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Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…

Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…

This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…

Sparse coding networks, which utilize unsupervised learning to maximize coding efficiency, have successfully reproduced response properties found in primary visual cortex \cite{AN:OlshausenField96}. However, conventional sparse coding…

Methods exploiting sparsity have been popular in imaging and signal processing applications including compression, denoising, and imaging inverse problems. Data-driven approaches such as dictionary learning and transform learning enable one…

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular…

Optimal control provides a principled framework for transforming dynamical system models into intelligent decision-making, yet classical computational approaches are often too expensive for real-time deployment in dynamic or uncertain…

Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target…

We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…

State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations…

We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…

We develop a novel transfer learning framework to tackle the challenge of limited training data in image reconstruction problems. The proposed framework consists of two training steps, both of which are formed as bi-level optimizations. In…

Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…

In Programming by Demonstration, the robot learns novel skills from human demonstrations. After learning, the robot should be able not only to reproduce the skill, but also to generalize it to shifted domains without collecting new training…

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…

A general framework of unsupervised learning for combinatorial optimization (CO) is to train a neural network (NN) whose output gives a problem solution by directly optimizing the CO objective. Albeit with some advantages over traditional…

Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space…

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…

Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…