Optimal Sampling Operator for Signal Restoration in the Presence of Signal Space and Observation Space Noises

Aqeel SYED  Hidemitsu OGAWA  

IEICE TRANSACTIONS on Information and Systems   Vol.E88-D   No.12   pp.2828-2838
Publication Date: 2005/12/01
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Processing and Video Processing
signal restoration,  partial projection filter,  sampling operator,  reproducing kernel,  pseudo orthogonal bases,  

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The partial projection filter (PTPF) for a given observation operator provides an optimal signal restoration in the presence of both the signal space and observation space noises. However, restoration error by the filter still depends on the observation operator which consists of measurement and sampling processes. In this paper, we determine a sampling operator which minimizes the restoration error by the PTPF. We see that under some assumptions about noise statistics, the restoration error by the PTPF is divided into two terms corresponding to the error arising from the signal space noise and that from the observation space noise. It has been found that although the restoration error due to the signal space noise is independent of the sampling operator, the restoration error arising from the observation space noise can arbitrarily be decreased by increasing the number of sample points in the proposed sampling operator. An illustrative example of optimal sampling in the trigonometric polynomial space is also given.