Entropy Coding Research Articles

Quantization and Entropy Coding in the Versatile Video Coding (VVC) Standard

The paper provides an overview of the quantization and entropy coding methods in the Versatile Video Coding (VVC) standard. Special focus is laid on techniques that improve coding efficiency relative to the methods included in the High Efficiency Video Coding (HEVC) standard: The inclusion of trellis-coded quantization, the advanced context modeling for entropy coding of transform coefficient levels, the arithmetic coding engine with multi-hypothesis probability estimation, and the joint coding of chroma residuals. Beside a description of the design concepts, the paper also discusses motivations and implementation aspects. The effectiveness of the quantization and entropy coding methods specified in VVC is validated by experimental results.

An entropy minimization histogram mergence scheme and its application in image compression

In this paper, we propose an entropy minimization histogram mergence (EMHM) scheme that can significantly reduce the number of grayscales with nonzero pixel populations (GSNPP) without visible loss to image quality. We proved in theory that the entropy of an image is reduced after histogram mergence and that the reduction in entropy is maximized using our EMHM. The reduction in image entropy is good for entropy encoding considering that the minimum average code word length per source symbol is the entropy of the source signal according to Shannon’s first theorem. Extensive experimental results show that our EMHM can significantly reduce the code length of entropy coding, such as Huffman, Shannon, and arithmetic coding, by over 20% while preserving the image subjective and objective quality very well. Moreover, the performance of some classic lossy image compression techniques, such as the Joint Photographic Experts Group (JPEG), JPEG2000, and Better Portable Graphics (BPG), can be improved by preprocessing images using our EMHM.

JPEG XS—A New Standard for Visually Lossless Low-Latency Lightweight Image Coding

Joint Photographic Experts Group (JPEG) XS is a new International Standard from the JPEG Committee (formally known as ISO/International Electrotechnical Commission (IEC) JTC1/SC29/WG1). It defines an interoperable, visually lossless low-latency lightweight image coding that can be used for mezzanine compression within any AV market. Among the targeted use cases, one can cite video transport over professional video links (serial digital interface (SDI), internet protocol (IP), and Ethernet), real-time video storage, memory buffers, omnidirectional video capture and rendering, and sensor compression (for example, in cameras and the automotive industry). The core coding system is composed of an optional color transform, a wavelet transform, and a novel entropy encoder, processing groups of coefficients by coding their magnitude level and packing the magnitude refinement. Such a design allows for visually transparent quality at moderate compression ratios, scalable end-to-end latency that ranges from less than one line to a maximum of 32 lines of the image, and a low-complexity real-time implementation in application-specific integrated circuit (ASIC), field-programmable gate array (FPGA), central processing unit (CPU), and graphics processing unit (GPU). This article details the key features of this new standard and the profiles and formats that have been defined so far for the various applications. It also gives a technical description of the core coding system. Finally, the latest performance evaluation results of recent implementations of the standard are presented, followed by the current status of the ongoing standardization process and future milestones.

Polar Lattices for Lossy Compression

In this work, we propose a new construction of polar lattices to achieve the rate-distortion bound of a memoryless Gaussian source. The structure of the proposed polar lattices allows to integrate entropy coding into the lattice quantizer, which greatly simplifies the compression process. The overall complexity of encoding and decoding is O(N log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> N) for any target distortion and fixed rate larger than the rate-distortion bound. Moreover, the nesting structure of polar lattices provides solutions to various multi-terminal coding problems. The Wyner-Ziv coding problem for a Gaussian source can be solved by using a capacity-achieving polar lattice for the Gaussian channel, nested with a rate-distortion bound achieving lattice, while the Gelfand-Pinsker problem can be solved in a reversed manner. The polar lattice quantizer is further extended to extract Wyner's common information of a pair of Gaussian sources or multiple Gaussian sources.

