Adaptive scaled mean square error filtering by neural networks Ling Guan Stuart W. Perry Edwin P. K. Wong University of Sydney Department of Electrical Engineering Sydney, New South Wales 2006, Australia E-mail: ling@ee.usyd.edu.au Abstract. An adaptive scaled mean square error (SMSE) filter us- ing a Hopfield neural-network-based algorithm is presented. We show the development of the original SMSE filter from the minimum mean square error (MMSE) filter and the parametric mean square error (PMSE) filter, both of which suffer from the oversmooth phe- nomena. The SMSE filter is more efficient than the PMSE filter in terms of noise removal as it does not take into account all the cor- relation factors used for image enhancement. To further improve the performance of the SMSE filter, an adaptive approach is introduced. The adaptive SMSE filter uses a mask operation technique. A user- defined mask is moved across the image and the filtering param- eters are computed based on the local image statistics of the region below the mask. The original and the adaptive SMSE filters are implemented using a Hopfield neural-network-based algorithm. A number of experiments were performed to test the filter characteris- tics. © 1996 SPIE and IS&T. 1 Introduction Pictorial data can provide us with important information such as that carried in x-ray and satellite images etc. Un- fortunately, the data may be corrupted by noise and/or dis- tortion. Therefore some of the valuable information can be lost. The objective of image filtering is therefore to remove noise as much as possible, so that the pictorial information can be recovered or enhanced. There are two types of filters for image processing. 1,2 The first type is called heuristic filtering, which includes linear filters such as the high-pass filter, the low-pass filter, etc., and nonlinear filters such as the median filter, the maximum filter, etc. These filters are based on direct pixel operations. They are fast because the operations are simple arithmetic or direct comparison between pixels. The second type is known as statistical filtering such as the minimum mean square error MMSE filter, the parametric mean square error PMSE filter, 2,3 and the Kalman filter. 4 Statis- tical filtering is mathematically vigorous and is character- ized by complex matrix operations such as matrix inver- sion. These filters are complicated and require a longer processing time than the heuristic methods. Statistical fil- tering is usually employed for image filtering when quality is more important. Heuristic filtering is preferred when real-time processing is required. Nearly all filters suffer from some side effects. For ex- ample, the low-pass filter suffers from the loss of image details high-frequency components; the high-pass filter suffers from the loss of background information low- frequency components; and the MMSE and the PMSE fil- ters suffer from the oversmooth effect. To overcome the deficiency of these filters, a scaled mean square error SMSE filter was introduced and implemented by a vector- processing algorithm. 5 By exponentially reducing correla- tions between pixels, the oversmooth phenomenon is sub- stantially reduced by the SMSE filter. The vector- processing algorithm cuts down the time to execute statistical filters substantially. However, the vector- processing algorithm is still time consuming as matrix mul- tiplications are major operations in the processing. This paper reports a new development in statistical fil- tering. This investigation has two objectives. We first add adaptive features to the SMSE filter to further improve its performance. The parameters of the original filter must be set by the user before the filtering operation, i.e., they are fixed during the processing. The adaptive filter analyzes the image pixel by pixel through a mask operation and the filtering parameters vary according to local image statistics. We then introduce a neural network strategy to effi- ciently execute the SMSE filter. The filter operation is an iterative method based on the minimization of the network energy of a Hopfield-type neural network, 6 where the ob- jective of this method is to find the optimum pixel values that will give the maximum energy reduction. This paper is arranged as follows. Section 2 describes the SMSE filter. The adaptive SMSE filter is developed in Sec. 3. Section 4 details the implementation of the SMSE filters using a Hopfield-type neural network. Experimental results are presented and discussed in Sec. 5. The last sec- tion concludes the investigation. Paper RTI-05 received April 25, 1996; accepted for publication June 10, 1996. 1017-9909/96/$6.00 © 1996 SPIE and IS&T. Journal of Electronic Imaging 5(4), 460– 465 (October 1996). 460 / Journal of Electronic Imaging / October 1996 / Vol. 5(4) Downloaded¬from¬SPIE¬Digital¬Library¬on¬07¬Dec¬2009¬to¬141.117.68.122.¬Terms¬of¬Use:¬¬http://spiedl.org/terms