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Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
Magnetoencephalography (MEG) scanner has been shown to be more accurate than other medical devices in detecting mild traumatic brain injury (mTBI). However, MEG scan data in certain spectrum ranges can be skewed, multimodal and…
Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with…
We propose a new model for approximating spatiotemporal noise covariance for use in MEG/EEG source analysis. Our model is an extension of an existing model [1,2] that uses a single Kronecker product of a pair of matrices - temporal and…
Localizing the sources of electrical activity in the brain from Electroencephalographic (EEG) data is an important tool for non-invasive study of brain dynamics. Generally, the source localization process involves a high-dimensional inverse…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging,…
In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are…
EDIT: A revised version of this article has been published in the SIAM Journal on Scientific Computing, see https://epubs.siam.org/doi/full/10.1137/23M1582874. In the revised version, the name of the approach was changed from "localized…
The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical…
Non-invasive assessment of the electrical activation pattern can significantly contribute to the diagnosis and treatment of cardiac arrhythmias, due to faster and safer diagnosis, improved surgical planning and easier follow-up. One…
Electroencephalogram (EEG) classification has been widely used in various medical and engineering applications, where it is important for understanding brain function, diagnosing diseases, and assessing mental health conditions. However,…
A brain--machine interface (BMI) based on motor imagery (MI) enables the control of devices using brain signals while the subject imagines performing a movement. It plays a vital role in prosthesis control and motor rehabilitation. To…
The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…
We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matrix…
Electroencephalography (EEG) signals have been promising for long-term braking intensity prediction but are prone to various artifacts that limit their reliability. Here, we propose a novel framework that models EEG signals as mixtures of…
Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available…