High resolution multidimensional image data yield huge datasets. For compression and analysis, 2D approaches are often used, neglecting the information coherence in higher dimensions, which can be exploited for improved compression. We designed a wavelet compression algorithm suited for data of arbitrary dimensions, and assessed its ability for compression of 4D medical images. Basically, separable wavelet transforms are done in each dimension, followed by quantization and standard coding. Results were compared with conventional 2D wavelet. We found that in 4D heart images, this algorithm allowed high compression ratios, preserving diagnostically important image features. For similar image quality, compression ratios using the 3D/4D approaches were typically much higher (2-4 times per added dimension) than with the 2D approach. For low-resolution images created with the requirement to keep predefined key diagnostic information (contractile function of the heart), compression ratios up to 2000 could be achieved. Thus, higher-dimensional wavelet compression is feasible, and by exploitation of data coherence in higher image dimensions allows much higher compression than comparable 2D approaches. The proven applicability of this approach to multidimensional medical imaging has important implications especially for the fields of image storage and transmission and, specifically, for the emerging field of telemedicine.