This paper shows that an n x 1 integer vector can be exactly recovered from its Hadamard transform coefficients, even when 0.5 n log(2)(n) of the (less significant) bits of these coefficients are removed. The paper introduces a fast "lossless" dequantization algorithm for this purpose. To investigate the usefulness of the procedure in data compression, the paper investigates an embedded block image coding technique called the "LHAD" based on the algorithm. The results show that lossless compression ratios close to the state of the art can be achieved, but that techniques such as CALIC and S+P still perform better.