An Integer Approximation Method for Discrete Sinusoidal Transforms

Cintra, Renato J.

doi:10.1007/s00034-011-9318-5

Cited by 42 publications

(53 citation statements)

References 48 publications

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“…Then, employing the parametric-based optimization method described in [14], [17], we can derive an approximation for F 8 . The two constraints that were imposed on the proposed approximation are: (i) nearorthogonality and (ii) low-complexity.…”

Section: Low-complexity 8-point Dft Approximationmentioning

confidence: 99%

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Multi-beam receiver apertures using multiplierless 8-point approximate DFT

Kulasekera

Madanayake

Suarez

et al. 2015

2015 IEEE Radar Conference (RadarCon)

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Section: Low-complexity 8-point Dft Approximationmentioning

confidence: 99%

“…An 8-point approximate DFT was recently introduced in [13], being capable of small computational error [14]. At the same time, the implied computations are performed without multiplications [13].…”

Section: Introductionmentioning

confidence: 99%

Multi-beam receiver apertures using multiplierless 8-point approximate DFT

Kulasekera

Madanayake

Suarez

et al. 2015

2015 IEEE Radar Conference (RadarCon)

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“…The entries of the resulting transformation matrix are defined over {0, ±1}, therefore it is completely multiplierless. Above transformation can be orthogonalized according to the procedure described in [3,27,38].…”

Section: Definitionmentioning

confidence: 99%

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

Silveira

Oliveira

Bayer

et al. 2016

SIViP

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An orthogonal 16-point approximate discrete cosine transform (DCT) is introduced. The proposed transform requires neither multiplications nor bit-shifting operations. A fast algorithm based on matrix factorization is introduced, requiring only 44 additions-the lowest arithmetic cost in literature. To assess the introduced transform, computational complexity, similarity with the exact DCT, and coding performance measures are computed. Classical and state-of-the-art 16-point low-complexity transforms were used in a comparative analysis. In the context of image compression, the proposed approximation was evaluated via PSNR and SSIM measurements, attaining the best cost-benefit ratio among the competitors. For video encoding, the proposed approximation was embedded into a HEVC reference software for direct comparison with the original HEVC standard. Physically realized and tested using FPGA hardware, the proposed transform showed 35% and 37% improvements of area-time and area-time-squared VLSI metrics when compared to the best competing transform in the literature. IntroductionThe discrete cosine transform (DCT) [1, 2] is a fundamental building-block for several image and video processing applications. In fact, the DCT closely approximates the Karhunen-Loève transform (KLT) [1], which is capable of optimal data decorrelation and energy compaction of first-order stationary Markov signals [1].This class of signals is particularly appropriate for the modeling of natural images [1,3]. Thus, the DCT finds applications in several contemporary image and video compression standards, such as the JPEG [4] and the H.26x family of codecs [5][6][7]. Indeed, several fast algorithms for computing the exact DCT were proposed [8][9][10][11][12][13][14][15]. However, these methods require the use of arithmetic multipliers [16,17], which are time, power, and hardware demanding arithmetic operations, when compared to additions or bit-shifting operations [18].

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“…Among several orthogonalization methods [61,62], we separate the one based on the polar decomposition [63,64]. To orthogonalize T (α) 8 , such procedure requires only one matrix given by [65]:…”

Section: Orthogonality or Near Orthogonalitymentioning

confidence: 99%

“…where √ · denotes the matrix square root operation [53,66]. The resulting orthogonal DCT approximation is furnished by [40,48,49,65]:…”

Section: Orthogonality or Near Orthogonalitymentioning

confidence: 99%

A class of DCT approximations based on the Feig–Winograd algorithm

2015

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A new class of matrices based on a parametrization of the Feig-Winograd factorization of 8-point DCT is proposed. Such parametrization induces a matrix subspace, which unifies a number of existing methods for DCT approximation. By solving a comprehensive multicriteria optimization problem, we identified several new DCT approximations. Obtained solutions were sought to possess the following properties: (i) low multiplierless computational complexity, (ii) orthogonality or near orthogonality, (iii) low complexity invertibility, and (iv) close proximity and performance to the exact DCT. Proposed approximations were submitted to assessment in terms of proximity to the DCT, coding performance, and suitability for image compression. Considering Pareto efficiency, particular new proposed approximations could outperform various existing methods archived in literature.

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An Integer Approximation Method for Discrete Sinusoidal Transforms

Cited by 42 publications

References 48 publications

Multi-beam receiver apertures using multiplierless 8-point approximate DFT

Multi-beam receiver apertures using multiplierless 8-point approximate DFT

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

A class of DCT approximations based on the Feig–Winograd algorithm

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