arXiv subjects

Elena Loli Piccolomini

Publications and source records attributed to Elena Loli Piccolomini.

At least 19 recordsLinked to original sources

arXiv2026

Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures

Solving severely ill-posed imaging inverse problems requires recovering image structures that are unobservable or weakly constrained by the measurements. Diffusion models provide expressive learned priors for inferring such missing information, while posterior sampling incorporates measurement consistency along the reverse process. Standard diffusion posterior samplers, however, rely on instantaneous measurement-aware estimates, without explicitly exploiting information carried by previous posterior corrections. We introduce Consecutive Posterior Fusion Denoising Diffusion Null-Space Models (CPF-DDNM), an inference-time strategy that fuses consecutive measurement-aware estimates to improve the diffusive recovery of unobservable image structures, without requiring retraining or additional denoiser evaluations. We instantiate this principle within DDNM, whose range/null-space decomposition reveals that consecutive fusion preserves the measurement-determined component while acting exclusively on the prior-driven null-space estimate. We thus provide a geometric interpretation of CPF-DDNM and a local error analysis that characterizes the optimal time-dependent fusion coefficient, including the extrapolative regime. Experiments on sparse-view and simulated low-dose computed tomography, as well as medical image super-resolution, show consistent improvements over DDNM and competitive performance against diffusion-based inverse solvers.

cs.CV↗

arXiv2026

D-Score: A Spectral Hidden-State Signal for Hallucination Detection in Large Language Models

Large Language Models can produce fluent text that is false, unsupported by the available evidence, or inconsistent with information that appears to be internally represented by the model. We study hallucination detection from the geometry of hidden activations and introduce the D-Score, a simple spectral statistic computed from a single forward pass. For a fixed model, layer, and tolerance parameter, the D-Score counts how many singular directions of the hidden activation matrix have singular values that remain close to the leading one. We use this quantity as a hallucination score, classifying an input text as hallucinated when its D-Score is larger than a pre-defined quantity. The motivation is that, when a model processes a text that conflicts with information available in its own internal state, the hidden representation may encode both the asserted content and some form of counter-evidence, uncertainty, correction, or lack of support; this can make the hidden trajectory spread across additional singular directions. We formalize this intuition through a lightweight spectral argument and evaluate the resulting detector on FAVA-Annotation and RAGTruth. The experiments indicate that the D-Score is a strong hidden-state signal for hallucination detection, while requiring no external verifier, no retrieval step, and no multiple generations.

cs.CL↗

arXiv2026

CLeAN: Continual Learning Adaptive Normalization in Dynamic Environments

Artificial intelligence systems predominantly rely on static data distributions, making them ineffective in dynamic real-world environments, such as cybersecurity, autonomous transportation, or finance, where data shifts frequently. Continual learning offers a potential solution by enabling models to learn from sequential data while retaining prior knowledge. However, a critical and underexplored issue in this domain is data normalization. Conventional normalization methods, such as min-max scaling, presuppose access to the entire dataset, which is incongruent with the sequential nature of continual learning. In this paper we introduce Continual Learning Adaptive Normalization (CLeAN), a novel adaptive normalization technique designed for continual learning in tabular data. CLeAN involves the estimation of global feature scales using learnable parameters that are updated via an Exponential Moving Average (EMA) module, enabling the model to adapt to evolving data distributions. Through comprehensive evaluations on two datasets and various continual learning strategies, including Resevoir Experience Replay, A-GEM, and EwC we demonstrate that CLeAN not only improves model performance on new data but also mitigates catastrophic forgetting. The findings underscore the importance of adaptive normalization in enhancing the stability and effectiveness of tabular data, offering a novel perspective on the use of normalization to preserve knowledge in dynamic learning environments.

cs.LG↗

arXiv2026

A Diffusion-Based Generative Prior Approach to Sparse-view Computed Tomography

The reconstruction of X-rays CT images from sparse or limited-angle geometries is a highly challenging task. The lack of data typically results in artifacts in the reconstructed image and may even lead to object distortions. For this reason, the use of deep generative models in this context has great interest and potential success. In the Deep Generative Prior (DGP) framework, the use of diffusion-based generative models is combined with an iterative optimization algorithm for the reconstruction of CT images from sinograms acquired under sparse geometries, to maintain the explainability of a model-based approach while introducing the generative power of a neural network. There are therefore several aspects that can be further investigated within these frameworks to improve reconstruction quality, such as image generation, the model, and the iterative algorithm used to solve the minimization problem, for which we propose modifications with respect to existing approaches. The results obtained even under highly sparse geometries are very promising, although further research is clearly needed in this direction.

