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

Multidim Syst Sign Process

et al. 2018

The principal component analysis (PCA) is widely used for data decorrelation and dimensionality reduction. However, the use of PCA may be impractical in real-time applications, or in situations were energy and computing constraints are severe. In this context, the discrete cosine transform (DCT) becomes a low-cost alternative to data decorrelation. This paper presents a method to derive computationally efficient approximations to the DCT. The proposed method aims at the minimization of the angle between the rows of the exact DCT matrix and the rows of the approximated transformation matrix. The resulting transformations matrices are orthogonal and have extremely low arithmetic complexity. Considering popular performance measures, one of the proposed transformation matrices outperforms the best competitors in both matrix error and coding capabilities. Practical applications in image and video coding demonstrate the relevance of the proposed transformation. In fact, we show that the proposed approximate DCT can outperform the exact DCT for image encoding under certain compression ratios. The proposed transform and its direct competitors are also physically realized as digital prototype circuits using FPGA technology.

Section: Fast Algorithmmentioning

confidence: 88%

Low-complexity 8-point DCT approximation based on angle similarity for image and video coding

Oliveira

Multidim Syst Sign Process

et al. 2018

“…Some important and well-known DCT approximations are nonorthogonal [30,34]. Nevertheless, such transformations are nearly orthogonal [39,54]. Let A be a square matrix.…”

Section: Near Orthogonalitymentioning

confidence: 99%

Low-Complexity Loeffler DCT Approximations for Image and Video Coding

Coelho

et al. 2018

JLPEA

This paper introduced a matrix parametrization method based on the Loeffler discrete cosine transform (DCT) algorithm. As a result, a new class of 8-point DCT approximations was proposed, capable of unifying the mathematical formalism of several 8-point DCT approximations archived in the literature. Pareto-efficient DCT approximations are obtained through multicriteria optimization, where computational complexity, proximity, and coding performance are considered. Efficient approximations and their scaled 16- and 32-point versions are embedded into image and video encoders, including a JPEG-like codec and H.264/AVC and H.265/HEVC standards. Results are compared to the unmodified standard codecs. Efficient approximations are mapped and implemented on a Xilinx VLX240T FPGA and evaluated for area, speed, and power consumption.

“…These metrics are relevant, because they quantify the transform capacity of removing signal redundancy, as well as data compression and decorrelation [53]. Hence, following the methodology in [54], we propose the following multicriteria optimization problem:…”

Section: Optimization Problemmentioning

confidence: 99%

Low-Complexity Image and Video Coding Based on an Approximate Discrete Tchebichef Transform

Oliveira

IEEE Trans. Circuits Syst. Video Technol.

et al. 2017

The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The DTT transform kernel does not depend on the input data and fast algorithms can be developed to real time applications. However, the DTT fast algorithm presented in literature possess high computational complexity. In this work, we introduce a new low-complexity approximation for the DTT. The fast algorithm of the proposed transform is multiplication-free and requires a reduced number of additions and bit-shifting operations. Image and video compression simulations in popular standards shows good performance of the proposed transform. Regarding hardware resource consumption for FPGA shows 43.1% reduction of configurable logic blocks and ASIC place and route realization shows 57.7% reduction in the area-time figure when compared with the 2-D version of the exact DTT. KeywordsApproximate transforms, discrete Tchebichef transform, fast algorithms, image and video coding * Paulo A. M. Oliveira is with the Signal Processing Group,