Bayesian Image Reconstruction: From Sparsity-Based Methods to Deep Neural Networks—Part I
M. Unser
SIAM Conference on Imaging Science (IS'22), Virtual, March 21-25, 2022, MT2 - Part I of II.
Bayesian estimation is a powerful paradigm for image reconstruction. We demonstrate the claim by developing methods to solve ill-posed linear inverse problems (e.g., compressed sensing) under the hypothesis that the signal is the realization of a sparse stochastic process (SSP). This framework lends itself to an explicit derivation of the posterior probabilities. Under certain assumptions, it yields MAP estimators that are compatible with sparsity-promoting schemes such as TV denoising, LASSO, and wavelet shrinkage. It is also amenable to Gibbs sampling for the determination of the MMSE solution. Next, we discuss image-reconstruction methods that rely on convolutional neural networks (CNNs). After a brief description of the algorithms, we present an SSP-based Bayesian benchmarking environment. Finally, we revisit the model-based Bayesian estimators by replacing our stochastic signal generator with a generative adversarial network (GAN). All instances are illustrated with real-world image reconstructions.
@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser2204.html,
AUTHOR="Unser, M.",
TITLE="Bayesian Image Reconstruction: {F}rom Sparsity-Based Methods to
Deep Neural Networks---{P}art {I}",
BOOKTITLE="{SIAM} Conference on Imaging Science ({IS'22})",
YEAR="2022",
editor="",
volume="",
series="",
pages="",
address="Virtual",
month="March 21-25,",
organization="",
publisher="",
note="MT2")