization

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a suitable descent direction, based on the proximal operator associated to the convex part of the objective function, and an Armijo-like rule to determine the step size along this direction ensuring the sufficient decrease of the objective function. In this frame, we especially address the possibility of adopting a metric which may change at each iteration and an inexact computation of the proximal point defining the descent direction. For the more general nonconvex case, we prove that all limit points of the iterates sequence are stationary, while for convex objective functions we prove the convergence of the whole sequence to a minimizer, under the assumption that a minimizer exists. In the latter case, assuming also that the gradient of the smooth part of the objective function is Lipschitz, we also give a convergence rate estimate, showing the O(1/k) complexity with respect to the function values. We also discuss verifiable sufficient conditions for the inexact proximal point and we present the results of a numerical experience on a convex total variation based image restoration problem, showing that the proposed approach is competitive with another state-of-the-art method.

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arXiv2014

A new steplength selection for scaled gradient methods with application to image deblurring

Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the steplength parameter defining the descent direction, as in the case of the well-known Barzilai and Borwein rules. In a recent paper, a strategy for the steplength selection approximating the inverse of some eigenvalues of the Hessian matrix has been proposed for gradient methods applied to unconstrained minimization problems. In the quadratic case, this approach is based on a Lanczos process applied every m iterations to the matrix of the most recent m back gradients but the idea can be extended to a general objective function. In this paper we extend this rule to the case of scaled gradient projection methods applied to non-negatively constrained minimization problems, and we test the effectiveness of the proposed strategy in image deblurring problems in both the presence and the absence of an explicit edge-preserving regularization term.

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arXiv2013

On the filtering effect of iterative regularization algorithms for linear least-squares problems

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to provide the fastest methods for the reconstruction of the solution, involving choices of adaptive parameters and scaling matrices. However, in presence of an ill-conditioned model and real data, the need of a regularized solution instead of the least-squares one changed the point of view in favour of iterative algorithms able to combine a fast execution with a stable behaviour with respect to the restoration error. In this paper we want to analyze some classical and recent gradient approaches for the linear least-squares problem by looking at their way of filtering the singular values, showing in particular the effects of scaling matrices and non-negative constraints in recovering the correct filters of the solution.

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