A novel hybrid image encryption–compression scheme by combining chaos theory and number theory

Compression and encryption are often performed together for image sharing and/or storage. The order in which the two operations are carried out affects the overall efficiency of digital image services. For example, the encrypted data has less or no compressibility. On the other hand, it is challenging to ensure reasonable security without downgrading the compression performance. Therefore, incorporating one requirement into another is an interesting approach. In this study, we propose a novel hybrid image encryption and compression scheme that allows compression in the encryption domain. The encryption is based on Chaos theory and is carried out in two steps, i.e., permutation and substitution. The lossless compression is performed on the shuffled image and then the compressed bitstream is grouped into 8-bit elements for substitution stage. The lossless nature of the proposed method makes it suitable for medical image compression and encryption applications. The experimental results shows that the proposed method achieves the necessary level of security and preserves the compression efficiency of a lossless algorithm. In addition, to improve the performance of the entropy encoder of the compression algorithm, we propose a data-to-symbol mapping method based on number theory to represent adjacent pixel values as a block. With such representation, the compression saving is improved on average from 5.76% to 15.45% for UCID dataset.

Lossless ECG Encoder with Multi-Channel Adaptive Fuzzy Predictor and Enhanced Entropy Encoding in Wireless Body Sensor Networks

With the advancement of wireless technology, Wireless Body Sensor Networks, such as Electrocardiograms (ECGs) will serve as state-of-the-art method for electronic-healthcare systems and applications. Like other digital communications, however, ECGs highlight power consumption as the main design constraint and bottleneck as it affects device lifespan and data accuracy. Hence, power reduction and power management techniques and schemes have been developed to eliminate this constraint such as hardware optimization, source and channel coding, signal conditioning, and resolution control. This paper proposes a lossless ECG encoder that combines existing data compression techniques specifically the adaptive fuzzy predictor based on fuzzy decision making and an enhanced entropy encoding that utilizes algorithms in both run length encoding (RLE) and incremental prefix encoding. Simulation results that the proposed scheme outperforms the entropy encoding using Huffman, RLE, and predictive encoding schemes in compression ratio (CR), with the enhanced entropy encoding leading the pre-existing compression techniques by 24.0907 on RLE and 23.6580 on Huffman.

VLSI Implementation of Multi-Channel ECG Lossless Compression System

Electrocardiogram (ECG) is used to record the electrical activity of heart. If the instrument monitoring the signal for a long time, it will produce large amount of data. So, the effective lossless ECG compression system can help to reduce the storage space. This brief presents a hardware architecture of multi-channel lossless ECG compression system. The system is based on the algorithm including multi-channel linear prediction and adaptive linear prediction. Also, Golomb rice code (GRC) is used for entropy coding. The hardware implementation has been designed with low hardware complexity usage while using optimum hardware resources. And the architecture can process multiple channels in parallel that can obtain the high throughput. PTB database has been used for verification and testing purposes. This design was implemented in TSMC 180nm. The implementation results show the gate count is 476K and power consumption is 69.18μW while working frequency is 1 KHz.

Improved JPEG Coding by Filtering 8 × 8 DCT Blocks.

The JPEG format, consisting of a set of image compression techniques, is one of the most commonly used image coding standards for both lossy and lossless image encoding. In this format, various techniques are used to improve image transmission and storage. In the final step of lossy image coding, JPEG uses either arithmetic or Huffman entropy coding modes to further compress data processed by lossy compression. Both modes encode all the 8 × 8 DCT blocks without filtering empty ones. An end-of-block marker is coded for empty blocks, and these empty blocks cause an unnecessary increase in file size when they are stored with the rest of the data. In this paper, we propose a modified version of the JPEG entropy coding. In the proposed version, instead of storing an end-of-block code for empty blocks with the rest of the data, we store their location in a separate buffer and then compress the buffer with an efficient lossless method to achieve a higher compression ratio. The size of the additional buffer, which keeps the information of location for the empty and non-empty blocks, was considered during the calculation of bits per pixel for the test images. In image compression, peak signal-to-noise ratio versus bits per pixel has been a major measure for evaluating the coding performance. Experimental results indicate that the proposed modified algorithm achieves lower bits per pixel while retaining quality.

HEMP: High-order entropy minimization for neural network compression

We formulate the entropy of a quantized artificial neural network as a differentiable function that can be plugged as a regularization term into the cost function minimized by gradient descent. Our formulation scales efficiently beyond the first order and is agnostic of the quantization scheme. The network can then be trained to minimize the entropy of the quantized parameters, so that they can be optimally compressed via entropy coding. We experiment with our entropy formulation at quantizing and compressing well-known network architectures over multiple datasets. Our approach compares favorably over similar methods, enjoying the benefits of higher order entropy estimate, showing flexibility towards non-uniform quantization (we use Lloyd-max quantization), scalability towards any entropy order to be minimized and efficiency in terms of compression. We show that HEMP is able to work in synergy with other approaches aiming at pruning or quantizing the model itself, delivering significant benefits in terms of storage size compressibility without harming the model’s performance.

