Our research activities are primarily focused on the signal processing and machine learning tool development for high-resolution high-sensitivity image reconstruction from real world bio-medical imaging systems. One of the most important and challenging issues in this regard is overcoming the fundamental limitations of resolution and sensitivity with minimal invasiveness. Such problems pose interesting challenges that often lead to investigations of fundamental problems in various branches of physics, mathematics, signal processing, biology, and medicine. While most of the biomedical imaging researchers are interested in addressing this problem using off-the-self tools from signal processing, machine learning, statistics, and optimization and combining their domain-specific knowledge, our approaches to biomedical imaging problems are unique in the sense that we believe that actual bio-medical imaging applications are a source of endless inspiration for new mathematical theories and we are eager to solve both specific applications and application-inspired fundamental theoretical problems. This perspective has provided me with many rewarding experiences and a unique academic status as summarized below:
- Academic Innovations: World-first demonstrations of high resolution compressed sensing dynamic MRI (k-t FOCUSS), self-reference quantitative phase microscopy, sparse dictionary learning for fMRI connectivity analysis, deep learning for low-dose CT reconstruction, and non-iterative exact inverse scattering methods for diffuse optical tomography, electric impedance tomography, and elastic wave imaging; world-first mathematical discoveries of the link between array signal processing and multiple measurement vector problems (Compressive-MUSIC), the link between Bedrosian identity and interior tomography problem, the link between structured matrix completion and the sampling theory of finite rate of innovation (ALOHA), and the link between deep learning and convolutional framelets (Deep Convolutional Framelets); the development of very popular toolboxes for functional near-infrared spectroscopy (NIRS-SPM) and super resolution microscopy (FALCON).
- Broad and In-depth Research Scope: My research covers extensive arrays of medical imaging modalities such as MRI, x-ray CT, PET, ultrasound, optics, and neuro-imaging based on strong physics, biology and mathematical background; I have produced the world-leading results by winning several international challenges and producing high impact papers.
- Truly Interdisciplinary Research: My research spans neuroscience/biology, optics experiments, physics, computational algorithms, and fundamental mathematical theory; I have collaborated extensively with medical doctors, biologists, physicists, mathematicians, and engineers, and supervised the research of bioengineers, electrical engineers, medical doctors, and mathematicians.
- Application-driven Mathematical Theory: Unlike the most mathematicians and signal processors, all my theoretical works are inspired by real-world biomedical imaging applications. Examples: Inverse scattering application-inspired fundamental theory of joint sparse recovery, accelerated MRI-inspired fundamental theory of compressive sampling using low-rank interpolation, and deep learning-inspired deep convolutional framelets theory
- Extensive Technology Transfer: Successful IP licensing of imaging technology to domestic venders