Leveraging Phase Information to Boost Unrolled Network Learning for Image Deblurring

While most image deblurring techniques directly restore thespatial image variable, we propose an amplitude and phase decomposi-tion recognizing the importance of accurate phase estimation in recover-ing sharp image details. To that end, we first develop novel linear min-imum mean squared (LMMSE) estimators of the amplitude and phaseof the blurred, noisy image observation. An iterative optimization algo-rithm follows that recovers the sharp image using the aforementionedLMMSE estimators. Finally, matrix parameters that are statistically de-termined and fixed in the iterative algorithm are now learned using atraining dataset of clean and degraded observations. Our deblurring en-gine is dubbed UPADNet – Unrolled Phase and Amplitude Decompo-sition Network, such that each iteration of the underlying phase andamplitude recovery algorithm is parameterized and trained end-to-end.Experiments over benchmark evaluation datasets such as GoPro, Real-Blur and COCO datasets confirm that UPADNet outperforms state ofthe art deep networks including those based on algorithm unrolling inthe image domain. The benefits of UPADNet are even more pronouncedin high noise and limited training data regimes.