Steganography algorithm for reversible data hiding using LSB and reversible image transformation

We present another reversible (lossless) information stowing away (inserting) strategy that takes into consideration careful recuperation of the first host signal after the implanted data is separated. The information installing approach is proposed as a speculation of the notable LSB (least significant cycle) update, which includes extra working focuses the limit contortion bend. Compacting portions of the sign that are helpless against installing spillage and dispersing these packed subtleties as a feature of the inserted payload considers lossless recovery of the first. The pressure effectiveness and in this manner the lossless information implanting capacity of a forecast based restrictive entropy coder that utilizes static segments of the host as side-data improves.

Modified Hilbert Curve for Rectangles and Cuboids and Its Application in Entropy Coding for Image and Video Compression.

In our previous work, by combining the Hilbert scan with the symbol grouping method, efficient run-length-based entropy coding was developed, and high-efficiency image compression algorithms based on the entropy coding were obtained. However, the 2-D Hilbert curves, which are a critical part of the above-mentioned entropy coding, are defined on squares with the side length being the powers of 2, i.e., 2n, while a subband is normally a rectangle of arbitrary sizes. It is not straightforward to modify the Hilbert curve from squares of side lengths of 2n to an arbitrary rectangle. In this short article, we provide the details of constructing the modified 2-D Hilbert curve of arbitrary rectangle sizes. Furthermore, we extend the method from a 2-D rectangle to a 3-D cuboid. The 3-D modified Hilbert curves are used in a novel 3-D transform video compression algorithm that employs the run-length-based entropy coding. Additionally, the modified 2-D and 3-D Hilbert curves introduced in this short article could be useful for some unknown applications in the future.

Low-Complexity Rate-Distortion Optimization for HEVC Encoders

Typical high efficiency video coding (HEVC) encoders use rate-distortion optimization (RDO) to select the best coding parameters among numerous candidates to achieve high compression efficiency. However, calculating the rate-distortion cost for each coding parameter entails high computational complexity, which limits the real-time application of these encoders. In this study, time-consuming processes, such as reconstruction and entropy coding, are removed during the calculation of the full RD cost to reduce the complexity of the encoder. Instead, RD costs are estimated for transformed coefficients by using the RD cost model, which is made up of a distortion model based on the distribution features of the transformed coefficients, a residual rate model based on the characteristics of the entropy coding module, and a simple and convenient header rate model. In addition to the full RD cost, typical encoders also adopt fast RD cost, which is composed of the sum of absolute transform differences (SATD) and header bit. To further reduce encoding complexity, three simplified SATD (SSATD) methods based on DCT and DST features are proposed to serve as substitutes for SATD in fast RD cost, thus reducing the computational complexity of SATD calculation. Experimental results show that 35.53%, 14.57%, and 14.37% of coding time can be reduced respectively under AI, RA and LDP configurations with negligible RD performance loss when applying the proposed RD cost model and the SSATD methods to HM16.7. Besides, the proposed methods also can reduce 4%-9% of encoding time and exhibits the same RD performance as state-of-the-art methods.

State-Of-The-Art In Video Processing: Compression, Optimization And Retrieval

Video compression plays a vital role in the modern social media networking with plethora of multimedia applications. It empowers transmission medium to competently transfer videos and enable resources to store the video efficiently. Nowadays high-resolution video data are transferred through the communication channel having high bit rate in order to send multiple compressed videos. There are many advances in transmission ability, efficient storage ways of these compressed video where compression is the primary task involved in multimedia services. This paper summarizes the compression standards, describes the main concepts involved in video coding. Video compression performs conversion of large raw bits of video sequence into a small compact one, achieving high compression ratio with good video perceptual quality. Removing redundant information is the main task in the video sequence compression. A survey on various block matching algorithms, quantization and entropy coding are focused. It is found that many of the methods having computational complexities needs improvement with optimization.

