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Numerical methods for phase retrieval (2012)

by Eliyahu Osherovich
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"... Abstract. Recent blind deconvolution methods rely on either salient edges or the power spectrum of the input image for estimating the blur kernel, but not both. In this work we show that the two methods are inherently complimentary to each other. Edge-based methods work well for images containing la ..."
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Abstract. Recent blind deconvolution methods rely on either salient edges or the power spectrum of the input image for estimating the blur kernel, but not both. In this work we show that the two methods are inherently complimentary to each other. Edge-based methods work well for images containing large salient structures, but fail on small-scale textures. Power-spectrum-based methods, on the contrary, are efficient on textural regions but not on structural edges. This ob-servation inspires us to propose a hybrid approach that combines edge-based and power-spectrum-based priors for more robust deblurring. Given an input image, our method first derives a structure prediction that coincides with the edge-based priors, and then extracts dominant edges from it to eliminate the errors in com-puting the power-spectrum-based priors. These two priors are then integrated in a combined cost function for blur kernel estimation. Experimental results show that the proposed approach is more robust and achieves higher quality results than previous methods on both real world and synthetic examples. 1
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...tions to overcome different kinds of stagnate. Luke [18] proposes a Relaxed Averaged Alternating Reflection (RAAR) algorithm which is later adopted by Goldstein and Fattal’s approach [11]. Osherovich =-=[19]-=- recently proposes a method that achieves fast and accurate phase retrieval from a rough initialization. 2 Overview 2.1 Blur model To model the camera shake in a blurred image, we use a conventional c...

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