835 research outputs found

    Low-Power Computer Vision: Improve the Efficiency of Artificial Intelligence

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    Energy efficiency is critical for running computer vision on battery-powered systems, such as mobile phones or UAVs (unmanned aerial vehicles, or drones). This book collects the methods that have won the annual IEEE Low-Power Computer Vision Challenges since 2015. The winners share their solutions and provide insight on how to improve the efficiency of machine learning systems

    ํšจ์œจ์ ์ธ ์ถ”๋ก ์„ ์œ„ํ•œ ํ•˜๋“œ์›จ์–ด ์นœํ™”์  ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ ๋ฐ ๊ฐ€์†๊ธฐ ์„ค๊ณ„

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    ํ•™์œ„๋…ผ๋ฌธ (๋ฐ•์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ์ „๊ธฐยท์ •๋ณด๊ณตํ•™๋ถ€, 2020. 8. ์ดํ˜์žฌ.๋จธ์‹  ๋Ÿฌ๋‹ (Machine Learning) ๋ฐฉ๋ฒ• ์ค‘ ํ˜„์žฌ ๊ฐ€์žฅ ์ฃผ๋ชฉ๋ฐ›๊ณ  ์žˆ๋Š” ๋”ฅ๋Ÿฌ๋‹(Deep Learning)์— ๊ด€ํ•œ ์—ฐ๊ตฌ๋“ค์ด ํ•˜๋“œ์›จ์–ด์™€ ์†Œํ”„ํŠธ์›จ์–ด ๋‘ ์ธก๋ฉด์—์„œ ๋ชจ๋‘ ํ™œ๋ฐœํ•˜๊ฒŒ ์ง„ํ–‰๋˜๊ณ  ์žˆ๋‹ค. ๋†’์€ ์„ฑ๋Šฅ์„ ์œ ์ง€ํ•˜๋ฉด์„œ๋„ ํšจ์œจ์ ์œผ๋กœ ์ถ”๋ก ์„ ํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ๋ชจ๋ฐ”์ผ์šฉ ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ(Neural Network Architecture) ์„ค๊ณ„ ๋ฐ ํ•™์Šต๋œ ๋ชจ๋ธ ์••์ถ• ๋“ฑ ์†Œํ”„ํŠธ์›จ์–ด ์ธก๋ฉด์—์„œ์˜ ์ตœ์ ํ™” ๋ฐฉ๋ฒ•๋“ค์ด ์—ฐ๊ตฌ๋˜๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋ฏธ ํ•™์Šต๋œ ๋”ฅ๋Ÿฌ๋‹ ๋ชจ๋ธ์ด ์ฃผ์–ด์กŒ์„ ๋•Œ ๋น ๋ฅธ ์ถ”๋ก ๊ณผ ๋†’์€ ์—๋„ˆ์ง€ํšจ์œจ์„ฑ์„ ๊ฐ–๋Š” ๊ฐ€์†๊ธฐ๋ฅผ ์„ค๊ณ„ํ•˜๋Š” ํ•˜๋“œ์›จ์–ด ์ธก๋ฉด์—์„œ์˜ ์—ฐ๊ตฌ๊ฐ€ ๋™์‹œ์— ์ง„ํ–‰๋˜๊ณ  ์žˆ๋‹ค. ์ด๋Ÿฌํ•œ ๊ธฐ์กด์˜ ์ตœ์ ํ™” ๋ฐ ์„ค๊ณ„ ๋ฐฉ๋ฒ•์—์„œ ๋” ๋‚˜์•„๊ฐ€ ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ์ƒˆ๋กœ์šด ํ•˜๋“œ์›จ์–ด ์„ค๊ณ„ ๊ธฐ์ˆ ๊ณผ ๋ชจ๋ธ ๋ณ€ํ™˜ ๋ฐฉ๋ฒ• ๋“ฑ์„ ์ ์šฉํ•˜์—ฌ ๋” ํšจ์œจ์ ์ธ ์ถ”๋ก  ์‹œ์Šคํ…œ์„ ๋งŒ๋“œ๋Š” ๊ฒƒ์„ ๋ชฉํ‘œ๋กœ ํ•œ๋‹ค. ์ฒซ ๋ฒˆ์งธ, ์ƒˆ๋กœ์šด ํ•˜๋“œ์›จ์–ด ์„ค๊ณ„ ๋ฐฉ๋ฒ•์ธ ํ™•๋ฅ  ์ปดํ“จํŒ…(Stochastic computing)์„ ๋„์ž…ํ•˜์—ฌ ๋” ํšจ์œจ์ ์ธ ๋”ฅ๋Ÿฌ๋‹ ๊ฐ€์† ํ•˜๋“œ์›จ์–ด๋ฅผ ์„ค๊ณ„ํ•˜์˜€๋‹ค. ํ™•๋ฅ  ์ปดํ“จํŒ…์€ ํ™•๋ฅ  ์—ฐ์‚ฐ์— ๊ธฐ๋ฐ˜์„ ๋‘” ์ƒˆ๋กœ์šด ํšŒ๋กœ ์„ค๊ณ„ ๋ฐฉ๋ฒ•์œผ๋กœ ๊ธฐ์กด์˜ ์ด์ง„ ์—ฐ์‚ฐ ํšŒ๋กœ(Binary system)๋ณด๋‹ค ํ›จ์”ฌ ๋” ์ ์€ ํŠธ๋žœ์ง€์Šคํ„ฐ๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๋™์ผํ•œ ์—ฐ์‚ฐ ํšŒ๋กœ๋ฅผ ๊ตฌํ˜„ํ•  ์ˆ˜ ์žˆ๋‹ค๋Š” ์žฅ์ ์ด ์žˆ๋‹ค. ํŠนํžˆ, ๋”ฅ๋Ÿฌ๋‹์—์„œ ๊ฐ€์žฅ ๋งŽ์ด ์‚ฌ์šฉ๋˜๋Š” ๊ณฑ์…ˆ ์—ฐ์‚ฐ์„ ์œ„ํ•˜์—ฌ ์ด์ง„ ์—ฐ์‚ฐ ํšŒ๋กœ์—์„œ๋Š” ๋ฐฐ์—ด ์Šน์‚ฐ๊ธฐ(Array Multiplier)๋ฅผ ํ•„์š”๋กœ ํ•˜์ง€๋งŒ ํ™•๋ฅ  ์ปดํ“จํŒ…์—์„œ๋Š” AND ๊ฒŒ์ดํŠธํ•˜๋‚˜๋กœ ๊ตฌํ˜„์ด ๊ฐ€๋Šฅํ•˜๋‹ค. ์„ ํ–‰ ์—ฐ๊ตฌ๋“ค์ด ํ™•๋ฅ  ์ปดํ“จํŒ… ํšŒ๋กœ๋ฅผ ๊ธฐ๋ฐ˜ํ•œ ๋”ฅ๋Ÿฌ๋‹ ๊ฐ€์†๊ธฐ๋“ค์„ ์„ค๊ณ„ํ•˜๊ณ  ์žˆ๋Š”๋ฐ, ์ธ์‹๋ฅ ์ด ์ด์ง„ ์—ฐ์‚ฐ ํšŒ๋กœ์— ๋น„ํ•˜์—ฌ ๋งŽ์ด ๋’ค์ณ์ง€๋Š” ๊ฒฐ๊ณผ๋ฅผ ๋ณด์—ฌ์ฃผ์—ˆ๋‹ค. ์ด๋Ÿฌํ•œ ๋ฌธ์ œ๋“ค์„ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ์—ฐ์‚ฐ์˜ ์ •ํ™•๋„๋ฅผ ๋” ๋†’์ผ ์ˆ˜ ์žˆ๋„๋ก ๋‹จ๊ทน์„ฑ ๋ถ€ํ˜ธํ™”(Unipolar encoding) ๋ฐฉ๋ฒ•์„ ํ™œ์šฉํ•˜์—ฌ ๊ฐ€์†๊ธฐ๋ฅผ ์„ค๊ณ„ํ•˜์˜€๊ณ , ํ™•๋ฅ  ์ปดํ“จํŒ… ์ˆซ์ž ์ƒ์„ฑ๊ธฐ (Stochastic number generator)์˜ ์˜ค๋ฒ„ํ—ค๋“œ๋ฅผ ์ค„์ด๊ธฐ ์œ„ํ•˜์—ฌ ํ™•๋ฅ  ์ปดํ“จํŒ… ์ˆซ์ž ์ƒ์„ฑ๊ธฐ๋ฅผ ์—ฌ๋Ÿฌ ๊ฐœ์˜ ๋‰ด๋Ÿฐ์ด ๊ณต์œ ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•˜์˜€๋‹ค. ๋‘ ๋ฒˆ์งธ, ๋” ๋†’์€ ์ถ”๋ก  ์†๋„ ํ–ฅ์ƒ์„ ์œ„ํ•˜์—ฌ ํ•™์Šต๋œ ๋”ฅ๋Ÿฌ๋‹ ๋ชจ๋ธ์„ ์••์ถ•ํ•˜๋Š” ๋ฐฉ๋ฒ• ๋Œ€์‹ ์— ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ๋ฅผ ๋ณ€ํ™˜ ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์‹œํ•˜์˜€๋‹ค. ์„ ํ–‰ ์—ฐ๊ตฌ๋“ค์˜ ๊ฒฐ๊ณผ๋ฅผ ๋ณด๋ฉด, ํ•™์Šต๋œ ๋ชจ๋ธ์„ ์••์ถ•ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ตœ์‹  ๊ตฌ์กฐ๋“ค์— ์ ์šฉํ•˜๊ฒŒ ๋˜๋ฉด ๊ฐ€์ค‘์น˜ ํŒŒ๋ผ๋ฏธํ„ฐ(Weight Parameter)์—๋Š” ๋†’์€ ์••์ถ•๋ฅ ์„ ๋ณด์—ฌ์ฃผ์ง€๋งŒ ์‹ค์ œ ์ถ”๋ก  ์†๋„ ํ–ฅ์ƒ์—๋Š” ๋ฏธ๋ฏธํ•œ ํšจ๊ณผ๋ฅผ ๋ณด์—ฌ์ฃผ์—ˆ๋‹ค. ์‹ค์งˆ์ ์ธ ์†๋„ ํ–ฅ์ƒ์ด ๋ฏธํกํ•œ ๊ฒƒ์€ ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ๊ฐ€ ๊ฐ€์ง€๊ณ  ์žˆ๋Š” ๊ตฌ์กฐ์ƒ์˜ ํ•œ๊ณ„์—์„œ ๋ฐœ์ƒํ•˜๋Š” ๋ฌธ์ œ์ด๊ณ , ์ด๊ฒƒ์„ ํ•ด๊ฒฐํ•˜๋ ค๋ฉด ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ๋ฅผ ๋ฐ”๊พธ๋Š”๊ฒƒ์ด ๊ฐ€์žฅ ๊ทผ๋ณธ์ ์ธ ํ•ด๊ฒฐ์ฑ…์ด๋‹ค. ์ด๋Ÿฌํ•œ ๊ด€์ฐฐ ๊ฒฐ๊ณผ๋ฅผ ํ† ๋Œ€๋กœ ๋ณธ ๋…ผ๋ฌธ์—์„œ๋Š” ์„ ํ–‰์—ฐ๊ตฌ๋ณด๋‹ค ๋” ๋†’์€ ์†๋„ ํ–ฅ์ƒ์„ ์œ„ํ•˜์—ฌ ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ๋ฅผ ๋ณ€ํ™˜ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•˜์˜€๋‹ค. ๋งˆ์ง€๋ง‰์œผ๋กœ, ๊ฐ ์ธต๋งˆ๋‹ค ์„œ๋กœ ๋‹ค๋ฅธ ๊ตฌ์กฐ๋ฅผ ๊ฐ€์งˆ ์ˆ˜ ์žˆ๋„๋ก ํƒ์ƒ‰ ๋ฒ”์œ„๋ฅผ ๋” ํ™•์žฅ์‹œํ‚ค๋ฉด์„œ๋„ ํ•™์Šต์„ ๊ฐ€๋Šฅํ•˜๊ฒŒ ํ•˜๋Š” ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ ํƒ์ƒ‰ ๋ฐฉ๋ฒ•์„ ์ œ์‹œํ•˜์˜€๋‹ค. ์„ ํ–‰ ์—ฐ๊ตฌ์—์„œ์˜ ์‹ ๊ฒฝ๋ง ๊ตฌ์กฐ ํƒ์ƒ‰์€ ๊ธฐ๋ณธ ๋‹จ์œ„์ธ ์…€(Cell)์˜ ๊ตฌ์กฐ๋ฅผ ํƒ์ƒ‰ํ•˜๊ณ , ๊ทธ ๊ฒฐ๊ณผ๋ฅผ ๋ณต์‚ฌํ•˜์—ฌ ํ•˜๋‚˜์˜ ํฐ ์‹ ๊ฒฝ๋ง์œผ๋กœ ๋งŒ๋“œ๋Š” ๋ฐฉ๋ฒ•์„ ์ด์šฉํ•œ๋‹ค. ํ•ด๋‹น ๋ฐฉ๋ฒ•์€ ํ•˜๋‚˜์˜ ์…€ ๊ตฌ์กฐ๋งŒ ์‚ฌ์šฉ๋˜๊ธฐ ๋•Œ๋ฌธ์— ์œ„์น˜์— ๋”ฐ๋ฅธ ์ž…๋ ฅ ํŠน์„ฑ๋งต(Input Feature Map)์˜ ํฌ๊ธฐ๋‚˜ ๊ฐ€์ค‘์น˜ ํŒŒ๋ผ๋ฏธํ„ฐ์˜ ํฌ๊ธฐ ๋“ฑ์— ๊ด€ํ•œ ์ •๋ณด๋Š” ๋ฌด์‹œํ•˜๊ฒŒ ๋œ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ์ด๋Ÿฌํ•œ ๋ฌธ์ œ์ ๋“ค์„ ํ•ด๊ฒฐํ•˜๋ฉด์„œ๋„ ์•ˆ์ •์ ์œผ๋กœ ํ•™์Šต์„ ์‹œํ‚ฌ ์ˆ˜ ์žˆ๋Š” ๋ฐฉ๋ฒ•์„ ์ œ์‹œํ•˜์˜€๋‹ค. ๋˜ํ•œ, ์—ฐ์‚ฐ๋Ÿ‰๋ฟ๋งŒ์•„๋‹ˆ๋ผ ๋ฉ”๋ชจ๋ฆฌ ์ ‘๊ทผ ํšŸ์ˆ˜์˜ ์ œ์•ฝ์„ ์ฃผ์–ด ๋” ํšจ์œจ์ ์ธ ๊ตฌ์กฐ๋ฅผ ์ฐพ์„ ์ˆ˜ ์žˆ๋„๋ก ๋„์™€์ฃผ๋Š” ํŽ˜๋„ํ‹ฐ(Penalty)๋ฅผ ์ƒˆ๋กœ์ด ๊ณ ์•ˆํ•˜์˜€๋‹ค.Deep