Medical image encryption and compression by adaptive sigma filterized synorr certificateless signcryptive Levenshtein entropy-coding-based deep neural learning

Pre-processing of medical images plays a vibrant part in the field of medicine to detect patient’s disease at an earlier stage. Hospitals and medical centers generate an enormous volume of digital medical images day by day, which is used for several purposes of diagnostic procedures. Because of many images,for secured transmission, image compression is required to reduce the redundancies in the image and to accomplish the proficient image communication. To reduce the redundancies in the image and to accomplish the proficient communication of images. A competent Adaptive sigma filterized synorr certificateless signcryptive Levenshtein entropy coding-based deep neural learning (ASFSCSLEC-DNL) technique is presented to develop the image encryption and compression. The main goal of the ASFSCSLEC-DNL technique was to improve the security level of medical image transmission. The deep feed-forward artificial neural network was applied in the ASFSCSLEC-DNL technique for medical image pre-processing, encryption, and compression with multiple layers. The adaptive sigma filter was employed to denoise the medical image. The medical image encryption and signature generation were done with synorr certificateless signcryption. Finally, Levenshtein entropy encoding was applied to compress images. Then the compressed image was sent to the receiver where the decompression and decryption are implemented using Levenshtein entropy decoding and synorr certificateless decryption. Investigational estimation was carried out in chest X-ray medical images and the results of ASFSCSLEC-DNL technique proved more capable in terms of higher peak signal to noise ratio and compression ratio with lesser encryption time compared to the existing state-of-the-art methods.

Design and Implementation of VLSI for Finite State Entropy Encoding

<p indent=0mm>The Zstd (Zstandard) lossless compression algorithm that implemented by software is difficult to meet the demand of compression speed in specific application field when processing massive data. It is an effective solution to this problem by using the hardware acceleration scheme, especially for the hardware acceleration of FSE (finite state entropy). Thus, a hardware implementation of the compression and decompression in FSE is proposed for Zstd. This scheme determines the optimal hardware acceleration step by fixing the size of compression table, reduces the storage space and improves the transmission speed by adding hardware modules of sequence mapping, enhances the time of parallel processing by dividing the seven-stages of flow and realizes the architecture by software and hardware collaboration. The proposed architecture is implemented in the TSMC <sc>55 nm</sc> process, and the highest frequency can reach <sc>750 MHz.</sc> The experimental results show that compared with the software implementation, the speed of the whole compression is more than 9 times faster, the speed of the whole decompression is more than the 100 times faster.

About the Development of a High-Speed Simplified Image Codec

In order to develop a high-speed simplified image codec, an analysis of the influence of known image compression algorithms and other parameters on performance was done. The relevance and expediency of developing a high-speed simplified image codec for the Internet of Things in order to increase the level of autonomy of IoT devices, reduce the cost of construction and dissemination of IoT infrastructure were substantiated. The efficiency coefficient of image compression algorithms was introduced, which is determined by the ratio between the computational complexity of the algorithms and their contribution to the final result. Simplification and reduction of the number of algorithms for predicting pixel values ​​were proposed and substantiated, because at this stage a significant number of computational operations is added by the procedure of comparing different prediction algorithms with each other. It is proposed to use only one block integer transformation with fast low complexity algorithms of calculating, which will significantly reduce the complexity of the block transformation stage, including due to the lack of high computational complexity of the algorithm for comparing the quality of block transformations. At the stage of entropy coding, it is also proposed to use simplified algorithms, because the contribution of this stage to the overall result in the general background is quite small, and the computational complexity is high (50 – 70 % of all calculations). A new algorithm for progressive image transfer was proposed - the transfer of a reduced image followed by the transfer of the original image on demand. The considered approaches and algorithms for the development of high-speed simplified image codec can be applied to further development of high-speed simplified video codec. Keywords: computational complexity, fast transforms, computational efficiency, progressive data transfer, intra-prediction algorithms, simplified image codec, IoT.

