Tin Vlašić

Tin Vlašić, Hieu Nguyen, AmirEhsan Khorashadizadeh et al.

Implicit representation of shapes as level sets of multilayer perceptrons has recently flourished in different shape analysis, compression, and reconstruction tasks. In this paper, we introduce an implicit neural representation-based framework for solving the inverse obstacle scattering problem in a mesh-free fashion. We express the obstacle shape as the zero-level set of a signed distance function which is implicitly determined by network parameters. To solve the direct scattering problem, we implement the implicit boundary integral method. It uses projections of the grid points in the tubular neighborhood onto the boundary to compute the PDE solution directly in the level-set framework. The proposed implicit representation conveniently handles the shape perturbation in the optimization process. To update the shape, we use PyTorch's automatic differentiation to backpropagate the loss function w.r.t. the network parameters, allowing us to avoid complex and error-prone manual derivation of the shape derivative. Additionally, we propose a deep generative model of implicit neural shape representations that can fit into the framework. The deep generative model effectively regularizes the inverse obstacle scattering problem, making it more tractable and robust, while yielding high-quality reconstruction results even in noise-corrupted setups.

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.

AmirEhsan Khorashadizadeh, Ali Aghababaei, Tin Vlašić et al.

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and noise can make this single estimate inaccurate or misleading. While deep networks such as conditional normalizing flows can be used to sample posteriors in inverse problems, they often yield low-quality samples and uncertainty estimates. In this paper, we propose U-Flow, a Bayesian U-Net based on conditional normalizing flows, which generates high-quality posterior samples and estimates physically-meaningful uncertainty. We show that the proposed model significantly outperforms the recent normalizing flows in terms of posterior sample quality while having comparable performance with the U-Net in point estimation.

Rafael Josip Penić, Tin Vlašić, Roland G. Huber et al.

While RNA has recently been recognized as an interesting small-molecule drug target, many challenges remain to be addressed before we take full advantage of it. This emphasizes the necessity to improve our understanding of its structures and functions. Over the years, sequencing technologies have produced an enormous amount of unlabeled RNA data, which hides a huge potential. Motivated by the successes of protein language models, we introduce RiboNucleic Acid Language Model (RiNALMo) to unveil the hidden code of RNA. RiNALMo is the largest RNA language model to date, with 650M parameters pre-trained on 36M non-coding RNA sequences from several databases. It can extract hidden knowledge and capture the underlying structure information implicitly embedded within the RNA sequences. RiNALMo achieves state-of-the-art results on several downstream tasks. Notably, we show that its generalization capabilities overcome the inability of other deep learning methods for secondary structure prediction to generalize on unseen RNA families.