"Task-Adapted Reconstruction in Computed Tomography: Microlocal Analysis meets Deep Learning"Andrade Loarca, HectorMicrolocal analysis plays an important role in tomography, characterizing the transformation of oriented singularities under the Radon transform. The oriented singularities can be described in terms of their location and orientation, also known as the wavefront set. Having the possibility of extracting the wavefront set of a sinogram allows one to compute the singularities of the reconstruction with a low computational cost. In addition, the singularities of an image contain most of the semantic information and are therefore a powerful prior for the reconstruction. Following the idea of task adapted reconstruction proposed by Adler et al., we propose a learned estimator for the tomographic inversion which jointly learns the reconstruction and its wavefront set. In this fashion, we are able to adapt the reconstruction for the task purposes, in this case, wavefront set extraction. In fact, this already represents an important amount of semantic information. In this approach, both the inverse estimator and the task operator are modeled as a deep neural network, which allows us to train them jointly by optimizing over the two corresponding loss functions. In addition, the task operator, also known as the wavefront set extractor, makes use of the optimal oriented edge representation given by a shearlet system, thereby allowing to reduce the number of parameters to learn without affecting the accuracy. The inverse estimator in this case is the learned iterative method, known as the learned primal-dual, also acting on the shearlet coefficients of the images. In this talk, we will present a detailed description of the problem and our proposed approach. We will also discuss the possible ways to use classical model-based mathematical tools coming from image processing techniques and harmonic analysis combined with data-driven models, to boost the quality of reconstruction and decision making on biomedical imaging. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Andrade Loarca _2021-07_HectorAndrade_ICCHA.pdf |
« back