Abstract
We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator requires knowing only the second-order moments of X and Y, making it of potential interest in various applications. We demonstrate the utility of PLMMSE estimation in recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version of it. We apply the method to the problem of image enhancement from blurred/noisy image pairs. In this setting the PLMMSE estimator performs better than denoising or deblurring alone, compared to state-of-the-art algorithms. Its performance is slightly worse than joint denoising/deblurring methods, but it runs an order of magnitude faster.
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© 2012 Springer-Verlag Berlin Heidelberg
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Michaeli, T., Sigalov, D., Eldar, Y.C. (2012). Partially Linear Estimation with Application to Image Deblurring Using Blurred/Noisy Image Pairs. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_2
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DOI: https://doi.org/10.1007/978-3-642-28551-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28550-9
Online ISBN: 978-3-642-28551-6
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