Optimal Rate-distortion Performance Research Articles

A convolutional neural network-based rate control algorithm for VVC intra coding

The Versatile Video Coding (VVC) has shown significant improvements in Rate-Distortion (R-D) performance compared to its predecessor, High Efficiency Video Coding (HEVC). However, it still encounters several challenges. One of these challenges is the efficient allocation of bits among all Coding Tree Units (CTUs). Additionally, there is a lack of prior information for intra-frame coding, particularly for the first frame. After CTU-level bit allocation, only fixed parameters can be used to determine the λ for CTUs, which does not result in optimal rate–distortion performance. To tackle above challenges, we propose a rate control solution based on Convolutional Neural Network (CNN). This approach utilizes CNN to predict the key parameters α and β in the R-D model, addressing the problem of lacking prior information in intra-frame coding. Subsequently, the predicted α and β values are used to adaptively allocate bits for each CTU. Our proposed algorithm is implemented in VTM-16.0 under Common Test Conditions (CTC). Experimental results show that, compared to the default rate control algorithm in VTM-16.0, our proposed algorithm enhances R-D performance by 0.96% while maintaining rate control accuracy.

Rate-Distortion Optimization Based on Two-Pass Encoding for HEVC

Rate-distortion optimization (RDO) is a crucial technique in block-based hybrid video encoders, which determines the coding option for a certain coding unit to achieve optimal rate-distortion (R-D) performance. However, the current RDO, which is implemented into High Efficiency Video Coding (HEVC) test model, i.e., HM, is far from being global optimal as it ignores the interaction among coding options. Recent studies have shown that the dependent RDO methods can improve the coding efficiency of encoders by exploring the R-D dependency among coding units, but these methods do not consider the R-D characteristics of coding units. In this paper, we proposed a two-pass encoding based RDO method, which combines both the R-D dependency and R-D characteristics, to further improve the coding efficiency. First, a frame is encoded with the original HEVC scheme to obtain the R-D model of coding tree units (CTU) and the bit budget of the frame. Second, an optimal equation combines the R-D model and R-D dependency is established to adaptively determine the Lagrange multiplier and quantization parameter (QP) for each CTU. Finally, the current frame is encoded with a new scheme again. Experimental results show that compared with the original HM, the proposed method obtains R-D performance improvements of 5.3% and 5.6% on average under configurations of low-delay B and P frames, respectively.

Generalized Gaussian Multiterminal Source Coding: The Symmetric Case

Consider a generalized multiterminal source coding system, where $\binom{\ell }{ m}$ encoders, each observing a distinct size- $m$ subset of $\ell $ ( $\ell \geq 2$ ) zero-mean unit-variance exchangeable Gaussian sources with correlation coefficient $\rho $ , compress their observations in such a way that a joint decoder can reconstruct the sources within a prescribed mean squared error distortion based on the compressed data. The optimal rate-distortion performance of this system was previously known only for the two extreme cases $m=\ell $ (the centralized case) and $m=1$ (the distributed case), and except when $\rho =0$ , the centralized system can achieve strictly lower compression rates than the distributed system under all non-trivial distortion constraints. Somewhat surprisingly, it is established in the present paper that the optimal rate-distortion performance of the afore-described generalized multiterminal source coding system with $m\geq 2$ coincides with that of the centralized system for all distortions when $\rho \leq 0$ and for distortions below an explicit positive threshold (depending on $m$ ) when $\rho > 0$ . Moreover, when $\rho > 0$ , the minimum achievable rate of generalized multiterminal source coding subject to an arbitrary positive distortion constraint $d$ is shown to be within a finite gap (depending on $m$ and $d$ ) from its centralized counterpart in the large $\ell $ limit except for possibly the critical distortion $d=1-\rho $ .