learning is the most promising machine learning algorithm, and it is already used in real life. Actually, the latest smartphone use a neural network for better photograph and voice recognition. However, as the performance of the neural network improved, the hardware cost dramatically increases. Until the past few years, many researches focus on only a single side such as hardware or software, so its actual cost is hardly improved. Therefore, hardware and software co-optimization is needed to achieve further improvement. For this reason, this dissertation proposes the efficient inference system considering the hardware accelerator to the network architecture design. The first part of the dissertation is a deep neural network accelerator with stochastic computing. The main goal is the efficient stochastic computing hardware design for a convolutional neural network. It includes stochastic ReLU and optimized max function, which are key components in the convolutional neural network. To avoid the range limitation problem of stochastic numbers and increase the signal-to-noise ratio, we perform weight normalization and upscaling. In addition, to reduce the overhead of binary-to-stochastic conversion, we propose a scheme for sharing stochastic number generators among the neurons in the convolutional neural network. The second part of the dissertation is a neural architecture transformation. The network recasting is proposed, and it enables the network architecture transformation. The primary goal of this method is to accelerate the inference process through the transformation, but there can be many other practical applications. The method is based on block-wise recasting; it recasts each source block in a pre-trained teacher network to a target block in a student network. For the recasting, a target block is trained such that its output activation approximates that of the source block. Such a block-by-block recasting in a sequential manner transforms the network architecture while preserving accuracy. This method can be used to transform an arbitrary teacher network type to an arbitrary student network type. It can even generate a mixed-architecture network that consists of two or more types of block. The network recasting can generate a network with fewer parameters and/or activations, which reduce the inference time significantly. Naturally, it can be used for network compression by recasting a trained network into a smaller network of the same type. The third part of the dissertation is a fine-grained neural architecture search. InheritedNAS is the fine-grained architecture search method, and it uses the coarsegrained architecture that is found from the cell-based architecture search. Basically, fine-grained architecture has a very large search space, so it is hard to find directly. A stage independent search is proposed, and this method divides the entire network to several stages and trains each stage independently. To break the dependency between each stage, a two-point matching distillation method is also proposed. And then, operation pruning is applied to remove the unimportant operation. The block-wise pruning method is used to remove the operations rather than the node-wise pruning. In addition, a hardware-aware latency penalty is proposed, and it covers not only FLOPs but also memory access.1 Introduction 1 1.1 DNN Accelerator with Stochastic Computing 2 1.2 Neural Architecture Transformation 4 1.3 Fine-Grained Neural Architecture Search 6 2 Background 8 2.1 Stochastic Computing 8 2.2 Neural Network 10 2.2.1 Network Compression 10 2.2.2 Neural Network Accelerator 13 2.3 Knowledge Distillation 17 2.4 Neural Architecture Search 19 3 DNN Accelerator with Stochastic Computing 23 3.1 Motivation 23 3.1.1 Multiplication Error on Stochastic Computing 23 3.1.2 DNN with Stochastic Computing 24 3.2 Unipolar SC Hardware for CNN 25 3.2.1 Overall Hardware Design 25 3.2.2 Stochastic ReLU function 27 3.2.3 Stochastic Max function 30 3.2.4 Efficient Average Function 36 3.3 Weight Modulation for SC Hardware 38 3.3.1 Weight Normalization for SC 38 3.3.2 Weight Upscaling for Output Layer 43 3.4 Early Decision Termination 44 3.5 Stochastic Number Generator Sharing 49 3.6 Experiments 53 3.6.1 Accuracy of CNN using Unipolar SC 53 3.6.2 Synthesis Result 57 3.7 Summary 58 4 Neural Architecture Transformation 59 4.1 Motivation 59 4.2 Network Recasting 61 4.2.1 Recasting from DenseNet to ResNet and ConvNet 63 4.2.2 Recasting from ResNet to ConvNet 63 4.2.3 Compression 63 4.2.4 Block Training 65 4.2.5 Sequential Recasting and Fine-tuning 67 4.3 Experiments 69 4.3.1 Visualization of Filter Reduction 70 4.3.2 CIFAR 71 4.3.3 ILSVRC2012 73 4.4 Summary 76 5 Fine-Grained Neural Architecture Search 77 5.1 Motivation 77 5.1.1 Search Space Reduction Versus Diversity 77 5.1.2 Hardware-Aware Optimization 78 5.2 InheritedNAS 79 5.2.1 Stage Independent Search 79 5.2.2 Operation Pruning 82 5.2.3 Entire Search Procedure 83 5.3 Hardware-aware Penalty Design 85 5.4 Experiments 87 5.4.1 Fine-Grained Architecture Search 88 5.4.2 Penalty Analysis 90 5.5 Summary 92 6 Conclusion 93 Abstract (In Korean) 113Docto