cs.CV↗

arXiv2025

Frugality in second-order optimization: floating-point approximations for Newton's method

Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can deliver greater accuracy and faster convergence, yet are often avoided due to their computational cost. This work analyzes the impact of finite-precision arithmetic on Newton steps and establishes a convergence theorem for mixed-precision Newton optimizers, including "quasi" and "inexact" variants. The theorem provides not only convergence guarantees but also a priori estimates of the achievable solution accuracy. Empirical evaluations on standard regression benchmarks demonstrate that the proposed methods outperform Adam on the Australian and MUSH datasets. The second part of the manuscript introduces GN_k, a generalized Gauss-Newton method that enables partial computation of second-order derivatives. GN_k attains performance comparable to full Newton's method on regression tasks while requiring significantly fewer derivative evaluations.

cs.LG↗

arXiv2025

Blind Restoration of High-Resolution Ultrasound Video

Ultrasound imaging is widely applied in clinical practice, yet ultrasound videos often suffer from low signal-to-noise ratios (SNR) and limited resolutions, posing challenges for diagnosis and analysis. Variations in equipment and acquisition settings can further exacerbate differences in data distribution and noise levels, reducing the generalizability of pre-trained models. This work presents a self-supervised ultrasound video super-resolution algorithm called Deep Ultrasound Prior (DUP). DUP employs a video-adaptive optimization process of a neural network that enhances the resolution of given ultrasound videos without requiring paired training data while simultaneously removing noise. Quantitative and visual evaluations demonstrate that DUP outperforms existing super-resolution algorithms, leading to substantial improvements for downstream applications.

cs.CV↗

arXiv2025

Adaptive Weighted Total Variation boosted by learning techniques in few-view tomographic imaging

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate approximation of the true image (or its gradient magnitude) through a neural network. Our approach operates without requiring prior knowledge of the noise intensity in the data and avoids the iterative recomputation of weights. Additionally, the paper includes a theoretical analysis of the proposed method, establishing its validity as a regularization approach. This framework integrates advanced neural network capabilities within a regularization context, thereby making the results of the networks interpretable. The results are promising as they enable high-quality reconstructions from limited-view tomographic measurements.

math.NA↗

arXiv2024

Deep Guess acceleration for explainable image reconstruction in sparse-view CT

Sparse-view Computed Tomography (CT) is an emerging protocol designed to reduce X-ray dose radiation in medical imaging. Traditional Filtered Back Projection algorithm reconstructions suffer from severe artifacts due to sparse data. In contrast, Model-Based Iterative Reconstruction (MBIR) algorithms, though better at mitigating noise through regularization, are too computationally costly for clinical use. This paper introduces a novel technique, denoted as the Deep Guess acceleration scheme, using a trained neural network both to quicken the regularized MBIR and to enhance the reconstruction accuracy. We integrate state-of-the-art deep learning tools to initialize a clever starting guess for a proximal algorithm solving a non-convex model and thus computing an interpretable solution image in a few iterations. Experimental results on real CT images demonstrate the Deep Guess effectiveness in (very) sparse tomographic protocols, where it overcomes its mere variational counterpart and many data-driven approaches at the state of the art. We also consider a ground truth-free implementation and test the robustness of the proposed framework to noise.

math.NA↗

arXiv2024

A data-dependent regularization method based on the graph Laplacian

We investigate a variational method for ill-posed problems, named $\texttt{graphLa+}Ψ$, which embeds a graph Laplacian operator in the regularization term. The novelty of this method lies in constructing the graph Laplacian based on a preliminary approximation of the solution, which is obtained using any existing reconstruction method $Ψ$ from the literature. As a result, the regularization term is both dependent on and adaptive to the observed data and noise. We demonstrate that $\texttt{graphLa+}Ψ$ is a regularization method and rigorously establish both its convergence and stability properties. We present selected numerical experiments in 2D computerized tomography, wherein we integrate the $\texttt{graphLa+}Ψ$ method with various reconstruction techniques $Ψ$, including Filter Back Projection ($\texttt{graphLa+FBP}$), standard Tikhonov ($\texttt{graphLa+Tik}$), Total Variation ($\texttt{graphLa+TV}$), and a trained deep neural network ($\texttt{graphLa+Net}$). The $\texttt{graphLa+}Ψ$ approach significantly enhances the quality of the approximated solutions for each method $Ψ$. Notably, $\texttt{graphLa+Net}$ is outperforming, offering a robust and stable application of deep neural networks in solving inverse problems.

