#### Technical Report USC-SIPI-100

“Image Restoration and Speckle Suppression Using the Noise Updating Repeated Wiener Filter”

by Shiaw Shiang Jiang

January 1986

In recent years, the adaptive noise smoothing filter using local statistics, which is also referred to as the locally linear minimum mean square error (LLMMSE) filter, has been found to be an effective algorithm for image noise smoothing. The calculation of the local statistics is critical to the quality of the restored image. Various methods for calculating the local statistics are reviewed and their results are compared by computer simulation. Deriving an explicit updated noise variance expression for the LLMMSE filter, we develop a cascaded LLMMSE filter algorithm called the noise updating repeated Wiener (NURW) filter to improve the performance of the adaptive noise smoothing filter. These filters can be applied to images degraded by signal-uncorrelated noise sources without blur. Multiplicative and Poisson noise sources, which are inherently signal-dependent, can be shown to belong to the class of signal-uncorrelated noise.

For images degraded by shift-invariant blur and noise, the restoration process is divided into two stages: deblurring and noise smoothing. A least square pseudoinverse (LSPI) filter is used for deblurring to avoid the ill-conditioning of an inverse filter. The effective noise, which is updated after applying the LSPI filter, becomes correlated and is treated as an uncorrelated one in approximation. The NURW filter is then applied to the output of the LSPI filter for noise smoothing to obtain the final restored image.

Speckle noise is commonly observed in images with a coherent illumination, such as ultrasonic images, synthetic aperture radar (SAR) images and coherent optical images. The speckle can be approximated by a multiplicative noise, which is an element in the class of signal-uncorrelated noise. Thus, the NURW filter is directly applied on the speckle noise suppression problem. Experimental results show that the NURW filter is an effective algorithm for speckle noise suppression.

#### To download the report in PDF format click here: USC-SIPI-100.pdf (16.7Mb)