The two-dimensional (2-D) discrete cosine transform (DCT) and the subsequent quantization of the transform coefficients are two computationally demanding steps of any DCT-based video encoder. In this paper, we propose an efficient joint implementation of these two steps, where the precision in computing the DCT can be exchanged for a reduction in the computational complexity. First, the quantization is embedded in the DCT, thus eliminating the need to explicitly quantize the transform coefficients. A multiplierless integer implementation of the quantized DCT (QDCT) is then proposed that performs shift and add operations instead of full multiplications. A sequence of multiplierless QDCT algorithms is obtained with increasing precision and number of computations. Finally, further savings in computations are obtained by terminating the DCT computations whenever intermediate results indicate that the transform and quantization steps will likely result in a block of zero values. The proposed algorithms are applied to, and results are presented for, high-quality MPEG-2 and low bit rate H.263 video encoding.

A typical MPEG-2 video encoder requires that DCT and quantization be performed in most cases. In this paper we show how to combine these two steps, reducing substantially the number of computations. The new nonlinear transform is called the quantized discrete cosine transform, or QDCT. We also introduce a new method to trade-off the computational complexity and the precision of the QDCT. Although the QDCT is independent of the input data, better trade-offs can be obtained by making it data dependent, which is appropriate in multimedia applications such as MPEG-2 video coding. The results presented in this paper can also be extended to other linear transforms and/or other coding methods.

Image coding using the discrete wavelet transform can attain very good results compared to traditional methods. In fact, most of the best known results for image coding have been related to the DWT. A simple scheme to code the DWT coefficients is the embedded zero-tree wavelet algorithm by Shapiro (1993). The embedded zero-tree wavelet can exploit both the similarity among subbands and the sparseness of the subbands. We propose a new simple image coder based on the DWT. The DWT coefficients are coded in bitplanes. Each bi-level pixel is coded in a context formed by its parental and surrounding pixels. In this way, both the similarity and the sparseness among subbands are exploited. We show the experimental results, both in terms of distortion measurement and visual comparison, and compare them to well-known methods.