The two-dimensional discrete cosine transform (2-D DCT) has been widely recognized as the most effective technique in image data compression. In this paper, we propose a new algorithm to compute the 2-D DCT from a frame-recursive point of view. Based on this approach, two real-time parallel lattice structures for successive frame and block 2-D DCT are developed. The systems is fully-pipelined with throughput rate N clock cycles for N x N successive input data frame. This is the fastest pipelined structure for the 2-D DCT known so far. Moreover, the 2-D DCT architecture is module, regular, and locally-connected and requires only two 1-D DCT blocks which can be extended directly from the 1-D DCT structure without transposition. Therefore, it is very suitable for VLSI implementation for the high speed HDTV systems. We also propose a parallel 2-D DCT architecture and a new scanning pattern for the HDTV system to achieve higher performance. The VLSI implementation of the 2-D DCT using distributed arithmetics to increase computational efficiency and reduce round off error is also discussed.