    A Machine Learning-oriented Survey on Tiny Machine Learning

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    The emergence of Tiny Machine Learning (TinyML) has positively revolutionized the field of Artificial Intelligence by promoting the joint design of resource-constrained IoT hardware devices and their learning-based software architectures. TinyML carries an essential role within the fourth and fifth industrial revolutions in helping societies, economies, and individuals employ effective AI-infused computing technologies (e.g., smart cities, automotive, and medical robotics). Given its multidisciplinary nature, the field of TinyML has been approached from many different angles: this comprehensive survey wishes to provide an up-to-date overview focused on all the learning algorithms within TinyML-based solutions. The survey is based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodological flow, allowing for a systematic and complete literature survey. In particular, firstly we will examine the three different workflows for implementing a TinyML-based system, i.e., ML-oriented, HW-oriented, and co-design. Secondly, we propose a taxonomy that covers the learning panorama under the TinyML lens, examining in detail the different families of model optimization and design, as well as the state-of-the-art learning techniques. Thirdly, this survey will present the distinct features of hardware devices and software tools that represent the current state-of-the-art for TinyML intelligent edge applications. Finally, we discuss the challenges and future directions.Comment: Article currently under review at IEEE Acces

    Design of a High-Speed Architecture for Stabilization of Video Captured Under Non-Uniform Lighting Conditions

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    Video captured in shaky conditions may lead to vibrations. A robust algorithm to immobilize the video by compensating for the vibrations from physical settings of the camera is presented in this dissertation. A very high performance hardware architecture on Field Programmable Gate Array (FPGA) technology is also developed for the implementation of the stabilization system. Stabilization of video sequences captured under non-uniform lighting conditions begins with a nonlinear enhancement process. This improves the visibility of the scene captured from physical sensing devices which have limited dynamic range. This physical limitation causes the saturated region of the image to shadow out the rest of the scene. It is