Math + Data

Research Overview

Imaging Sciences

Variational Methods

Computational Mathematics

Data Science

Other Projects - Applied Mathematics - Imaging/Data Science

Note that these contain prior major research projects in the areas of Applied Mathematics, Image Processing, and Computer Vision 2004 to 2018 i.e. before the start of Prasath Lab @ CCHMC in March 2018. Although we continue to work on these areas the major focus of our lab are now in various Bio + Medical Informatics (BMI) areas.

I. Analysis & PDEs with Image Processing Applications

Nonlinear, anisotropic diffusion partial differential equations (PDEs), Weak/viscosity/dissipative/Young measure solutions, Perona-Malik type diffusion PDEs, variable exponent PDEs, p-Laplacian, p(t,x)-Laplacian, complex diffusion, higher order PDEs, adaptive PDEs and computational methods (finite differences, finite elements) for solving them are major themes. Linear, nonlinear scale space theory and applications - smoothing, denoising, deblurring, super-resolution, fusion, segmentation, decomposition.

Project pages:

II. Variational Methods, Regularization Techniques 

In this direction the primary focus is to regularize ill-posed problems arising in signal processing, image processing, computer vision, and machine learning. Total variation (TV), total generalized variation (TGV), higher order total variation (HOTV), nonlocal TV, L0, L1, and Lp, mixed-norm optimization, elastic net, sparse representation, convex, non-convex regularization, optimization, energy minimization, and corresponding numerical schemes (dual minimization, split Bregman, ADMM, LMM) are major thrust areas.

Project pages:

III. Remote Sensing, Biometrics, Other Image Processing/Computer Vision Problems and Data Science Domains 

Image speckle denoising, segmentation for SAR, PolSAR images. Road network extraction from aerial imagery. Wavelets, Shearlets for image processing. Regression analysis, Robust M-estimators, Discontinuity adaptive smoothing schemes, image filters (global, local, nonlocal, self-similarity) and kernel smoothing. Image and data fusion, multi-focus fusion, multi-sensor fusion, sensor networks. Biometrics - ocular, periocular, fingerprint, iris, retina, face, palm print. Multi-view geometry, shape from X, segmentation, optical flow, mosaicing, blending, registration, point cloud processing, tracking, large scale 3D reconstruction for full motion video (FMV), wide area motion imagery (WAMI), video surveillance, summarization, event detection. DTM/DEM, edge detection, super-resolution, deblocking, decompression, saliency detection, watermarking, steganography, Kinect depth data processing, local binary patterns, registration, video data analysis. Feature analysis, deep learning for image processing and computer vision problems. Sensor networks with emphasize on visual sensors, internet of things (IoT), natural language processing (NLP), text mining, summarization, affective computing, sentiment analysis from text, social media data, emotion recognition from image data. Topological data analysis (TDA) for signals, imaging and biomedical informatics problems.

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Interested in Computational Mathematics?

Check out the opportunists at our lab - see Positions and reach out to us for collaborative projects!