Perception-based adaptive quantization for transform-domain Wyner-Ziv video coding

Distributed video coding (DVC) is desirable for encoding systems with tight power or computational constraints, for which the popular practical solution is transform-domain Wyner-Ziv video coding (TD-WZVC). To achieve the similar coding performance with H.264/AVC, quantization is a key factor in TD-WZVC. Practically, the quantization matrix is trained offline and remains fixed value during coding. Optimal rate-distortion (RD) performance cannot be achieved due to the varying quality of side information (SI) frame. In this paper, a novel model of perceptual distortion probability is developed to estimate the perceptual distortion of SI frame and to derive the target perceptual distortion. With the two perceptual distortion probabilities, three components (i.e. quality of SI frame, perceptual features and RD optimization) are integrated to determine the optimal quantization matrix adaptively, which improves the coding performance. Extensive experiments demonstrate that the proposed scheme can adaptively determine proper quantization matrix online and achieve similar visual quality with less bit-rate, as compared to other adaptive quantization schemes in TD-WZVC.

Direct Techniques for Optimal Sub-Pixel Motion Accuracy Estimation and Position Prediction

Direct techniques for the optimal resolution estimation and position prediction of subpel motion vectors (MVs) based on integer-pel MVs are investigated in this paper. Although it is common to determine the optimal MV position by fitting a local error surface using integer-pel MVs, the characteristics of the error surface have not been thoroughly studied in the past. Here, we use an approximate condition number of the Hessian matrix of the error surface to characterize its shape in a local region. By exploiting this shape information, we propose a block-based subpel MV resolution estimation method that allows each block to choose its optimal subpel MV resolution for the optimal rate-distortion (R-D) performance adaptively. Furthermore, we propose two MV position prediction schemes for ill and well-conditioned error surfaces, respectively. All proposed techniques are direct methods, where no iteration is required. Experimental results are given to show the R-D performance of the proposed subpel MV resolution estimation and position prediction schemes.

Feedback-free rate-allocation scheme for transform domain Wyner–Ziv video coding

In most existing Wyner---Ziv video coding schemes, a feedback channel (FC) is expected at the decoder in order to allocate a proper bit rate for each Wyner---Ziv frame. However, FC not only results in additional latency but also increases decoding complexity due to the several feedback-decoding iterations. Moreover, FC may be unavailable in many practical video applications. In this paper, we propose a novel feedback-free rate-allocation scheme for transform domain Wyner---Ziv video coding (TD-WZVC), which predicts the rate for each Wyner---Ziv frame at the encoder without significantly increasing the complexity of the encoder. First, a correlation estimation model is presented to characterize the relationship between the source frame and the reference frame estimated at the encoder in TD-WZVC. Then, an efficient FC-free rate-allocation algorithm is proposed and a linear model is built to avoid both overestimation and underestimation of the real rate and obtain an optimal rate-distortion performance. Experimental results show that the proposed scheme is able to achieve a good encoder rate allocation while still maintaining consistent coding efficiency.

Parameter Selection for Wyner–Ziv Coding of Laplacian Sources with Additive Laplacian or Gaussian Innovation

A large number of practical coding scenarios deal with sources such as transform coefficients that can be well modeled as Laplacians. For regular coding of such sources, samples are often quantized by a family of uniform quantizers possibly with a deadzone, and then entropy coded. For the Wyner-Ziv coding problem when correlated side-information is available at the decoder, the side-information can be modeled as obtained by independent additive Laplacian or Gaussian innovation on the source. This paper deals with optimal choice of parameters for practical Wyner-Ziv coding in such scenarios, using the same quantizer family as in the regular codec to cover a range of rate-distortion tradeoffs, given the variances of the source and additive noise. We propose and analyze a general encoding model based on multilevel coset codes that combines source coding and channel coding and show that at practical block lengths and code complexities, not pure channel coding but a hybrid combination of source coding and channel coding with right parameters provide optimal rate-distortion performance. We also provide a framework for on-the-fly parameter choice based on nonparametric representation of a set of seed functions, for use in scenarios where variances are estimated during encoding. A good insight in the optimal parameter selection mechanism is essential for building practical distributed codecs.

