A multiplierless pruned DCT-like transformation for image and video compression that requires ten additions only

Coutinho, Vítor A.; Cintra, Renato J.; Bayer, Fábio M.; Kulasekera, Sunera; Madanayake, Arjuna

doi:10.1007/s11554-015-0492-8

Cited by 22 publications

(6 citation statements)

References 41 publications

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“…To the best of our knowledge, we cannot identify any methodology that could furnish necessary mathematical tools to design optimal approximations for image compression in an a priori manner, i.e., before search space approaches, optimization problem solving, or numerical simulation. In [3,5,25,61,79,80], a large number of methods is listed; all of them aim at good approximations. Although the problem of matrix approximation is quite simple to state, it is also very tricky and offers several non-linearities when combined to a more sophisticate system, such as image compression codecs.…”

Section: Discussionmentioning

confidence: 99%

“…For instance, a single image frame of high-definition TV (HDTV) contains 32.400 8×8 image subblocks. Therefore, computational savings in the DCT step may effect significant performance gains, both in terms of speed and power consumption [24,25]. Being quite a mature area of research [26], there is little room for improvement on the exact DCT computation.…”

Section: Introductionmentioning

confidence: 99%

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

Oliveira

Cintra

Bayer

et al. 2018

Multidim Syst Sign Process

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Oliveira

Cintra

Bayer

et al. 2018

Multidim Syst Sign Process

Self Cite

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“…Even error resilient DCTs have already been proposed [25], [26]. Image encoding algorithms used for instance in JPEG encoding generally compute the DCT per pixel blocks.…”

Section: A Conventional Dctmentioning

confidence: 99%

Design and Applications of Approximate Circuits by Gate-Level Pruning

Schlachter

Camus

Palem

et al. 2017

IEEE Trans. VLSI Syst.

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Abstract-Energy-efficiency is a critical concern for many systems, ranging from IoT objects and mobile devices to highperformance computers. Moreover, after 40 years of prosperity, Moore's law is starting to show its economic and technical limits. Noticing that many circuits are over-engineered and that many applications are error-resilient or require less precision than offered by the existing hardware, approximate computing has emerged as a potential solution to pursue improvements of digital circuits. In this regard, a technique to systematically trade off accuracy in exchange for area, power and delay savings in digital circuits is proposed: Gate-Level Pruning. A CAD tool is build and integrated into a standard digital flow to offer a wide range of costs-accuracy tradeoffs for any conventional design. The methodology is first demonstrated on adders, achieving up to 78 % energy-delay-area reduction for 10 % mean relative error. It is then detailed how this methodology can be applied on a more complex system composed of a multitude of arithmetic blocks and memory: the Discrete Cosine Transform (DCT), which is a key building block for image and video processing applications. Even though arithmetic circuits represent less than 4 % of the entire DCT area, it is shown that the Gate-Level Pruning technique can lead to 21 % energy-delay-area savings over the entire system for a reasonable image quality loss of 24 dB. This significant saving is achieved thanks to the pruned arithmetic circuits which sets some nodes at constant values, enabling the synthesis tool to further simplify the circuit and memory.

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“…In the past few years, several works proposed low-complexity DCT approximations, mostly of length 8, capable of compromising between arithmetic complexity and coding efficiency [5, 10-14, 19, 28, 40, 48, 60]. Most of these linear transformation matrices have entries defined over the set C = {0,± 1 2 ,±1,±2}, and, thus, can be implemented using only addition and bit-shifting operations [13,19,21]. Indeed, multiplication-free transforms are remarkable for reducing circuitry, chip area, and power consumption in hardware implementations [35,53].…”

Section: Introductionmentioning

confidence: 99%

“…On the one hand, the RDCT outperforms the current state-of-the-art lowcomplexity DCT approximations in terms of energy compaction properties [35,47] at the expense of 22 additions. On the other hand, the MRDCT is a very low-complexity DCT-like transform that requires only 14 additions, the lowest arithmetic cost among the meaningful approximate DCTs archived in literature [21,23].…”

Section: Introductionmentioning

confidence: 99%

A Class of Low-complexity DCT-like Transforms for Image and Video Coding

da Silveira,

Canterle,

Coelho

et al. 2022

Preprint

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The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards-such as JPEG and HEVC-adopt the DCT as a fundamental building block for compression. Recent works have introduced low-complexity approximations for the DCT, which become paramount in applications demanding real-time computation and low-power consumption. The design of DCT approximations involves a trade-off between computational complexity and performance. This paper introduces a new multiparametric transform class encompassing the round-off DCT (RDCT) and the modified RDCT (MRDCT), two relevant multiplierless 8-point approximate DCTs. The associated fast algorithm is provided. Four novel orthogonal lowcomplexity 8-point DCT approximations are obtained by solving a multicriteria optimization problem. The optimal 8-point transforms are scaled to lengths 16 and 32 while keeping the arithmetic complexity low. The proposed methods are assessed by proximity and coding measures with respect to the exact DCT. Image and video coding experiments hardware realization are performed. The novel transforms perform close to or outperform the current state-of-the-art DCT approximations.

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A multiplierless pruned DCT-like transformation for image and video compression that requires ten additions only

Cited by 22 publications

References 41 publications

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

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

Design and Applications of Approximate Circuits by Gate-Level Pruning

A Class of Low-complexity DCT-like Transforms for Image and Video Coding

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