Damir Seršić

Tin Vlašić, Tomislav Matulić, Damir Seršić

Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET imaging, both iterative and deep learning, return a single estimate without quantifying the associated uncertainty. Due to ill-posedness and noise, a single solution can be misleading or inaccurate. Thus, providing a measure of uncertainty in PET image reconstruction can help medical practitioners in making critical decisions. This paper proposes a deep learning-based method for uncertainty quantification in PET image reconstruction via posterior sampling. The method is based on training a conditional generative adversarial network whose generator approximates sampling from the posterior in Bayesian inversion. The generator is conditioned on reconstruction from a low-dose PET scan obtained by a conventional reconstruction method and a high-quality magnetic resonance image and learned to estimate a corresponding standard-dose PET scan reconstruction. We show that the proposed model generates high-quality posterior samples and yields physically-meaningful uncertainty estimates.

Tomislav Matulić, Damir Seršić

In this paper, we provide a precise mathematical model of crystal-to-crystal response which is used to generate the white image - a necessary compensation model needed to overcome the physical limitations of the PET scanner. We present a closed-form solution, as well as several accurate approximations, due to the complexity of the exact mathematical expressions. We prove, experimentally and analytically, that the difference between the best approximations and real crystal-to-crystal response is insignificant. The obtained responses are used to generate the white image compensation model. It can be written as a single closed-form expression making it easy to implement in known reconstruction methods. The maximum likelihood expectation maximization (MLEM) algorithm is modified and our white image model is integrated into it. The modified MLEM algorithm is not based on the system matrix, rather it is based on ray-driven projections and back-projections. The compensation model provides all necessary information about the system. Finally, we check our approach on synthetic and real data. For the real-world acquisition, we use the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed approach overperforms competitive, non-compensated reconstruction methods.

Ivica Kopriva, Damir Sersic

Subspace clustering (SC) algorithms utilize the union of subspaces model to cluster data points according to the subspaces from which they are drawn. To better address separability of subspaces and robustness to noise we propose a wavelet packet (WP) based transform domain subspace clustering. Depending on the number of resolution levels, WP yields several representations instantiated in terms of subbands. The first approach combines original and subband data into one complementary multi-view representation. Afterward, we formulate joint representation learning as a low-rank MERA tensor network approximation problem. That is motivated by the strong representation power of the MERA network to capture complex intra/inter-view dependencies in corresponding self-representation tensor. In the second approach, we use a self-stopping computationally efficient method to select the subband with the smallest clustering error on the validation set. When existing SC algorithms are applied to the chosen subband, their performance is expected to improve. Consequently, both approaches enable the re-use of SC algorithms developed so far. Improved clustering performance is due to the dual nature of subbands as representations and filters, which is essential for noise suppression. We exemplify the proposed WP domain approach to SC on the MERA tensor network and eight other well-known linear SC algorithms using six well-known image datasets representing faces, digits, and objects. Although WP domain-based SC is a linear method, it achieved clustering performance comparable with some best deep SC algorithms and outperformed many other deep SC algorithms by a significant margin. That is in particular case for the WP MERA SC algorithm. On the COIL100 dataset, it achieves an accuracy of 87.45% and outperforms the best deep SC competitor in the amount of 14.75%.