therefore desirable to bring back a more uniform scene which eliminates the shadows to a certain extent. Stabilization of video requires the estimation of global motion parameters. By obtaining reliable background motion, the video can be spatially transformed to the reference sequence thereby eliminating the unintended motion of the camera. A reflectance-illuminance model for video enhancement is used in this research work to improve the visibility and quality of the scene. With fast color space conversion, the computational complexity is reduced to a minimum. The basic video stabilization model is formulated and configured for hardware implementation. Such a model involves evaluation of reliable features for tracking, motion estimation, and affine transformation to map the display coordinates of a stabilized sequence. The multiplications, divisions and exponentiations are replaced by simple arithmetic and logic operations using improved log-domain computations in the hardware modules. On Xilinx\u27s Virtex II 2V8000-5 FPGA platform, the prototype system consumes 59% logic slices, 30% flip-flops, 34% lookup tables, 35% embedded RAMs and two ZBT frame buffers. The system is capable of rendering 180.9 million pixels per second (mpps) and consumes approximately 30.6 watts of power at 1.5 volts. With a 1024ร—1024 frame, the throughput is equivalent to 172 frames per second (fps). Future work will optimize the performance-resource trade-off to meet the specific needs of the applications. It further extends the model for extraction and tracking of moving objects as our model inherently encapsulates the attributes of spatial distortion and motion prediction to reduce complexity. With these parameters to narrow down the processing range, it is possible to achieve a minimum of 20 fps on desktop computers with Intel Core 2 Duo or Quad Core CPUs and 2GB DDR2 memory without a dedicated hardware

    Development Of Efficient Multi-Level Discrete Wavelet Transform Hardware Architecture For Image Compression

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    Berfokuskan pengkomputeran intensif dalam gelombang kecil diskret (DWT), reka bentuk seni bina perkakasan efisen bagi pengkomputeran laju menjadi imperatif terutamanya dalam aplikasi masa nyata. Focusing on the intensive computations involved in the discrete wavelet transform (DWT), the design of efficient hardware architectures for a fast computation of the transform has become imperative, especially for real-time applications
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