Vector filtering technique for recovery of stationary stochastic processes contaminated by broad-band noise

Guy, Eugene Victor (1995) Vector filtering technique for recovery of stationary stochastic processes contaminated by broad-band noise. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (27MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

The objective of this project has been to develop a filtering technique which will enable the recovery of a wide-sense stationary, stochastic signal process, from a two-dimensional image. It is assumed that the image is contaminated by a stationary broad-band noise process, having a spatial extent of correlation, represented by c, which is much less than the spatial extent of correlation within the signal process. Under such conditions, it is possible to derive a three- channel Wiener filter which operates on the past values of a coherent data sequence, in order to predict a future value. By setting the prediction gap, α, to be greater than c, the predicted output sequence will be a noise-suppressed version of the input. The three-channel filler accepts as input, three rows of the image, and then produces a single output which is a filtered estimate of the signal process occurring within the middle row of the input triplet. Each row within this triplet is separated by a distance, β, which is held constant for all row triplets during the filtering operation. After operating on all possible row triplets, the same procedure is repeated for column triplets. It has been demonstrated that the three-channel filter has a greater capacity for noise- suppression, when compared to single-channel versions. By choosing the value of β to be greater than c, this noise suppression capability is optimized. -- This research has verified that the three-channel Wiener filter is effective in suppressing correlated speckle noise, within ocean wave scenes imaged by airborne Synthetic Aperture Radar, However, due to the exponentially-damped nature of the correlation functions which characterize the bandpass signal process within such images, it has also been shown that the filtered estimates are directly dependent upon the values chosen for α and β. In fact, if two different filtering operators are derived, each with a different combination of values for α and β, then they will each produce a different filtered estimate after operating on the same input image. Consequently, the accuracy of the filtering operation will vary according to the choices which are made regarding these parameters. The most accurate filtered estimates of the bandpass process are achieved with small parametric values. Since α must assume a value which is greater than c, and since it is preferable that β should also, it logically follows that the extent of noise correlation within any image will predetermine the degree of accuracy which can be achieved by use of this technique. -- The three-channel Wiener filtering technique will have practical noise-suppression applications, relating to the extraction of more accurate wave feature information from speckle- contaminated SAR images of ocean scenes. Furthermore, since the use of large α and β restricts recovery to only a portion of a bandpass signal, this technique may be suitable for the isolation and enhancement of low-frequency, low-power wave components, which may be otherwise obscured by higher-frequency wind-generated waves.

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