T. L. T. da Silveira

T. L. T. da Silveira, F. M. Bayer, R. J. Cintra et al.

A low-complexity orthogonal multiplierless approximation for the 16-point discrete cosine transform (DCT) was introduced. The proposed method was designed to possess a very low computational cost. A fast algorithm based on matrix factorization was proposed requiring only 60~additions. The proposed architecture outperforms classical and state-of-the-art algorithms when assessed as a tool for image and video compression. Digital VLSI hardware implementations were also proposed being physically realized in FPGA technology and implemented in 45 nm up to synthesis and place-route levels. Additionally, the proposed method was embedded into a high efficiency video coding (HEVC) reference software for actual proof-of-concept. Obtained results show negligible video degradation when compared to Chen DCT algorithm in HEVC.

C. J. Tablada, T. L. T. da Silveira, R. J. Cintra et al.

In this paper, two 8-point multiplication-free DCT approximations based on the Chen's factorization are proposed and their fast algorithms are also derived. Both transformations are assessed in terms of computational cost, error energy, and coding gain. Experiments with a JPEG-like image compression scheme are performed and results are compared with competing methods. The proposed low-complexity transforms are scaled according to Jridi-Alfalou-Meher algorithm to effect 16- and 32-point approximations. The new sets of transformations are embedded into an HEVC reference software to provide a fully HEVC-compliant video coding scheme. We show that approximate transforms can outperform traditional transforms and state-of-the-art methods at a very low complexity cost.

A. P. Radünz, T. L. T. da Silveira, F. M. Bayer et al.

The Karhunen-Loève transform (KLT) is often used for data decorrelation and dimensionality reduction. The KLT is able to optimally retain the signal energy in only few transform components, being mathematically suitable for image and video compression. However, in practice, because of its high computational cost and dependence on the input signal, its application in real-time scenarios is precluded. This work proposes low-computational cost approximations for the KLT. We focus on the blocklengths $N \in \{4, 8, 16, 32 \}$ because they are widely employed in image and video coding standards such as JPEG and high efficiency video coding (HEVC). Extensive computational experiments demonstrate the suitability of the proposed low-complexity transforms for image and video compression.

D. R. Canterle, T. L. T. da Silveira, F. M. Bayer et al.

Discrete transforms play an important role in many signal processing applications, and low-complexity alternatives for classical transforms became popular in recent years. Particularly, the discrete cosine transform (DCT) has proven to be convenient for data compression, being employed in well-known image and video coding standards such as JPEG, H.264, and the recent high efficiency video coding (HEVC). In this paper, we introduce a new class of low-complexity 8-point DCT approximations based on a series of works published by Bouguezel, Ahmed and Swamy. Also, a multiparametric fast algorithm that encompasses both known and novel transforms is derived. We select the best-performing DCT approximations after solving a multicriteria optimization problem, and submit them to a scaling method for obtaining larger size transforms. We assess these DCT approximations in both JPEG-like image compression and video coding experiments. We show that the optimal DCT approximations present compelling results in terms of coding efficiency and image quality metrics, and require only few addition or bit-shifting operations, being suitable for low-complexity and low-power systems.

R. S. Oliveira, R. J. Cintra, F. M. Bayer et al.

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.