Abstract: We present a moment-based fast algorithm for efficient computation of two dimensional(2-D) discrete Hartley transform(DHT).With a kernel map and Taylor expansion,2-D DHT is approximated by a linear sum of 2-D discrete moments.Computation of moments is realized in an all adder systolic structure.The algorithm is efficient and suitable for dealing sequence of any length with high precision.MRI image compressions show that the method can reach high peak signal-to-noise ratios.