A Mean-Field Variational Inference Approach to Deep Image Prior for Inverse Problems in Medical Imaging

Malte Tölle, Max-Heinrich Laves, Alexander Schlaefer
Proceedings of the Fourth Conference on Medical Imaging with Deep Learning, PMLR 143:745-760, 2021.

Abstract

Exploiting the deep image prior property of convolutional auto-encoder networks is especially interesting for medical image processing as it avoids hallucinations by omitting supervised learning. Its spectral bias towards lower frequencies makes it suitable for inverse image problems such as denoising and super-resolution, but manual early stopping has to be applied to act as a low-pass filter. In this paper, we present a novel Bayesian approach to deep image prior using mean-field variational inference. This allows for uncertainty quantification on a per-pixel level and, given the right prior distribution on the network weights, omits the need for early stopping. We optimize the parameters of the weight prior towards reconstruction accuracy using Bayesian optimization with Gaussian Process regression. We evaluate our approach on different inverse tasks on a variety of modalities and demonstrate that an optimized weight prior outperforms former state-of-the-art Bayesian deep image prior approaches. We show that a badly selected prior leads to worse accuracy and calibration and that it is sufficient to optimize the weight prior parameter per task domain.

Cite this Paper

BibTeX
@InProceedings{pmlr-v143-tolle21a, title = {A Mean-Field Variational Inference Approach to Deep Image Prior for Inverse Problems in Medical Imaging}, author = {T{\"o}lle, Malte and Laves, Max-Heinrich and Schlaefer, Alexander}, booktitle = {Proceedings of the Fourth Conference on Medical Imaging with Deep Learning}, pages = {745--760}, year = {2021}, editor = {Heinrich, Mattias and Dou, Qi and de Bruijne, Marleen and Lellmann, Jan and Schläfer, Alexander and Ernst, Floris}, volume = {143}, series = {Proceedings of Machine Learning Research}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v143/tolle21a/tolle21a.pdf}, url = {https://proceedings.mlr.press/v143/tolle21a.html}, abstract = {Exploiting the deep image prior property of convolutional auto-encoder networks is especially interesting for medical image processing as it avoids hallucinations by omitting supervised learning. Its spectral bias towards lower frequencies makes it suitable for inverse image problems such as denoising and super-resolution, but manual early stopping has to be applied to act as a low-pass filter. In this paper, we present a novel Bayesian approach to deep image prior using mean-field variational inference. This allows for uncertainty quantification on a per-pixel level and, given the right prior distribution on the network weights, omits the need for early stopping. We optimize the parameters of the weight prior towards reconstruction accuracy using Bayesian optimization with Gaussian Process regression. We evaluate our approach on different inverse tasks on a variety of modalities and demonstrate that an optimized weight prior outperforms former state-of-the-art Bayesian deep image prior approaches. We show that a badly selected prior leads to worse accuracy and calibration and that it is sufficient to optimize the weight prior parameter per task domain.} }
Endnote
%0 Conference Paper %T A Mean-Field Variational Inference Approach to Deep Image Prior for Inverse Problems in Medical Imaging %A Malte Tölle %A Max-Heinrich Laves %A Alexander Schlaefer %B Proceedings of the Fourth Conference on Medical Imaging with Deep Learning %C Proceedings of Machine Learning Research %D 2021 %E Mattias Heinrich %E Qi Dou %E Marleen de Bruijne %E Jan Lellmann %E Alexander Schläfer %E Floris Ernst %F pmlr-v143-tolle21a %I PMLR %P 745--760 %U https://proceedings.mlr.press/v143/tolle21a.html %V 143 %X Exploiting the deep image prior property of convolutional auto-encoder networks is especially interesting for medical image processing as it avoids hallucinations by omitting supervised learning. Its spectral bias towards lower frequencies makes it suitable for inverse image problems such as denoising and super-resolution, but manual early stopping has to be applied to act as a low-pass filter. In this paper, we present a novel Bayesian approach to deep image prior using mean-field variational inference. This allows for uncertainty quantification on a per-pixel level and, given the right prior distribution on the network weights, omits the need for early stopping. We optimize the parameters of the weight prior towards reconstruction accuracy using Bayesian optimization with Gaussian Process regression. We evaluate our approach on different inverse tasks on a variety of modalities and demonstrate that an optimized weight prior outperforms former state-of-the-art Bayesian deep image prior approaches. We show that a badly selected prior leads to worse accuracy and calibration and that it is sufficient to optimize the weight prior parameter per task domain.
APA
Tölle, M., Laves, M. & Schlaefer, A.. (2021). A Mean-Field Variational Inference Approach to Deep Image Prior for Inverse Problems in Medical Imaging. Proceedings of the Fourth Conference on Medical Imaging with Deep Learning, in Proceedings of Machine Learning Research 143:745-760 Available from https://proceedings.mlr.press/v143/tolle21a.html.

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