Modeling sparse connectivity between underlying brain sources for EEG/MEG

We propose a novel technique to assess functional brain connectivity in EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: (a) the EEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model, (b) the demixing is estimated jointly with the source MVAR parameters, (c) overfitting is avoided by using the Group Lasso penalty. This approach allows to extract the appropriate level cross-talk between the extracted sources and in this manner we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data, and compare to a number of existing algorithms with excellent results.Comment: 9 pages, 6 figure

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Comparison of super-resolution algorithms applied to retinal images

A critical challenge in biomedical imaging is to optimally balance the trade-off among image resolution, signal-to-noise ratio, and acquisition time. Acquiring a high-resolution image is possible; however, it is either expensive or time consuming or both. Resolution is also limited by the physical properties of the imaging device, such as the nature and size of the input source radiation and the optics of the device. Super-resolution (SR), which is an off-line approach for improving the resolution of an image, is free of these trade-offs. Several methodologies, such as interpolation, frequency domain, regularization, and learning-based approaches, have been developed over the past several years for SR of natural images. We review some of these methods and demonstrate the positive impact expected from SR of retinal images and investigate the performance of various SR techniques. We use a fundus image as an example for simulations