A Generalized Algorithm and Reconfigurable Architecture for Efficient and Scalable Orthogonal Approximation of DCT

Abstract

International audienceApproximation of discrete cosine transform (DCT) is useful for reducing its computational complexity without significant impact on its coding performance. Most of the existing algorithms for approximation of the DCT target only the DCT of small transform lengths, and some of them are non-orthogonal. This paper presents a generalized recursive algorithm to obtain orthogonal approximation of DCT where an approximate DCT of length N could be derived from a pair of DCTs of length (N/2) at the cost of N additions for input preprocessing. We perform recursive sparse matrix decomposition and make use of the symmetries of DCT basis vectors for deriving the proposed approximation algorithm. Proposed algorithm is highly scalable for hardware as well as software implementation of DCT of higher lengths, and it can make use of the existing approximation of 8-point DCT to obtain approximate DCT of any power of two length, N > 8. We demonstrate that the proposed approximation of DCT provides comparable or better image and video compression performance than the existing approximation methods. It is shown that proposed algorithm involves lower arithmetic complexity compared with the other existing approximation algorithms. We have presented a fully scalable reconfigurable parallel architecture for the computation of approximate DCT based on the proposed algorithm. One uniquely interesting feature of the proposed design is that it could be configured for the computation of a 32-point DCT or for parallel computation of two 16-point DCTs or four 8-point DCTs with a marginal control overhead. The proposed architecture is found to offer many advantages in terms of hardware complexity, regularity and modularity. Experimental results obtained from FPGA implementation show the advantage of the proposed method

SoC-Based Edge Computing Gateway in the Context of the Internet of Multimedia Things: Experimental Platform

“…In this level, a selection of algorithms with lightweight implementation is mandatory. Then, to further reduce the algorithmic computational complexity, the use of approximate computing as in [12,13] can be beneficial. The second issue is regarding the architectural design.…”

“…Since DCT is computationally intensive and its complexity grows nonlinearly with the image size, in this paper we propose to use an approximation of DCT as in [12,13]. The main objective of the DCT approximation is to get rid of the multiplications that consume most …”

“…Figure 3 depicts the encryption scheme, where a and s 0 are the initial conditions of chaotic generators, which are developed in the next section. We should finally note that the approximate DCTs are from [12,13]. The method of multiple image compression and encryption is from [23] and the chaotic generators are used in the literature.…”

“…They allow the computation of 32-, 16-and 8-point DCT/IDCT by using the same computation elements. This is possible thanks to our proposed algorithm in [12] which was validated in [13]. …”

Multiplierless 16-point DCT approximation for low-complexity image and video coding

“…In contrast to the 8-point DCT case-where dozens of approximations are available [21,25,27,28,30,34], -the 16-point DCT approximation methods are much less explored in literature. To the best of our knowledge, only the following orthogonal methods are available: the traditional Walsh-Hadamard transform (WHT) [35], the BAS-2010 [24] and BAS-2013 [26] approximations, and the transformations proposed in [31], [22], and [36].…”