An error-efficient Gaussian filter for image processing by using the expanded operand decomposition logarithm multiplication

Abstract

Digital signal processing and image processing applications require the noise free and efficient arithmetic operations. To overcome the noise problem, an efficient expanded operand decomposition (ExOD) based logarithm multiplication is proposed and applied for convolution of Gaussian smoothing filter to minimize the noise. The ExOD approach improves the average error percentage (AEP), mean square error (MSE) and the error rate in comparison of reported operand decomposition (OD) and improved operand decomposition (IOD). The peak signal-to-noise ratio (PSNR), MSE and the AEP of the ExOD logarithm multiplication method are improved as compared to the reported logarithm multiplication to the convolution operation. The ExOD method for logarithmic multiplication gives AEP of 0.276, 0.294 and 0.309%, whereas Mitchell’s algorithm gives 2.702, 2.661 and 2.830%, OD-Mitchell’s multiplication gives 1.441, 1.449 and 2.170% and IOD-Mitchell’s multiplication gives 1.627, 1.678 and 2.064% for 4-, 8-, and 16-bit operations respectively. ExOD-Mitchell’s multiplication gives 1.867% MSE, 45.453 db PSNR and 0.293% AEP, whereas Mitchell’s algorithm gives 18.688% MSE, 35.449 db PSNR and 2.731% AEP, OD-Mitchell’s multiplication gives 9.877% MSE, 38.218 db PSNR and 1.686% AEP and IOD-Mitchell’s multiplication gives 10.866% MSE, 37.804 db PSNR and 1.789% AEP. The proposed ExOD based Mitchell algorithm multiplication has useful applications in image processing with efficient accuracy.