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The four-dimensional (4D) images such as 4D magnetic resonance image (MRI), 4D computed tomography (CT) and other types of 4D medical images have high slice resolution up to 1024× 1024 or more at increasing pixel bit-depth. The limitations in storage space and transmission bandwidth has triggered a huge investigation on multidimensional and dynamic image compression to efficiently store and transmit the 4D images.

Since few decades ago, Discrete Cosine Transform (DCT) based digital image signal compression had been adopted as the JPEG international standard. Later, Discrete Wavelet Transform (DWT) has replaced the DCT and its being applied in medical image compression. JPEG 2000, the international standardization of DWT is using separable lifting structure where the multidimensional image signal is transformed separately in its horizontal and vertical direction. Besides that, each process is realized by cascading in lifting calculation. However, the necessity of waiting for previous step before calculating to the next step will make the overall delay time become longer. The delay time between input and output of WT is reduced as the proposed method reduces its lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced.