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The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take…
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding…
Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample…
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
The low-rank matrix reconstruction (LRMR) approach is widely used in direction-of-arrival (DOA) estimation. As the rank norm penalty in an LRMR is NP-hard to compute, the nuclear norm (or the trace norm for a positive semidefinite (PSD)…
Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…
This paper proposes a precise signal recovery method with multilayered non-convex regularization, enhancing sparsity/low-rankness for high-dimensional signals including images and videos. In optimization-based signal recovery, multilayered…
In the past five years, the use of generative and foundational AI systems has greatly improved the decoding of brain activity. Visual perception, in particular, can now be decoded from functional Magnetic Resonance Imaging (fMRI) with…
We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural…
Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the signal matrix are…
Decoding EEG signals of different mental states is a challenging task for brain-computer interfaces (BCIs) due to nonstationarity of perceptual decision processes. This paper presents a novel boosted convolutional neural networks (ConvNets)…
In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…
Magnetoencephalographic (MEG) measurements record magnetic fields generated from neurons while information is being processed in the brain. The inverse problem of identifying sources of biomagnetic fields and deducing their intensities from…
Simultaneous EEG-fMRI is a multi-modal neuroimaging technique that provides complementary spatial and temporal resolution. Challenging has been developing principled and interpretable approaches for fusing the modalities, specifically…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…
The problem of reconstructing brain activity from electric potential measurements performed on the surface of a human head is not an easy task: not just because the solution of the related inverse problem is fundamentally ill-posed (not…
Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…
Objective: Sparse Bayesian learning provides an effective scheme to solve the high-dimensional problem in brain signal decoding. However, traditional assumptions regarding data distributions such as Gaussian and binomial are potentially…
Electroencephalography (EEG) often shows significant variability among people. This fluctuation disrupts reliable acquisition and may result in distortion or clipping. Modulo sampling is now a promising solution to this problem, by folding…