BIVARIATEALGEBRAIC INTEGERENCODED ARAI ALGORITHM FOR EXACT COMPUTATION OF DCT

Sumi Thomas, M Mathurakani

Abstract: Discrete Cosine Transform (DCT) function is widely used in many standard image and signal processing applications. Error free architectures with high throughput and reduced hardware area is a major concern.This paper surveys and particularly collates all the information available on arai algorithm that uses algebraic integer coded computation.Bivariate Algebraic Integer(AI) encoded 2-D DCT algorithm ensuresquantization noise free implementation of2-D DCT. This algorithm realizes an error-free 2-D DCT without using Final Reconstruction Steps(FRS) between row–column transforms, leading to an 8×8 2-D DCT that is entirely free of quantization errors in AI basis,thereby avoiding the leakage of quantization noise between DCT channels.This architecture has infinite accuracy till the reconstruction step. The architecture enables low-noise high-dynamic range applications in image processing that requires full control of the finite-precision computation of the 2-D DCT. The 2D DCT algorithm is simulated under fourdifferent conditions, on a gray coded 512X512 image, and PSNR value is measured and compared using MATLAB

Keywords: Algebraic Integer quantization, Discrete Cosine Transform (DCT), Scaled DCT/IDCT, Quantization Noise, Fixed point representation

DOI: https://doi.org/10.15623/ijret.2014.0313008