arXiv subjects

Alessandro Benfenati

Publications and source records attributed to Alessandro Benfenati.

15 recordsLinked to original sources

arXiv2026

A Relaxed Gradient Step Denoiser for Splitting Methods in Poisson Inverse Problems

Plug and Play methods combine classical variational models with learned denoisers and have achieved strong results in imaging inverse problems. Their convergence has been widely studied for Gaussian data, whereas Poisson models require additional care because of the nonquadratic Kullback-Leibler fidelity. This work introduces GSDSplit+ , a splitting method built upon PnPSplit+, in which the generic denoising block is replaced by a relaxed Gradient Step Denoiser. The resulting method retains explicit Poisson fidelity updates. The denoiser is defined through the gradient of a learned convex potential parameterized by an Input Convex Neural Network. Its architecture and training promote both blind denoising capability and a smoothness condition sufficient for firm nonexpansiveness. Empirical smoothness estimates are used to select a relaxation parameter compatible with the convergence assumptions of PnPSplit+. Numerical experiments provide evidence that the trained denoiser operates in an FNE-compatible regime on the considered validation data. GSDSplit+ also yields stable reconstructions outside the empirically supported range and shows substantially lower sensitivity to the ADMM parameter, while remaining effective for different blur operators and Poisson noise levels.

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arXiv2025

Plug and Play Splitting Techniques for Poisson Image Restoration

Plug and Play (PnP) methods achieve remarkable results in the framework of image restoration problems for Gaussian data. Nonetheless, the theory available for the Gaussian case cannot be extended to the Poisson case, due to the non-Lipschitz gradient of the fidelity function, the Kullback-Leibler functional, or the absence of closed-form solution for the proximal operator of such term, leading to employ iterative solvers for the inner subproblem. In this work we extend the idea of PIDSplit+ algorithm, exploiting the Alternating Direction Method of Multipliers, to PnP scheme: this allows to provide a closed form solution for the deblurring step, with no need for iterative solvers. The convergence of the method is assured by employing a firmly non expansive denoiser. The proposed method, namely PnPSplit+, is tested on different Poisson image restoration problems, showing remarkable performance even in presence of high noise level and severe blurring conditions.

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arXiv2025

RELD: Regularization by Latent Diffusion Models for Image Restoration

In recent years, Diffusion Models have become the new state-of-the-art in deep generative modeling, ending the long-time dominance of Generative Adversarial Networks. Inspired by the Regularization by Denoising principle, we introduce an approach that integrates a Latent Diffusion Model, trained for the denoising task, into a variational framework using Half-Quadratic Splitting, exploiting its regularization properties. This approach, under appropriate conditions that can be easily met in various imaging applications, allows for reduced computational cost while achieving high-quality results. The proposed strategy, called Regularization by Latent Denoising (RELD), is then tested on a dataset of natural images, for image denoising, deblurring, and super-resolution tasks. The numerical experiments show that RELD is competitive with other state-of-the-art methods, particularly achieving remarkable results when evaluated using perceptual quality metrics.

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arXiv2024

Unveiling Transformer Perception by Exploring Input Manifolds

This paper introduces a general method for the exploration of equivalence classes in the input space of Transformer models. The proposed approach is based on sound mathematical theory which describes the internal layers of a Transformer architecture as sequential deformations of the input manifold. Using eigendecomposition of the pullback of the distance metric defined on the output space through the Jacobian of the model, we are able to reconstruct equivalence classes in the input space and navigate across them. Our method enables two complementary exploration procedures: the first retrieves input instances that produce the same class probability distribution as the original instance-thus identifying elements within the same equivalence class-while the second discovers instances that yield a different class probability distribution, effectively navigating toward distinct equivalence classes. Finally, we demonstrate how the retrieved instances can be meaningfully interpreted by projecting their embeddings back into a human-readable format.

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arXiv2024

A singular Riemannian Geometry Approach to Deep Neural Networks III. Piecewise Differentiable Layers and Random Walks on $n$-dimensional Classes

Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to study how and why these model reach their outputs. A common approach is to consider the data in an Euclidean settings: recent years has witnessed instead a shift from this paradigm, moving thus to more general framework, namely Riemannian Geometry. Two recent works introduced a geometric framework to study neural networks making use of singular Riemannian metrics. In this paper we extend these results to convolutional, residual and recursive neural networks, studying also the case of non-differentiable activation functions, such as ReLU. We illustrate our findings with some numerical experiments on classification of images and thermodynamic problems.

