Fixed-point arithmetic

Fixed-Point Hestenes SVD Algorithm for Computing Eigen Faces

The present paper discusses the development of fixedpoint Hestenes’ singular value decomposition (SVD) algorithm of symmetric matrices in computing eigen faces for image processing applications. Steps for developing fixed-point algorithm from floating-point version are discussed. Quantization noise propagation model for computationally intensive sections of the algorithm are derived and validated. The results are compared with the double precision floating-point version of the algorithm. Accuracy is measured in terms of number of accurate fractional bits, signalto-quantization-noise-ratio (SQNR), orthogonality and factorization errors. Results show that the constant fixed-point format performs better than variable one in terms of number of accurate fractional bits when the variables have close ranges. Variable fixed-point format implementation exhibits an overall better performance. A case study has been presented where variable fixed-point Hestenes’ SVD algorithm with three different wordlengths (WLs) is used as an image processing tool to compute eigen faces from one male and one female face database