math.NA↗

arXiv2024

Space-Variant Total Variation boosted by learning techniques in few-view tomographic imaging

This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary objective of the proposed optimization model is to achieve a good balance between denoising and the preservation of fine details and edges, overcoming the performance of the popular and largely used Total Variation (TV) regularization through the application of appropriate pixel-dependent weights. The proposed strategy leverages the role of gradient approximations for the computation of the space-variant TV weights. For this reason, a convolutional neural network is designed, to approximate both the ground truth image and its gradient using an elastic loss function in its training. Additionally, the paper provides a theoretical analysis of the proposed model, showing the uniqueness of its solution, and illustrates a Chambolle-Pock algorithm tailored to address the specific problem at hand. This comprehensive framework integrates innovative regularization techniques with advanced neural network capabilities, demonstrating promising results in achieving high-quality reconstructions from low-sampled tomographic data.

eess.IV↗

arXiv2024

To be or not to be stable, that is the question: understanding neural networks for inverse problems

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based on deep learning overwhelm the more traditional model-based approaches in performance, but they typically suffer from instability with respect to data perturbation. In this paper, we theoretically analyze the trade-off between stability and accuracy of neural networks, when used to solve linear imaging inverse problems for not under-determined cases. Moreover, we propose different supervised and unsupervised solutions to increase the network stability and maintain a good accuracy, by means of regularization properties inherited from a model-based iterative scheme during the network training and pre-processing stabilizing operator in the neural networks. Extensive numerical experiments on image deblurring confirm the theoretical results and the effectiveness of the proposed deep learning-based approaches to handle noise on the data.

math.NA↗

arXiv2023

Deep image prior inpainting of ancient frescoes in the Mediterranean Alpine arc

The unprecedented success of image reconstruction approaches based on deep neural networks has revolutionised both the processing and the analysis paradigms in several applied disciplines. In the field of digital humanities, the task of digital reconstruction of ancient frescoes is particularly challenging due to the scarce amount of available training data caused by ageing, wear, tear and retouching over time. To overcome these difficulties, we consider the Deep Image Prior (DIP) inpainting approach which computes appropriate reconstructions by relying on the progressive updating of an untrained convolutional neural network so as to match the reliable piece of information in the image at hand while promoting regularisation elsewhere. In comparison with state-of-the-art approaches (based on variational/PDEs and patch-based methods), DIP-based inpainting reduces artefacts and better adapts to contextual/non-local information, thus providing a valuable and effective tool for art historians. As a case study, we apply such approach to reconstruct missing image contents in a dataset of highly damaged digital images of medieval paintings located into several chapels in the Mediterranean Alpine Arc and provide a detailed description on how visible and invisible (e.g., infrared) information can be integrated for identifying and reconstructing damaged image regions.

cs.CV↗

arXiv2023

Ambiguity in solving imaging inverse problems with deep learning based operators

In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an ill-posed inverse problem and its solution is difficult to approximate when noise affects the data. Really, one limitation of neural networks for deblurring is their sensitivity to noise and other perturbations, which can lead to instability and produce poor reconstructions. In addition, networks do not necessarily take into account the numerical formulation of the underlying imaging problem, when trained end-to-end. In this paper, we propose some strategies to improve stability without losing to much accuracy to deblur images with deep-learning based methods. First, we suggest a very small neural architecture, which reduces the execution time for training, satisfying a green AI need, and does not extremely amplify noise in the computed image. Second, we introduce a unified framework where a pre-processing step balances the lack of stability of the following, neural network-based, step. Two different pre-processors are presented: the former implements a strong parameter-free denoiser, and the latter is a variational model-based regularized formulation of the latent imaging problem. This framework is also formally characterized by mathematical analysis. Numerical experiments are performed to verify the accuracy and stability of the proposed approaches for image deblurring when unknown or not-quantified noise is present; the results confirm that they improve the network stability with respect to noise. In particular, the model-based framework represents the most reliable trade-off between visual precision and robustness.

cs.CV↗

arXiv2022

RISING a new framework for few-view tomographic image reconstruction with deep learning

