Using state-of-the-art inverse problem techniques to develop reconstruction methods for fluorescence diffuse optical

An inverse problem is a mathematical framework that is used to obtain info about a physical object or system from observed measurements. It usually appears when we wish to obtain information about internal data from outside measurements and has many applications in science and technology such as medical imaging, geophysical imaging, image deblurring, image inpainting, electromagnetic scattering, acoustics, machine learning, mathematical finance, physics, etc. The main goal of this PhD thesis was to use state-of-the-art inverse problem techniques to develop modern reconstruction methods for solving the fluorescence diffuse optical tomography (fDOT) problem. fDOT is a molecular imaging technique that enables the quantification of tomographic (3D) bio-distributions of fluorescent tracers in small animals. One of the main difficulties in fDOT is that the high absorption and scattering properties of biological tissues lead to an ill-posed inverse problem, yielding multiple nonunique and unstable solutions to the reconstruction problem. Thus, the problem requires regularization to achieve a stable solution. The so called “non-contact fDOT scanners” are based on using CCDs as virtual detectors instead of optic fibers in contact with the sample. These non-contact systems generate huge datasets that lead to computationally demanding inverse problem. Therefore, techniques to minimize the size of the acquired datasets without losing image performance are highly advisable. The first part of this thesis addresses the optimization of experimental setups to reduce the dataset size, by using l₂–based regularization techniques. The second part, based on the success of l₁ regularization techniques for denoising and image reconstruction, is devoted to advanced regularization problem using l₁–based techniques, and the last part introduces compressed sensing (CS) theory, which enables further reduction of the acquired dataset size. The main contributions of this thesis are: 1) A feasibility study (the first one for fDOT to our ...