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arXiv2024

A Modular Deep Learning-based Approach for Diffuse Optical Tomography Reconstruction

Medical imaging is nowadays a pillar in diagnostics and therapeutic follow-up. Current research tries to integrate established - but ionizing - tomographic techniques with technologies offering reduced radiation exposure. Diffuse Optical Tomography (DOT) uses non-ionizing light in the Near-Infrared (NIR) window to reconstruct optical coefficients in living beings, providing functional indications about the composition of the investigated organ/tissue. Due to predominant light scattering at NIR wavelengths, DOT reconstruction is, however, a severely ill-conditioned inverse problem. Conventional reconstruction approaches show severe weaknesses when dealing also with mildly complex cases and/or are computationally very intensive. In this work we explore deep learning techniques for DOT inversion. Namely, we propose a fully data-driven approach based on a modularity concept: first data and originating signal are separately processed via autoencoders, then the corresponding low-dimensional latent spaces are connected via a bridging network which acts at the same time as a learned regularizer.

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arXiv2024

Constrained Regularization by Denoising with Automatic Parameter Selection

Regularization by Denoising (RED) is a well-known method for solving image restoration problems by using learned image denoisers as priors. Since the regularization parameter in the traditional RED does not have any physical interpretation, it does not provide an approach for automatic parameter selection. This letter addresses this issue by introducing the Constrained Regularization by Denoising (CRED) method that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements. The solution to the constrained problem is solved by designing an efficient method based on alternating direction method of multipliers (ADMM). Our experiments show that CRED outperforms the competing methods in terms of stability and robustness, while also achieving competitive performances in terms of image quality.

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arXiv2023

Majorization-Minimization for sparse SVMs

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular approaches in the machine learning arena. In this work, we investigate the training of SVMs through a smooth sparse-promoting-regularized squared hinge loss minimization. This choice paves the way to the application of quick training methods built on majorization-minimization approaches, benefiting from the Lipschitz differentiabililty of the loss function. Moreover, the proposed approach allows us to handle sparsity-preserving regularizers promoting the selection of the most significant features, so enhancing the performance. Numerical tests and comparisons conducted on three different datasets demonstrate the good performance of the proposed methodology in terms of qualitative metrics (accuracy, precision, recall, and F 1 score) as well as computational cost.

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arXiv2022

A singular Riemannian geometry approach to Deep Neural Networks II. Reconstruction of 1-D equivalence classes

In a previous work, we proposed a geometric framework to study a deep neural network, seen as sequence of maps between manifolds, employing singular Riemannian geometry. In this paper, we present an application of this framework, proposing a way to build the class of equivalence of an input point: such class is defined as the set of the points on the input manifold mapped to the same output by the neural network. In other words, we build the preimage of a point in the output manifold in the input space. In particular. we focus for simplicity on the case of neural networks maps from n-dimensional real spaces to (n - 1)-dimensional real spaces, we propose an algorithm allowing to build the set of points lying on the same class of equivalence. This approach leads to two main applications: the generation of new synthetic data and it may provides some insights on how a classifier can be confused by small perturbation on the input data (e.g. a penguin image classified as an image containing a chihuahua). In addition, for neural networks from 2D to 1D real spaces, we also discuss how to find the preimages of closed intervals of the real line. We also present some numerical experiments with several neural networks trained to perform non-linear regression tasks, including the case of a binary classifier.

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arXiv2022

A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations

Deep Neural Networks are widely used for solving complex problems in several scientific areas, such as speech recognition, machine translation, image analysis. The strategies employed to investigate their theoretical properties mainly rely on Euclidean geometry, but in the last years new approaches based on Riemannian geometry have been developed. Motivated by some open problems, we study a particular sequence of maps between manifolds, with the last manifold of the sequence equipped with a Riemannian metric. We investigate the structures induced trough pullbacks on the other manifolds of the sequence and on some related quotients. In particular, we show that the pullbacks of the final Riemannian metric to any manifolds of the sequence is a degenerate Riemannian metric inducing a structure of pseudometric space, we show that the Kolmogorov quotient of this pseudometric space yields a smooth manifold, which is the base space of a particular vertical bundle. We investigate the theoretical properties of the maps of such sequence, eventually we focus on the case of maps between manifolds implementing neural networks of practical interest and we present some applications of the geometric framework we introduced in the first part of the paper.

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arXiv2022

A Learned-SVD approach for Regularization in Diffuse Optical Tomography

Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT reconstruction implies the solution of a severely ill-posed inverse problem, for which regularization techniques are mandatory in order to achieve reasonable results. Traditionally, regularization techniques put a variance prior on the desired solution/gradient via regularization parameters, whose choice requires a fine tuning, specific for each case. In this work we explore deep learning techniques in a fully data-driven approach, able of reconstructing the generating signal (optical absorption coefficient) in an automated way. We base our approach on the so-called Learned Singular Value Decomposition, which has been proposed for general inverse problems, and we tailor it to the DOT application. We perform tests with increasing levels of noise on the measure, and compare it with standard variational approaches.

