Scene Adaptive Coder

where a(u, v) denotes the standard deviation of a coefficient. The inverse transform is given by The maximum coefficient value for the cosine transform can be derived from (1) as (3) (2) for w = <P for w = 1, 2, "', N-1. [ (2j + 1)U1T] [(2k + 1)V1T] • cos cos 2N 2N 1 !v' 2 I X I! p(x; u , v) = exp-Vi a(u, v) a(u, v) 1 C(w) = Vi N-1N-1 fO, k) = ~ ~ C(u)C(v)F(u, v) u=O v=O for i, k = 0, 1, "', N-1. Among the class of transform possessing fast computational algorithms, the cosine transform has a superior energy compaction property [6]-[9]. The following sections present some other properties of the cosine transform, which are useful to the subsequent discussion. The two-dimensional discrete cosine transform of a sequence f(j, k) for j, k = 0, 1, "', N-1, can be defined as [6] \ 4C(u)C(v) N-1N-1 F(u,v) = 2 ~ ~ fO, k) N j=O k=O • cos [(2 j-:;)U1TJ cos [(2k :;)V1T ] Let the pixel array f(j, k) represent a sample of a random process with zero mean represented in two's complement format over an integer range-M ~ f(j, k) ~ (M-1). The probability density of the cosine transform coefficients F(u, v) has been modeled by a number of functions [3], [ 12]. Among them, the Laplacian density has been shown to provide the best fit [12]. This function can be written as Abstract-An efficient single-pass adaptive bandwidth compression technique using the discrete cosine transform is described. The coding process involves a simple thresholding and normalization operation on the transform coefficients. Adaptivity is achieved by using a rate buffer for channel rate equalization. The buffer status and input rate are monitored to generate a feedback normalization factor. Excellent results are demonstrated for coding of color images at 0.4 bits/pixel corresponding to real-time color television transmission over a 1.5 Mbit/s channel.