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Langevin Dynamics in Image Restoration
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Bahjat Kawar, M.Sc. Thesis Seminar
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Tuesday, 24.8.2021, 10:30
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Zoom Lecture: 92909089448
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Advisor:  Prof. Michael Elad
Inverse problems in image processing refer to a family of problems in which we aim to recover an original signal given degraded measurements of it. Various techniques and algorithms have been suggested for general inverse problems, with a special emphasis dedicated to the most prominent example -- image denoising. Recent deep neural network approaches for these tasks focus on minimizing the mean squared error (MSE) between the original and the reconstructed signals. However, in moderate to severe degradation conditions, an MSE minimizer (MMSE) produces blurry, washed-out reconstructions. In our work we introduce an alternative approach for solving inverse problems: Sampling from the posterior distribution of the signal given the degraded measurements. We present a novel stochastic algorithm that samples from the posterior, starting image denoising and inpainting, and generalizing this approach to general inverse problems. The developed algorithm in our work is based on Langevin dynamics and Newton's method in optimization. Due to its stochasticity, the proposed algorithm can produce a variety of outputs for a given input, all shown to be legitimate results, achieving a significantly higher perceptual quality than the MMSE counterpart. In this self-contained talk we will present the necessary background on Langevin dynamics, and describe our novel algorithm, along with the intricate mathematical derivations that led to its success. We will also demonstrate its results on various inverse problems, such as image denoising, inpainting, deblurring, super resolution, and compressive sensing.
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