An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior relative to the DCT was adopted as design criterion. The proposed algorithm is superior to the signed discrete cosine transform. It could also outperform state-of-the-art algorithms in low and high image compression scenarios, exhibiting at the same time a comparable computational complexity.

A low-complexity 8-point orthogonal approximate DCT is introduced. The proposed transform requires no multiplications or bit-shift operations. The derived fast algorithm requires only 14 additions, less than any existing DCT approximation. Moreover, in several image compression scenarios, the proposed transform could outperform the well-known signed DCT, as well as state-of-the-art algorithms.

In this paper, we propose a collection of approximations for the 8-point discrete cosine transform (DCT) based on integer functions. Approximations could be systematically obtained and several existing approximations were identified as particular cases. Obtained approximations were compared with the DCT and assessed in the context of JPEG-like image compression. IntroductionThe discrete cosine transform (DCT) is widely regarded as a key operation in digital signal processing [15,51].In fact, the Karhunen-Loève transform (KLT) is the asymptotic equivalent of the DCT, being the former an optimal transform in terms of decorrelation and energy compaction properties [1,15,18,23,37,51]. When high correlated first-order Markov signals are considered [15, 51]-such as natural images [37]-the DCT can closely emulate the KLT [1]. The DCT has been considered and effectively adopted in a number of methods for image and video coding [6]. In fact, the DCT is the central mathematical operation for the following standards: JPEG [46,58], MPEG-1 [52], MPEG-2 [28], H.261 [30], H.263 [31], H.264 [33,40,61,61], and the recent HEVC [8,49,54]. In all above standards, the particular 8-point DCT is considered.Thus, developing fast algorithms for the efficient evaluation of the 8-point DCT is a main task in the circuits, systems, and signal processing communities. Archived literature contains a multitude of fast algorithms for this particular blocklength [26,57]. Remarkably extensive reports have been generated amalgamating scattered results for the 8-point DCT [15, 51]. Among the most popular techniques, we mention the following algorithms: Wang factorization [59], Lee DCT for power-of-two blocklengths [35], Arai DCT scheme [2], Loeffler algorithm [39], Vetterli-Nussbaumer algorithm [57], Hou algorithm [26], and Feig-Winograd factorization [20]. All these methods are classical results in the field and have been considered for practical applications [38,52,56]. For instance, the Arai DCT scheme was employed in various recent hardware implementations of the DCT [19,42,50].Naturally, DCT fast algorithms that result in major computational savings compared to direct computation of the DCT were already developed decades ago. In fact, the intense research in the field has led * R. J. Cintra is with the Signal Processing

Video processing systems such as HEVC requiring low energy consumption needed for the multimedia market has lead to extensive development in fast algorithms for the efficient approximation of 2-D DCT transforms. The DCT is employed in a multitude of compression standards due to its remarkable energy compaction properties. Multiplier-free approximate DCT transforms have been proposed that offer superior compression performance at very low circuit complexity. Such approximations can be realized in digital VLSI hardware using additions and subtractions only, leading to significant reductions in chip area and power consumption compared to conventional DCTs and integer transforms. In this paper, we introduce a novel 8-point DCT approximation that requires only 14 addition operations and no multiplications. The proposed transform possesses low computational complexity and is compared to state-of-the-art DCT approximations in terms of both algorithm complexity and peak signal-to-noise ratio. The proposed DCT approximation is a candidate for reconfigurable video standards such as HEVC. The proposed transform and several other DCT approximations are mapped to systolic-array digital architectures and physically realized as digital prototype circuits using FPGA technology and mapped to 45 nm CMOS technology.

No abstract