Applications of multi-transforms to 3-D spatial signal representation

Three dimensional spatial signal representation employing transforms is generally performed by applying a 2-D transform to the 2-D slices of the 3-D data or a 3-D transform for the entire data. Transforms such as DCT, Walsh and Haar are frequently considered because of their ease of computation. This paper develops a technique called the multi-transform technique for the efficient representation of 3-D spatial data. The main feature of the technique is that two or more transforms can be applied to represent the signal thus benefiting from the compression qualities of each of the transforms. The signal to noise ratio (SNR) of the reconstructed signal employing the proposed technique is higher than the SNR of the signal employing a single transform alone. Results are presented for a 3-D MRI signal representation using the 2-D and 3-D multi-transform techniques employing the DCT/Walsh combination. Comparisons with using DCT alone are made for both cases