Abstract
We propose easy-to-implement algorithms to perform blind deconvolution of nonnegative images in the presence of noise of Poisson type. Alternate minimization of a regularized Kullback-Leibler cost function is achieved via multiplicative update rules. The scheme allows to prove convergence of the iterates to a stationary point of the cost function. Numerical examples are reported to demonstrate the feasibility of the proposed method.
Highlights
Alternating multiplicative update rules have been popularized recently by Lee and Seung [1] for the task of nonnegative matrix factorization, i.e. given Y a n × m nonnegative matrix of observations, the task of finding a n × p nonnegative matrix K and a p × m nonnegative matrix X such that Y = KX
The minimization of this latter cost function is the usual model for the case where the data Y are affected by photon-counting noise, i.e. obey a Poisson distribution
We focus on a special instance of this problem namely blind deconvolution in incoherent optical imaging, where the original image X, the blurred image Y and the space-invariant point spread function (PSF) K are nonnegative light intensities
Summary
We focus on a special instance of this problem namely blind deconvolution in incoherent optical imaging, where the original image X, the blurred image Y and the space-invariant point spread function (PSF) K are nonnegative light intensities. For the special case of blind deconvolution, the above alternate minimization algorithm has been discussed previously in the literature by different authors dating back to [4, 5].
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