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Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…

The Steered Mixture of Experts regression framework has demonstrated strong performance in image reconstruction, compression, denoising, and super-resolution. However, its high computational cost limits practical applications. This work…

Mutual information is a measure of the dependence between random variables that has been used successfully in myriad applications in many fields. Generalized mutual information measures that go beyond classical Shannon mutual information…

Laser absorption spectroscopy (LAS) is a well-established technique for non-intrusive measurement of gas species in combustion and atmospheric environments, but conventional methods struggle with multi-species mixtures under dynamic or…

This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary.…

Multilook coherent imaging is a widely used technique in applications such as digital holography, ultrasound imaging, and synthetic aperture radar. A central challenge in these systems is the presence of multiplicative noise, commonly known…

Embeddings in machine learning are low-dimensional representations of complex input patterns, with the property that simple geometric operations like Euclidean distances and dot products can be used for classification and comparison tasks.…

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among…

Sparse data approximation has become a popular research topic in signal processing. However, in most cases only a single measurement vector (SMV) is considered. In applications, the multiple measurement vector (MMV) case is more usual,…

Recovering 3D information from scenes via multi-view stereo reconstruction (MVS) and novel view synthesis (NVS) is inherently challenging, particularly in scenarios involving sparse-view setups. The advent of 3D Gaussian Splatting (3DGS)…

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…

This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…

Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…

Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models…

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…

The use of Gaussian processes (GPs) is a common approach to account for correlated noise in exoplanet time series, particularly for transmission and emission spectroscopy. This analysis has typically been performed for each wavelength…

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…

Speckle patterns in ultrasound images often obscure anatomical details, leading to diagnostic uncertainty. Recently, various deep learning (DL)-based techniques have been introduced to effectively suppress speckle; however, their high…

This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…