A mixed transform approach for efficient compression of medical images

A novel technique is presented to compress medical data employing two or more mutually nonorthogonal transforms. Both lossy and lossless compression implementations are considered. The signal is first resolved into subsignals such that each subsignal is compactly represented in a particular transform domain. An efficient lossy representation of the signal is achieved by superimposing the dominant coefficients corresponding to each subsignal. The residual error, which is the difference between the original signal and the reconstructed signal is properly formulated. Adaptive algorithms in conjunction with an optimization strategy are developed to minimize this error. Both two-dimensional (2-D) and three-dimensional (3-D) approaches for the technique are developed. It is shown that for a given number of retained coefficients, the discrete cosine transform (DCT)-Walsh mixed transform representation yields a more compact representation than using DCT or Walsh alone. This lossy technique is further extended for the lossless case. The coefficients are quantized and the signal is reconstructed. The resulting reconstructed signal samples are rounded to the nearest integer and the modified residual error is computed. This error is transmitted employing a lossless technique such as the Huffman coding. It is shown that for a given number of retained coefficients, the mixed transforms again produces the smaller rms-modified residual error. The first-order entropy of the error is also smaller for the mixed-transforms technique than for the DCT, thus resulting in smaller length Huffman codes.