Multi-dimensional Compression Using JPEG2000

Summary form only given. JPEG2000 Part 2 by Taubman, D.S. and Marcellin, M.W. (2002) supports the use of multi-component transforms (MCT) to decorrelate multi-component image data along the component direction. Three types of point transforms are allowed: linear block transforms, dependency transforms and wavelet transforms. Besides these transforms, Part 2 also allows grouping of arbitrary subsets of components into ´component collections.´ Any of the three transform types can be used for each such collection. These Part 2 extensions have been used for compressing 3-D images in many applications such as medical, hyper-spectral and video. It is widely believed that the MCT extensions are applicable only to 3-D data. In this work, we demonstrate their use for compressing N-datasets for any N ges 3. Let (M₁, M₂,..., M_N-2, X, Y) denote the dimensions (size) of an N-dataset. The data can then be interpreted as a collection of 2-D (X, Y) images (or components). The number of such components is T = pi _k=1 ^N-2 M_k. Each component is indexed by an N - 2 dimensional vector: [m₁,m₂,...,m_N-2] where m_k isin {1, 2,..., M_k}. To compress an N-D dataset, the T components are processed by N - 2 stages of MCT. Specifically, each stage has T input components and produces T output components, which in turn are used as inputs to the next stage. Consider the k^th (k isin {1, 2,..., N - 2}) stage of the MCT which is used to decorrelate the data along the k dimension. The input components are first reordered to form collections. A collection is formed by grouping all components having the same value of the N - 3 dimensional index [m₁, m₂,...,m_k+1,...m_N-2]. There are then T/M_k collections, each containing M_k components. For each collection, a point transform is applied, resulting in decorrelation- of the data along the k^th dimension. The output components of the final MCT stage (N - 2) are compressed using the 2-D wavelet transform and block coding of JPEG2000. It should be noted that the encoding procedure described above will result in a code-stream that is entirely compliant with JPEG2000 Part 2. Two major applications of multi-dimensional sources are medical images (fMRI, 4-D cardiac and ultrasound) and multi-view video. We have applied the proposed methodology to a 5-D (X, Y, slice, time, trial) fMRI dataset. A PSNR (Peak Signal to Noise Ratio) gain of 8 to 14.9 dB is observed at various bit rates, when 3 stages of MCT (5-D) are used as opposed to the usual single stage of MCT (3-D). The proposed scheme can support scalability in all N dimensions. Additionally, incremental processing can be used to achieve considerable savings in memory usage.