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We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
Fredholm integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. They model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear…
Chronic neck pain is a leading cause of disability worldwide, and current treatment selection remains largely trial and error. We present a machine learning framework that uses electroencephalography to predict treatment efficacy in…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
A significant challenge in the electroencephalogram EEG lies in the fact that current data representations involve multiple electrode signals, resulting in data redundancy and dominant lead information. However extensive research conducted…
An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an…
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…
Eye movements can reveal valuable insights into various aspects of human mental processes, physical well-being, and actions. Recently, several datasets have been made available that simultaneously record EEG activity and eye movements. This…
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode…
Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for…
Electroencephalography (EEG) plays a crucial role in the diagnosis of various neurological disorders. However, small hospitals and clinics often lack advanced EEG signal analysis systems and are prone to misinterpretation in manual EEG…
Electrocorticography (ECoG) or intracranial electroencephalography (iEEG) monitors electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery when paired with numerical…
Invasive intracranial electroencephalography (iEEG) or electrocorticography (ECoG) measures electric potential directly on the surface of the brain and can be used to inform treatment planning for epilepsy surgery. Combined with numerical…
This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…
Lensless in-line holography is a simple, portable, and cost-effective method of imaging especially for the biomedical microscopy applications. We propose a multiplicative gradient descent optimization based method to obtain multi-depth…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We recently found that the electromagnetic scattering problem can be very fast in an approach expressing the fields in terms of orthonormal basis functions. In this paper we apply computational conformal geometry with the conformal energy…
Electroencephalography (EEG) is a vital tool to measure and record brain activity in neuroscience and clinical applications, yet its potential is constrained by signal heterogeneity, low signal-to-noise ratios, and limited labeled datasets.…