convex_learning swMATH ID: 32735 Software Authors: Chambolle, A.; Holler, M.; Pock, T. Description: A convex variational model for learning convolutional image atoms from incomplete data. A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is convex and allows for simultaneous image reconstruction and atom learning in a general, inverse problems context. Further, motivated by an improved numerical performance, also a semi-convex variant is included in the analysis and the experiments of the paper. For both settings, fundamental analytical properties allowing in particular to ensure well-posedness and stability results for inverse problems are proven in a continuous setting. Exploiting convexity, globally optimal solutions are further computed numerically for applications with incomplete, noisy and blurry data and numerical results are shown. Homepage: https://link.springer.com/article/10.1007/s10851-019-00919-7 Source Code: https://github.com/hollerm/convex_learning Keywords: variational methods; learning approaches; inverse problems; functional lifting; convex relaxation; convolutional Lasso; machine learning; texture reconstruction Related Software: GitHub; DeepAdverserialRegulariser; TensorFlow; compsensing_dip; NETT; PyTorch; ODL; Adam; PyOpenCL; PyCUDA; PDCO; BM3D; SPORCO; Wasserstein GAN; DGM; VoxelMorph; Quicksilver; PDE-Net; BUQO; U-Net Cited in: 5 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A convex variational model for learning convolutional image atoms from incomplete data. Zbl 1434.68625Chambolle, A.; Holler, M.; Pock, T. 2020 all top 5 Cited by 13 Authors 2 Öktem, Ozan 1 Arridge, Simon R. 1 Calvetti, Daniela 1 Chambolle, Antonin 1 Habring, Andreas 1 Holler, Martin 1 Köhler, Thomas 1 Maass, Peter 1 Pock, Thomas 1 Pragliola, Monica 1 Rudzusika, Jevgenija 1 Schönlieb, Carola-Bibiane 1 Somersalo, Erkki Cited in 5 Serials 1 Journal of Mathematical Imaging and Vision 1 Acta Numerica 1 Inverse Problems and Imaging 1 SIAM Journal on Imaging Sciences 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 6 Fields 5 Information and communication theory, circuits (94-XX) 3 Numerical analysis (65-XX) 3 Computer science (68-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 1 Biology and other natural sciences (92-XX) Citations by Year