Optimization models for inverse problems in image processing
Alireza Hosseini - Assistant Professor, University of Tehran
Sun, 18-Apr-2021 / 18:00 / Link:
Video Slides Poster


Inverse problems in image processing involve estimating parameters or data from inadequate observations where observations are often noisy and contain incomplete information about the target parameter or data due to physical limitations of the measurement devices. Consequently, solutions to inverse problems are non-unique.

As an example, we know that if focus is not adjusted properly during the photography or the object is moving, the resulting image may be blurred. This criteria can be formulated mathematically as a blurring operator (linear or nonlinear) that operates on a clean image and turns it into a blurred image. This process is named image blurring and the inverse problem aiming to restore the clean image from a given blurred image is called deblurring.

Various problems in image processing such as denoising, upscaling, deconvolution and MRI restoration problems can be formulated as inverse problems.

In this talk, we introduce some inverse problems in image processing and we also explain how these problems may be formulated as convex optimization problems. Finally, some popular numerical algorithms to solve such problems will be discussed.

Keywords: Inverse problems; Total variation; Optimization; Medical imaging.


Alireza Hosseini received the B.Sc. degree in mathematics from Shiraz University, Shiraz, Iran, in 2003, the M.Sc. degree in applied mathematics from Sharif University of Technology, Tehran, Iran in 2006, and the Ph.D. degree in applied mathematics from Tarbiat Modares University, Tehran, Iran, in 2013.

He was affiliated with the school of Mathematics, Institute for Research in Fundamental Sciences (IPM) as a non-resident researcher during the periods 2014-2016 and 2017-2019.

He is currently an Assistant Professor in the School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Iran.

His current research interests include numerical analysis, mathematical image processing, medical imaging, sparse representation, optimization theory and applications, and artificial neural networks.