In this work we describe and analyze sequential and parallel algorithms for the lossless compression of angiography sequences. These algorithms are based on the three-dimensional wavelet transform (3D-WT) and the SPIHT coding method. We consider two different approaches: a 3D wavelet pyramidal structure method and a temporal wavelet decomposition method. We describe our parallel implementations developed on a shared memory system, an SGI Origin 3800 supercomputer, and using a message-passing paradigm ensuring the inter-processor synchronization. We evaluate and analyze the overall processing time and the speedup factor by varying the number of nodes and the video coding parameters.