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This paper increases the coding performance for four-dimensional (4D) image based on the region of interest (ROI) coding implemented in the non-separable double lifting structure of 4D integer wavelet transform (WT). The WT has succeeded its predecessor, the discrete cosine transform (DCT), which has been widely used in image compression international standard, the JPEG 2000 since more than a decade ago. The conventional lifting structure which is known as the separable structure has many rounding operators that will increase the rounding noise inside the transform. The higher the rounding noise inside the transform, the lower the coding performance. Thus, a non-separable structure of double lifting WT is introduced to reduce the rounding noise. The non-separable structure is compatible with the conventional wavelet-based JPEG 2000. Furthermore, an ROI coding based non-separable integer WT is …