Representation and Compression of Multidimensional Piecewise Functions Using Surflets

We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing edges, video sequences of moving objects, and seismic data containing geological horizons. For both function classes, we derive the optimal asymptotic approximation and compression rates based on Kolmogorov metric entropy. For piecewise constant functions, we develop a multiresolution predictive coder that achieves the optimal rate-distortion performance; for piecewise smooth functions, our coder has near-optimal rate-distortion performance. Our coder for piecewise constant functions employs surflets, a new multiscale geometric tiling consisting of M-dimensional piecewise constant atoms containing polynomial discontinuities. Our coder for piecewise smooth functions uses surfprints, which wed surflets to wavelets for piecewise smooth approximation. Both of these schemes achieve the optimal asymptotic approximation performance. Key features of our algorithms are that they carefully control the potential growth in surflet parameters at higher smoothness and do not require explicit estimation of the discontinuity. We also extend our results to the corresponding discrete function spaces for sampled data. We provide asymptotic performance results for both discrete function spaces and relate this asymptotic performance to the sampling rate and smoothness orders of the underlying functions and discontinuities. For approximation of discrete data, we propose a new scale-adaptive dictionary that contains few elements at coarse and fine scales, but many elements at medium scales. Simulation results on synthetic signals provide a comparison between surflet-based coders and previously studied approximation schemes based on wedgelets and wavelets.

The Virtue of Patience in Low-Complexity Scheduling of Packetized Media With Feedback

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We consider streaming pre-encoded and packetized media over best-effort networks in the presence of acknowledgment feedbacks. We first review a rate-distortion (RD) optimization framework that can be employed in such scenarios. As part of the framework, a scheduling algorithm selects the data to send over the network at any given time, so as to minimize the end-to-end distortion, given an estimate of channel resources and a history of previous transmissions and received acknowledgements. In practice, a greedy scheduling strategy is often considered to limit the solution search space, and reduce the computational complexity associated to the RD optimization framework. Our work observes that popular greedy schedulers are strongly penalized by early retransmissions. Therefore, we propose a scheduling algorithm that avoids premature retransmissions, while preserving the low computational complexity aspect of the greedy paradigm. Such a scheduling strategy maintains close to optimal RD performance when adapting to network bandwidth fluctuations. Our experimental results demonstrate that the proposed patient greedy scheduler provides a reduction of up to 50% in transmission rate relative to conventional greedy approaches, and that it brings up to 2 dB of quality improvement in scheduling classical MPEG-based packet video streams. </para>

Vector Quantization in Multiresolution Mesh Compression

Irregularly sampled triangular meshes contain vertices in a geometric space with arbitrary connectivity degrees. From a compression point of view, this letter presents a multiresolution analysis for irregular meshes using progressive vector quantization (VQ). We show that VQ exploits the joint distribution of coordinates in the geometric space, thus improving the compression efficiency. Based on the presented compression algorithm, we further propose an equalization algorithm that properly balances between connectivity downsampling and geometry quantization and achieves the optimal rate-distortion performance under constrained bit rates

Bit Rate Distribution for Motion Estimation in H.264 Coding

In this paper, we analyze the bit rate distribution of the full search and the fast search motion estimation algorithms in H.264. It shows both experimentally and theoretically that a well-designed fast block-matching algorithm not only speeds up motion estimation process, but also improves the rate-distortion performance. This is in contrast to the common belief that full search always yields optimal rate-distortion performance under the same test condition.

