A Unified Algorithm for Subband‐Based Discrete Cosine Transform

Abstract

Discrete cosine transform (DCT) and inverse DCT (IDCT) have been widely used in many image processing systems and real-time computation of nonlinear time series. In this paper, the unified DCT/IDCT algorithm based on the subband decompositions of a signal is proposed. It is derived from the data flow of subband decompositions with factorized coefficient matrices in a recursive manner. The proposed algorithm only requires(4(log2n)−1−1)and(4(log2n)−1−1)/3multiplication time forn-point DCT and IDCT, with a single multiplier and a single processor, respectively. Moreover, the peak signal-to-noise ratio (PSNR) of the proposed algorithm outperforms the conventional DCT/IDCT. As a result, the subband-based approach to DCT/IDCT is preferable to the conventional approach in terms of computational complexity and system performance. The proposed reconfigurable architecture of linear array DCT/IDCT processor has been implemented by FPGA.

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“…half of the computation is wasted. In time domain the imaginary part of the signal is all zero, and in frequency domain, both real and imaginary parts of the spectrum are symmetric [ 38 ]. Discrete cosine transform (DCT) generates real spectrum of a real signal and thereby avoids redundant data and computation [ 39 ].…”

A Fast DCT Algorithm for Watermarking in Digital Signal Processor

“…Direct computation of 2D DCT (N × N pixel size of a block) requires 4 multiplications, while direct realization (with the row-column separation) of 8 × 8 DCT 2 × 8 3 = 1024 multiplications. Although many algorithms have been [7] 31 Sung et al [8] 25 Manoria and Dixit [9] 28 Khan et al [10] 40 FDCT algorithm (this work) 24…”

“…proposed to optimize multiplications, they either required huge amount of computation [6][7][8]10] or suffered from low efficiency [4,5,9]. Table 1 lists the number of multiplications required in preview works compared with the proposed FDCT algorithm.…”

“…Jridi et al [5] designed a low complexity DCT engine in digital video and image processing. Subband decomposition algorithms based on DCT have also been used in transmitting image data of low resolution to rebuilt image of better quality [6][7][8], but they required high complexity and thus time-consuming computation. Stassen's matrix multiplication algorithm was proposed to reduce complex matrix multiplication in DCT [9].…”

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“…Discrete cosine transform DCT has been adopted in various international standards, for example, JPEG, MPEG, and H.264 11 . The miscellaneous DCT algorithms and architectures have been proposed [12][13][14][15] . The fractional discrete cosine transform FDCT 16,17 , which is a generalized DCT, is yet more applicable in the digital signal processing applications.…”