Mathematical and learning based image processing and analysis techniques have gained increasing popularity nowadays. Because of its wide applications in medical imaging, astronomy, astrophysics, surveillance, image compression, and transmission. In many photon-limited imaging systems, acquired data is usually corrupted by Poisson noise. Unlike Gaussian noise commonly considered due to easy implementation, Poisson noise depends on image intensity, making image restoration very challenging. In addition, blurring is inevitable, as the data recorded by a digital device is an average over neighboring pixels, leading to a blurred image. The blurring process can be modeled as a convolution of an underlying image with a point spread function (PSF). We consider both non-blind and blind image deblurring models, in which blind refers to the case of an unknown PSF. Finally, we extend our work to a CT and MRI reconstruction problem. In the pursuit of high-order smoothness of a restored image, we incorporate the fractional-order total variation (FOTV) to deal with various image restoration problems. We adopt the alternating direction method of multipliers (ADMM) with guaranteed convergence to efficiently solve the proposed models. A bridge between mathematical models and Deep learning framework will also be discussed. A variety of numerical experiments demonstrate that the proposed algorithms can efficiently recover piecewise-smooth images over the state-of-the art in image denoising, deblurring, MRI, and CT reconstruction.
BIO: Mujib Chowdhury received his Ph.D. in Mathematics from the University of Texas at Dallas in 2020. He also received an M.S. degree in Mathematics, an M.S. degree in Data Science (with Mathematics) from Lamar University and UT Dallas in 2015 and 2019. He is currently working as a Visiting Assistant Professor at Oregon State University (OSU). Before joining OSU, he was a Postdoctoral Research Fellow at UT Dallas. He also worked at Northern University of Bangladesh and Southern Methodist University as a Lecturer. His research interests are mathematical image processing, medical imaging, and machine learning. His current research focused on image denoising, deconvolution, MRI, and CT reconstruction.