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Solving a linear system of the type Ax + n = y with many more unknowns than equations is a fundamental ingredient in a plethora of applications. The classical approach to this inverse problem is by formulating an optimization problem consisting a data fidelity term and a signal prior, and minimizing it using an iterative algorithm. Imagine we have a wonderful iterative algorithm but real-time limitations allows only to execute five iterations thereof. Will it achieve the best accuracy within this budget? Imagine another setting in which an iterative algorithm pursues a certain data model, which is known to be accurate only to a certain amount. Can this knowledge be used to design faster iterations? In this talk, I will try to answer these questions by showing how the introduction of controlled inaccuracy can significantly increase the convergence speed of iterative algorithms used to solve various inverse problems. I will also elucidate connections to deep learning an provide a theoretical justification of the very successful LISTA networks. Examples of applications in computational imaging and audio processing will be provided.
This presentation is part of Minisymposium “MS29 - Geometry and Learning in 3D Shape Analysis”
organized by: Ronald Lui (Chinese University of Hong Kong) , Rongjie Lai (Rensselaer Polytechnic Institute) .