A Lossless Hadamard Transform Using Independence of Lower Bits of Coefficients

Abstract

In this paper, we propose a method for lossless Hadamard transform. Firstly, it is shown that 2nd Least Significant Bit (LSB) plane coincides with the binarized pattern of transform basis. Secondly, we make clear the characteristic that when the LSB plane and the 2nd LSB plane of Hadamard transformed coefficients are inversely transformed, each bit plane is converted to integer value.
By using of these characteristics, we propose a new lossless Hadamard transform named a partial retransform method. In this method, Hadamard linear transformed coefficients are divided into an integer part and a decimal part. And, only decimal part is retransformed. Then, the retransformed result of the decimal part is added to the integer part. Processing the lossless transformed coefficients with same method as above, original data are reconstructed.
By applying the partial retransform method to 2D 4×4 points Hadamard transform, we construct a new lossless 2D 4×4 points Hadamard transform.