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arXiv2022

Binary interaction methods for high dimensional global optimization and machine learning

In this work we introduce a new class of gradient-free global optimization methods based on a binary interaction dynamics governed by a Boltzmann type equation. In each interaction the particles act taking into account both the best microscopic binary position and the best macroscopic collective position. In the mean-field limit we show that the resulting Fokker-Planck partial differential equations generalize the current class of consensus based optimization (CBO) methods. For the latter methods, convergence to the global minimizer can be shown for a large class of functions. Algorithmic implementations inspired by the well-known direct simulation Monte Carlo methods in kinetic theory are derived and discussed. Several examples on prototype test functions for global optimization are reported including applications to machine learning.

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arXiv2021

Unsupervised deep learning techniques for powdery mildew recognition based on multispectral imaging

Objectives. Sustainable management of plant diseases is an open challenge which has relevant economic and environmental impact. Optimal strategies rely on human expertise for field scouting under favourable conditions to assess the current presence and extent of disease symptoms. This labor-intensive task is complicated by the large field area to be scouted, combined with the millimeter-scale size of the early symptoms to be detected. In view of this, image-based detection of early disease symptoms is an attractive approach to automate this process, enabling a potential high throughput monitoring at sustainable costs. Methods. Deep learning has been successfully applied in various domains to obtain an automatic selection of the relevant image features by learning filters via a training procedure. Deep learning has recently entered also the domain of plant disease detection: following this idea, in this work we present a deep learning approach to automatically recognize powdery mildew on cucumber leaves. We focus on unsupervised deep learning techniques applied to multispectral imaging data and we propose the use of autoencoder architectures to investigate two strategies for disease detection: i) clusterization of features in a compressed space; ii) anomaly detection. Results. The two proposed approaches have been assessed by quantitative indices. The clusterization approach is not fully capable by itself to provide accurate predictions but it does cater relevant information. Anomaly detection has instead a significant potential of resolution which could be further exploited as a prior for supervised architectures with a very limited number of labeled samples.

cs.CV↗

arXiv2021

A Deep Learning Generative Model Approach for Image Synthesis of Plant Leaves

Objectives. We generate via advanced Deep Learning (DL) techniques artificial leaf images in an automatized way. We aim to dispose of a source of training samples for AI applications for modern crop management. Such applications require large amounts of data and, while leaf images are not truly scarce, image collection and annotation remains a very time--consuming process. Data scarcity can be addressed by augmentation techniques consisting in simple transformations of samples belonging to a small dataset, but the richness of the augmented data is limited: this motivates the search for alternative approaches. Methods. Pursuing an approach based on DL generative models, we propose a Leaf-to-Leaf Translation (L2L) procedure structured in two steps: first, a residual variational autoencoder architecture generates synthetic leaf skeletons (leaf profile and veins) starting from companions binarized skeletons of real images. In a second step, we perform translation via a Pix2pix framework, which uses conditional generator adversarial networks to reproduce the colorization of leaf blades, preserving the shape and the venation pattern. Results. The L2L procedure generates synthetic images of leaves with a realistic appearance. We address the performance measurement both in a qualitative and a quantitative way; for this latter evaluation, we employ a DL anomaly detection strategy which quantifies the degree of anomaly of synthetic leaves with respect to real samples. Conclusions. Generative DL approaches have the potential to be a new paradigm to provide low-cost meaningful synthetic samples for computer-aided applications. The present L2L approach represents a step towards this goal, being able to generate synthetic samples with a relevant qualitative and quantitative resemblance to real leaves.

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arXiv2014

Scaling techniques for $\epsilon$-subgradient projection methods

The recent literature on first order methods for smooth optimization shows that significant improvements on the practical convergence behaviour can be achieved with variable stepsize and scaling for the gradient, making this class of algorithms attractive for a variety of relevant applications. In this paper we introduce a variable metric in the context of the $\epsilon$-subgradient projection methods for nonsmooth, constrained, convex problems, in combination with two different stepsize selection strategies. We develop the theoretical convergence analysis of the proposed approach and we also discuss practical implementation issues, as the choice of the scaling matrix. In order to illustrate the effectiveness of the method, we consider a specific problem in the image restoration framework and we numerically evaluate the effects of a variable scaling and of the steplength selection strategy on the convergence behaviour.

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