Microarray BASICA: Background Adjustment, Segmentation, Image Compression and Analysis of Microarray Images

This paper presents microarray BASICA: an integrated image processing tool for background adjustment, segmentation, image compression, and analysis of cDNA microarray images. BASICA uses a fast Mann-Whitney test-based algorithm to segment cDNA microarray images and performs postprocessing to eliminate the segmentation irregularities. The segmentation results, along with the foreground and background intensities obtained with the background adjustment, are then used for independent compression of the foreground and background. We introduce a new distortion measurement for cDNA microarray image compression and devise a coding scheme by modifying the embedded block coding with optimized truncation (EBCOT) algorithm (Taubman, 2000) to achieve optimal rate-distortion performance in lossy coding while still maintaining outstanding lossless compression performance. Experimental results show that the bit rate required to ensure sufficiently accurate gene expression measurement varies and depends on the quality of cDNA microarray images. For homogeneously hybridized cDNA microarray images, BASICA is able to provide from a bit rate as low as 5 bpp the gene expression data that are 99% in agreement with those of the original 32 bpp images.

Bidirectional variable size blockmotion compensation

The authors present a new motion compensation technique for bidirectional predictive video coding, which partitions a frame into variable size blocks according to the local motion contents and yields an optimal rate-distortion performance. Preliminary results show that this method is more efficient than the conventional fixed-size method.

The Impact of Rate Control Algorithms on System-Level VLSI Design

This paper presents an evaluation of rate control algorithms from a system-level VLSI design viewpoint. Rate control in video coding has a significant influence on the coded bit rate and image quality. Many rate control algorithms have been proposed mainly focusing on the optimal rate-distortion performance without considering their performance on the VLSI implementation. The purpose of this study is not to propose a hardware architecture for any specific algorithm but to study the algorithm impact on hardware design. Based on our finding, a system designer should choose an algorithm not only good in rate control performance but also good in hardware implementation. When implementing and comparing a few rate control algorithms using a generic processor structure, we found that, in addition to the ordinary computational complexity, the internal buffer size is also very critical in VLSI realization. Several picture sequences have been tested including one sequence constructed specifically to simulate a difficult case for rate control. In this paper, three different types of popular rate control algorithms have been analyzed based on their picture quality, the internal buffer size, and the hardware cost. The methodology and results presented here provide useful guidelines for selecting an appropriate rate control algorithm for system-level VLSI designers.

Theoretical and experimental rate distortion performance in compression of ambulatory ECGs

We compare ECG data compression algorithms based on signal entropy for a given mean-square-error (MSE) compression distortion. By defining the distortion in terms of the MSE and assuming the ECG signal to be a Gaussian process we are able to estimate theoretical rate distortion bounds from average ECG power spectra. These rate distortion bounds give estimates of the minimum bits per second (bps) required for storage of ECG data with a given MSE regardless of compression method. From average power spectra of the MIT/BIH arrhythmia database we have estimated rate distortion bounds for ambulatory ECG data, both before and after average beat subtraction. These rate distortion estimates indicate that, regardless of distortion, average beat subtraction reduces the theoretical minimum data rate required for ECG storage by approximately 100 bits per second (bps). Our estimates also indicate that practical ambulatory recording requires a compression distortion on the order of 11 microV rms. We have compared the performance of common ECG compression algorithms on data from the MIT/BIH database. We sampled and quantized the data to give distortion levels of 2, 5, 8, 11, and 14 microV rms. These results indicate that, when sample rates and quantization levels are chosen for optimal rate distortion performance, minimum data rates can be achieved by average beat subtraction followed by first differencing of the residual signal. Achievable data rates approximate our theoretical estimates at low distortion levels and are within 60 bps at higher distortion levels.

On the structure of vector quantizers

Vector quantization is intrinsically superior to predictive coding, transform coding, and other suboptimal and {\em ad hoc} procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded. The key limitation of existing techniques is the very large randomly generated code books which must be stored, and the computational complexity of the associated encoding procedures. The quantization operation is decomposed into its rudimentary structural components. This leads to a simple and elegant approach to derive analytical properties of optimal quantizers. Some useful properties of quantizers and algorithmic approaches are given, which are relevant to the complexity of both storage and processing in the encoding operation. Highly disordered quantizers, which have been designed using a clustering algorithm, are considered. Finally, lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices. The code vectors are algorithmically generated in a simple manner rather than stored in a code book, and fast algorithms perform the encoding algorithm with negligible complexity.