Alessandro Benfenati

Diffuse Optical Tomography (DOT) is a non-invasive medical imaging technique that makes use of Near-Infrared (NIR) light to recover the spatial distribution of optical coefficients in biological tissues for diagnostic purposes. Due to the intense scattering of light within tissues, the reconstruction process inherent to DOT is severely ill-posed. In this paper, we propose to tackle the ill-conditioning by learning a prior over the solution space using an autoencoder-type neural network. Specifically, the decoder part of the autoencoder is used as a generative model. It maps a latent code to estimated physical parameters given in input to the forward model. The latent code is itself the result of an optimization loop which minimizes the discrepancy of the solution computed by the forward model with available observations. The structure and interpretability of the latent space are enhanced by minimizing the rank of its covariance matrix, thereby promoting more effective utilization of its information-carrying capacity. The deep learning-based prior significantly enhances reconstruction capabilities in this challenging domain, demonstrating the potential of integrating advanced neural network techniques into DOT.

The so-called Deep Image Prior approach is an unsupervised deep learning methodology which has gained great interest in recent years due to its effectiveness in tackling imaging problems. However, a well known drawback of Deep Image Prior is the need for a proper early stopping technique to prevent undesired corruptions in the reconstructed images. Determining the optimal number of iterations depends on both the specific application and the features of the images being processed. As a consequence, several numerical trials are typically required to decide when to stop the Deep Image Prior procedure, resulting in significant computational costs and time requirements. This paper aims to introduce two early stopping techniques for Deep Image Prior, based on different approaches and different perspectives. The first approach relies on the neural architecture search (NAS) strategy. The aim is to equip the neural network used in Deep Image Prior with hyperparameter configurations that produce high-quality reconstructed images that are (i) comparable to those obtained with the optimally stopped, originally configured Deep Image Prior, and (ii) achieved with significantly fewer iterations. The second proposed early stopping strategy is based on a modified version of the BRISQUE metric, a no-reference image quality measure, and it aims to track the behaviour of the PSNR curve, obtained by applying Deep Image Prior, without knowing the ground truth image. While the NAS-based early stopping technique is particularly suited in those situations where the computational time is limited, this latter one is also relevant when a larger number of iterations is allowed. Several numerical experiments on different denoising applications show a promising performance of Deep Image Prior combined with the suggested early stopping procedures.

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.

Within the framework of an increasing water scarcity, fostered by the climate change, in this study we investigate the environmental impact associated with current food consumption by means of the Water footprint indicator focusing on the case of Italy. For the analysis of the real food consumption and its impact, we selected the Mediterranean diet as a benchmark, since previous evidence shows that Italians are shifting their dietary habits away from the traditional Mediterranean Diet in favor of dietary patterns rich in animal-based products, especially meat. To promote more sustainable food choices, we applied a Sustainable Diet Model to analyze alternative diets that can reduce the Water footprint associated with food consumption. The results of the analysis show that by adopting slight changes in the consumption of certain categories of foods, it is possible to reduce the Water footprint of diets. The findings of this research are useful for supporting policies for the promotion of sustainable food consumption that would lead to a reduction in the exploitation of a scarce resource such as water, improving the allocation of this resource and achieving the objectives of the 2030 Agenda.

The Plug-and-Play framework has demonstrated that a denoiser can implicitly serve as the image prior for model-based methods for solving various inverse problems such as image restoration tasks. This characteristic enables the integration of the flexibility of model-based methods with the effectiveness of learning-based denoisers. However, the regularization strength induced by denoisers in the traditional Plug-and-Play framework lacks a physical interpretation, necessitating demanding parameter tuning. This paper addresses this issue by introducing the Constrained Plug-and-Play (CPnP) method, which reformulates the traditional PnP as a constrained optimization problem. In this formulation, the regularization parameter directly corresponds to the amount of noise in the measurements. The solution to the constrained problem is obtained through the design of an efficient method based on the Alternating Direction Method of Multipliers (ADMM). Our experiments demonstrate that CPnP outperforms competing methods in terms of stability and robustness while also achieving competitive performance for image quality.