Adaptive local statistics filtering

Abstract

One important image processing task concerns the restoration of blurred images degraded by additive noise. This thesis describes and compares locally adaptive Wiener filtering techniques in the spatial and frequency domains. The Wiener filter minimizes the Mean Squared Error (MSE).

The first technique describes an extension of locally adaptive Wiener filtering in the spatial domain. Assuming an exponentially decaying autocorrelation function, a non-causal filter is developed whose adaptive properties are dependent on the local signal autocorrelation. The development yields a recursive filter with pole positions based on local signal and noise variance and local signal autocorrelation. A two dimensional discrete implementation of this filter in the form of a recursive noncausal linear difference equation is derived. The properties of this filter are discussed and an iterative implementation is presented.

The second filtering technique is a Wiener filter based on the local power spectrum estimate. This technique makes no assumptions about the signal model and instead directly estimates the local power spectrum but requires a sufficient local neighbourhood for a reliable estimate.

Both these techniques are tested using synthetic and real images to demonstrate the adaptive nature. The results so far show that the spatial domain version provides effective smoothing due to a large region of support, reasonable edge preservation especially in noisy and low contrast conditions and smoothing along edges. The mean squared error is less than that of other noncausal Wiener filters and less than that of the Lee filter.