The problem of reconstructing biomedical images based on measurements from our acquisition system (microscopy, X-ray tomography, etc) is known as an inverse problem, which is typically formulated and solved as an optimization task. When one has some prior knowledge on the form of image (eg, sparsity in a transform domain or smoothness), one can enforce that the reconstructed image follow this prior by adding a suitable regularization term to the cost function. In this project, we consider a multicomponent image model, where each component follows different priors. More specifically, the first component is assumed to be piecewise-constant and is treated with total-variation regularization; the second is assumed to be smooth and is treated with a Laplacian-based regularizer. The reconstruction is done in the continuous domain by using a spline basis. The reconstruction algorithm will be implemented in Matlab using the GlobalBioIm library [1]. The student should be interested in biomedical imaging, optimization and functional analysis.
References:
[1] Soubies, E., Soulez, F., McCann, M. T., Pham, T. A., Donati, L., Debarre, T., ... & Unser, M. (2019). Pocket guide to solve inverse problems with GlobalBioIm. Inverse Problems, 35(10), 104006.