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Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse…

We introduce a novel method, called Dispersion Entropy for Graph Signals, $DE_G$, as a powerful tool for analysing the irregularity of signals defined on graphs. We demonstrate the effectiveness of $DE_G$ in detecting changes in the…

This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…

Semi-Supervised Instance Segmentation (SSIS) aims to leverage an amount of unlabeled data during training. Previous frameworks primarily utilized the RGB information of unlabeled images to generate pseudo-labels. However, such a mechanism…

Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it exhibits sensitivity to the noise in the observed data,…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

The concept of Generalized Inverse based Decoding (GID) is introduced, as an algebraic framework for the syndrome decoding problem (SDP) and low weight codeword problem (LWP). The framework has ground on two characterizations by generalized…

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific…

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…

Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…

We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…

Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…

In recent works, both sparsity-based methods as well as learning-based methods have proven to be successful in solving several challenging linear inverse problems. However, sparsity priors for natural signals and images suffer from poor…

Global Navigation Satellite Systems (GNSS) are vital for reliable urban positioning. However, multipath and non-line-of-sight reception often introduce large measurement errors that degrade accuracy. Learning-based methods for predicting…

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…

We investigate the privacy of {\em any} algorithm whose outputs have Gaussian distribution. This work is motivated by the prevalence of such algorithms in several useful (ML) applications, and the comparatively little research that focuses…

In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…

We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data…