This paper proposes a new two-step procedure for sparse-view tomographic image reconstruction. It is called RISING, since it combines an early-stopped Rapid Iterative Solver with a subsequent Iteration Network-based Gaining step. So far, regularized iterative methods have widely been used for X-ray computed tomography image reconstruction from low-sampled data, since they converge to a sparse solution in a suitable domain, as upheld by the Compressed Sensing theory. Unfortunately, their use is practically limited by their high computational cost which imposes to perform only a few iterations in the available time for clinical exams. Data-driven methods, using neural networks to post-process a coarse and noisy image obtained from geometrical algorithms, have been recently studied and appreciated for both their computational speed and accurate reconstructions. However, there is no evidence, neither theoretically nor numerically, that neural networks based algorithms solve the mathematical inverse problem modeling the tomographic reconstruction process. In our two-step approach, the first phase executes very few iterations of a regularized model-based algorithm whereas the second step completes the missing iterations by means of a neural network. The resulting hybrid deep-variational framework preserves the convergence properties of the iterative method and, at the same time, it exploits the computational speed and flexibility of a data-driven approach. Experiments performed on a simulated and a real data set confirm the numerical and visual accuracy of the reconstructed RISING images in short computational times.

math.NA↗

arXiv2021

DeepCEL0 for 2D Single Molecule Localization in Fluorescence Microscopy

In fluorescence microscopy, Single Molecule Localization Microscopy (SMLM) techniques aim at localizing with high precision high density fluorescent molecules by stochastically activating and imaging small subsets of blinking emitters. Super Resolution (SR) plays an important role in this field since it allows to go beyond the intrinsic light diffraction limit. In this work, we propose a deep learning-based algorithm for precise molecule localization of high density frames acquired by SMLM techniques whose $\ell_{2}$-based loss function is regularized by positivity and $\ell_{0}$-based constraints. The $\ell_{0}$ is relaxed through its Continuous Exact $\ell_{0}$ (CEL0) counterpart. The arising approach, named DeepCEL0, is parameter-free, more flexible, faster and provides more precise molecule localization maps if compared to the other state-of-the-art methods. We validate our approach on both simulated and real fluorescence microscopy data.

cs.LG↗

arXiv2021

Plug-and-Play gradient-based denoisers applied to CT image enhancement

Blur and noise corrupting Computed Tomography (CT) images can hide or distort small but important details, negatively affecting the diagnosis. In this paper, we present a novel gradient-based Plug-and-Play algorithm, constructed on the Half-Quadratic Splitting scheme, and we apply it to restore CT images. In particular, we consider different schemes encompassing external and internal denoisers as priors, defined on the image gradient domain. The internal prior is based on the Total Variation functional. The external denoiser is implemented by a deep Convolutional Neural Network (CNN) trained on the gradient domain (and not on the image one, as in state-of-the-art works). We also prove a general fixed-point convergence theorem under weak assumptions on both internal and external denoisers. The experiments confirm the effectiveness of the proposed framework in restoring blurred noisy CT images, both in simulated and real medical settings. The achieved enhancements in the restored images are really remarkable, if compared to the results of many state-of-the-art methods.

math.NA↗

arXiv2020

Efficient $\ell^0$ gradient-based Super Resolution for simplified image segmentation

We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic $\ell^0$ regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in [1] for general signal recovery problems. For the numerical realisation of the model, we propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugate-gradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that $\ell^0$ gradient-regularised super-resolved images can be effectively used to improve the accuracy of standard segmentation algorithms when applied to QR and cell detection, and landcover classification problems, in comparison to the results achieved by other approaches.

eess.IV↗

arXiv2020

Recursive Deep Prior Video: a Super Resolution algorithm for Time-Lapse Microscopy of organ-on-chip experiments

Biological experiments based on organ-on-chips (OOCs) exploit light Time-Lapse Microscopy (TLM) for a direct observation of cell movement that is an observable signature of underlying biological processes. A high spatial resolution is essential to capture cell dynamics and interactions from recorded experiments by TLM. Unfortunately, due to physical and cost limitations, acquiring high resolution videos is not always possible. To overcome the problem, we present here a new deep learning-based algorithm that extends the well known Deep Image Prior (DIP) to TLM Video Super Resolution (SR) without requiring any training. The proposed Recursive Deep Prior Video (RDPV) method introduces some novelties. The weights of the DIP network architecture are initialized for each of the frames according to a new recursive updating rule combined with an efficient early stopping criterion. Moreover, the DIP loss function is penalized by two different Total Variation (TV) based terms. The method has been validated on synthetic, i.e., artificially generated, as well as real videos from OOC experiments related to tumor-immune interaction. Achieved results are compared with several state-of-the-art trained deep learning SR algorithms showing outstanding performances.

eess.IV↗