Multidimensional Algebraic-Integer Encoding for High Performance Implementation of the DCT and IDCT

V.S. Dimitrov and G.A. Jullien (Canada)


Image Processing and Applications, image compression, DCT, error-free computations


A recently introduced algebraic integer encoding scheme allows low complexity error-free computation of the DCT and IDCT. The idea of using algebraic integers in DSP applications was firstly explored by Cozzens and Finkelstein in their work devoted to the efficient implementation of the FFT by combining algebraic-integer quantization (first level of parallelism) and residue number system (second level of parallelism). All the previous applications of algebraic integers in signal processing have used a single variable quantization scheme. In this paper, we offer the use of multidimensional algebraic-integer encoding of the transformation matrix of the DCT and IDCT. Firstly, this increases the sparseness of the encoding matrix. Secondly, by making an appropriate choice of the variables, we reduce substantially the dynamic range of the ransformation coefficients, which leads to more efficient hardware implementation. Thirdly, the final reconstruction from algebraic integer for mat to binary is also simplified. The whole computational process up until the final reconstruction is completely error typical image compression applications.

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