Study and investigation of video steganography over uncompressed and compressed domain: a comprehensive review

In the technological era, the primary source of information is in the form of digital data, which has to be secured while storing or transmitting during communication over an unsecured network. Different approaches are used to provide security to digital data, viz. text, audio, image, and video. This paper initially explains the security system such as cryptography, watermarking, and steganography and their comparative analysis based on different characteristics, viz. satisfaction level of objective, type of carrier object and secret information to be used, dependency of security level, and quality assessment parameters. This review article focuses more on steganography methods applied over video. The various methods implemented for video steganography in compressed domain, viz. inter-frame and intra-frame prediction, motion vector estimation, entropy coding (CAVLC and CABAC), and transformed and quantized coefficients of DCT, DST, and DWT, etc. and the methods based on spatial and transform domain for uncompressed video are briefly described. It is followed by the detailed analysis of related work done by various researchers in video steganography and the obtained experimental results. Furthermore, the confidential data hiding in compressed videos are explained using Moving Picture Expert Group (MPEG—1, MPEG—2, MPEG—4), Advanced Video Coding (AVC)/H.264, and High-Efficiency Video Coding (HEVC)/H.265 that includes both spatial and transform domain. This paper summarizes and explains the detailed investigations of numerous techniques of video steganography based on the comprehensive literature survey. The methods used to assess the performance of video steganography are analyzed based on the quality assessment parameters such as imperceptibility; measured by peak signal to noise ratio (PSNR), mean square error (MSE), and structural similarity (SSIM), robustness; measured by bit error rate (BER) and similarity (Sim), and embedding capacity; measured by hiding ratio. The overall review of past literature facilitates to have in-depth knowledge for upgrading the video steganography.

Enhanced Binary MQ Arithmetic Coder with Look-Up Table

Binary MQ arithmetic coding is widely used as a basic entropy coder in multimedia coding system. MQ coder esteems high in compression efficiency to be used in JBIG2 and JPEG2000. The importance of arithmetic coding is increasing after it is adopted as a unique entropy coder in HEVC standard. In the binary MQ coder, arithmetic approximation without multiplication is used in the process of recursive subdivision of range interval. Because of the MPS/LPS exchange activity that happens in the MQ coder, the output byte tends to increase. This paper proposes an enhanced binary MQ arithmetic coder to make use of look-up table (LUT) for (A × Qe) using quantization skill to improve the coding efficiency. Multi-level quantization using 2-level, 4-level and 8-level look-up tables is proposed in this paper. Experimental results applying to binary documents show about 3% improvement for basic context-free binary arithmetic coding. In the case of JBIG2 bi-level image compression standard, compression efficiency improved about 0.9%. In addition, in the case of lossless JPEG2000 compression, compressed byte decreases 1.5% using 8-level LUT. For the lossy JPEG2000 coding, this figure is a little lower, about 0.3% improvement of PSNR at the same rate.

An extended context-based entropy hybrid modeling for image compression

Recently deep learning has been introduced to the field of image compression. In this paper, we present a hybrid coding framework that combines entropy coding, deep learning, and traditional coding framework. In the base layer of the encoding, we use convolutional neural networks to learn the latent representation and importance map of the original image respectively. The importance map is then used to guide the bit allocation of the latent representation. A context model is also developed to help the entropy coding after the masked quantization. Another network is used to get a coarse reconstruction of the image in the base layer. The residual between the input and the coarse reconstruction is then obtained and encoded by the traditional BPG codec as the enhancement layer of the bit stream. We only need to train a basic model and the proposed scheme can realize image compression at different bit rates, thanks to the use of the traditional codec. Experimental results using the Kodak, Urban100 and BSD100 datasets show that the proposed scheme outperforms many deep learning-based methods and traditional codecs including BPG in MS-SSIM metric across a wide range of bit rates. It also exceeds some latest hybrid schemes in RGB444 domain on Kodak dataset in both PSNR and MS-SSIM metrics.

Hyperspectral Parallel Image Compression on Edge GPUs

Edge applications evolved into a variety of scenarios that include the acquisition and compression of immense amounts of images acquired in space remote environments such as satellites and drones, where characteristics such as power have to be properly balanced with constrained memory and parallel computational resources. The CCSDS-123 is a standard for lossless compression of multispectral and hyperspectral images used in on-board satellites and military drones. This work explores the performance and power of 3 families of low-power heterogeneous Nvidia GPU Jetson architectures, namely the 128-core Nano, the 256-core TX2 and the 512-core Xavier AGX by proposing a parallel solution to the CCSDS-123 compressor on embedded systems, reducing development effort, compared to the production of dedicated circuits, while maintaining low power. This solution parallelizes the predictor on the low-power GPU while the entropy encoders exploit the heterogeneous multiple CPU cores and the GPU concurrently. We report more than 4.4 GSamples/s for the predictor and up to 6.7 Gb/s for the complete system, requiring less than 11 W and providing an efficiency of 611 Mb/s/W.