Zonal Sampling and Bit Allocation HT Coefficients in Image Data Compression

In this paper we report our investigation on zonal sampling, probability fitting tests, and bit allocation for Hadamard transform image data compression. The energy distribution of the transform coefficients suggests a sampling strategy which retains as much energy as possible for a fixed number of coefficients. The probability fitting tests indicate that Laplacian is a better model for non-dc coefficients, while Rayleigh or Gaussian fits better for the dc coefficient. Finally, the bit assignment is formulated as a constrained optimization problem. The mean square error performance is derived as a function of the number of retained coefficients for various average bit rates. The results are useful for designing a zonal coding system with optimum retained zone size and shape as well as their corresponding bit assignment.