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Audio-visual source localization is a challenging task that aims to predict the location of visual sound sources in a video. Since collecting ground-truth annotations of sounding objects can be costly, a plethora of weakly-supervised…

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…

The general problem of characterizing gas source parameters based on concentration measurements is known to be a difficult task. As many inverse problems, one of the main obstacles for accurate estimation is the non-uniqueness of solution,…

In this paper we generalise the results proved in [N. Katzourakis, An $L^\infty$ regularisation strategy to the inverse source identification problem for elliptic equations, SIAM J. Math. Anal. 51:2, 1349-1370 (2019)] by studying the…

The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…

Electroencephalography (EEG) serves as an effective diagnostic tool for mental disorders and neurological abnormalities. Enhanced analysis and classification of EEG signals can help improve detection performance. A new approach is examined…

Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

The electroencephalography classifier is the most important component of brain-computer interface based systems. There are two major problems hindering the improvement of it. First, traditional methods do not fully exploit multimodal…

Electroencephalography (EEG) plays a significant role in the Brain Computer Interface (BCI) domain, due to its non-invasive nature, low cost, and ease of use, making it a highly desirable option for widespread adoption by the general…

This paper proposes a practical approach to addressing limitations posed by use of single active electrodes in applications for sleep stage classification. Electroencephalography (EEG)-based characterizations of sleep stage progression…

This paper presents a new acoustic emission (AE) source localization for isotropic plates with reflecting boundaries. This approach that has no blind spot leverages multimodal edge reflections to identify AE sources with only a single…

Visual sound source localization is a fundamental perception task that aims to detect the location of sounding sources in a video given its audio. Despite recent progress, we identify two shortcomings in current methods: 1) most approaches…

Inferring patterns of synchronous brain activity from a heterogeneous sample of electroencephalograms (EEG) is scientifically and methodologically challenging. While it is intuitively and statistically appealing to rely on readings from…

The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smooth \ell_1/\ell_2 regularization term. As the mean…

Electroencephalography (EEG)-based P300 brain-computer interfaces (BCIs) enable communication without physical movement by detecting stimulus-evoked neural responses. Accurate and efficient decoding remains challenging due to high…

We propose an algorithm targeting the identification of more sources than channels for electroencephalography (EEG). Our overcomplete source identification algorithm, Cov-DL, leverages dictionary learning methods applied in the…

The symmetric formulation of the electroencephalography (EEG) forward problem is a well-known and widespread equation thanks to the high level of accuracy that it delivers. However, this equation is first kind in nature and gives rise to…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for…