Real-Time Interpolation Of Images Obtained By Image Detector Arrays

REAL-TIME INTERPOLATION OF IMAGES OBTAINED BY IMAGE DETECTOR ARRAYSO. K. ERSOY, Purdue University, School of Electrical Engineering, W. Lafayette, Indiana 47907, USAABSTRACTA real-time method of multidimensional interpolation based on the generalized real discrete Fourier transform (GRDFT) is presented. By factorizing the ID transform matrix into the preprocessing and postprocessing matrices, and approximating the postprocessing stage such that any degree of desired accuracy is obtained, increased speed of computation and feasibility of electro-optical or VLSI implementation at reduced cost are achieved.1. 2D INTERPOLATION WITH GRDFTIn many imaging applications, it is necessary to interpolate the images in a reliable way in real time for a variety of reasons such as the number of available detector elements arranged in an array being limited. This can be achieved using 2D generalized real discrete Fourier transform (GRDFT) [1]. There are actually 4 classes of GRDFT. We will use the first one, denoted by Rj. Its ID matrix will also be denoted by Rj. 2D Rl with NTxNT points (NT assumed to be a power of 2 may be chosen differently in the two directions) can be written as4 NT-I Nr-i 2701^1 27rn2k2y(nlfn2) = -^ £ £ xfk^k,) cos( *-*- + ^(nj) cos( f± + 02(n2)) (1) NT kx =0 k2=0 iNT ^Twhere #;( ), i being 1 or 2, is given by0i(n) = ^j(n) for 0 < n < NT/2 , and