A flexible structure for fully scalable motion-compensated 3-D DWT with emphasis on the impact of spatial scalability.

We investigate the implications of the conventional "t+2-D" motion-compensated (MC) three-dimensional (3-D) discrete wavelet/subband transform structure for spatial scalability and propose a novel flexible structure for fully scalable video compression. In this structure, any number of levels of "pretemporal" spatial wavelet decomposition are performed on the original full resolution frames, followed by MC temporal decomposition of the subbands within each spatial resolution level. Further levels of "posttemporal" spatial decomposition may be performed on the spatiotemporal subbands to provide additional levels of spatial scalability and energy compaction. This structure allows us to trade energy compaction against the potential for artifacts at reduced spatial resolutions. More importantly, the structure permits extensive study of the interaction between spatial aliasing, scalability and energy compaction. We show that where the motion model fails, the "t+2-D" structure inevitably produces misaligned spatial aliasing artifacts in reduced resolution sequences. These artifacts can be removed by using pretemporal spatial decomposition. On the other hand, we also show that the "t+2-D" structure necessarily maximizes compression efficiency. We propose different schemes to minimize the loss of compression efficiency associated with pretemporal spatial decomposition.     

Video denoising, deblocking, and enhancement through separable 4-d nonlocal spatiotemporal transforms

We propose a powerful video filtering algorithm that exploits temporal and spatial redundancy characterizing natural video sequences. The algorithm implements the paradigm of nonlocal grouping and collaborative filtering, where a higher dimensional transform-domain representation of the observations is leveraged to enforce sparsity, and thus regularize the data: 3-D spatiotemporal volumes are constructed by tracking blocks along trajectories defined by the motion vectors. Mutually similar volumes are then grouped together by stacking them along an additional fourth dimension, thus producing a 4-D structure, termed group, where different types of data correlation exist along the different dimensions: local correlation along the two dimensions of the blocks, temporal correlation along the motion trajectories, and nonlocal spatial correlation (i.e., self-similarity) along the fourth dimension of the group. Collaborative filtering is then realized by transforming each group through a decorrelating 4-D separable transform and then by shrinkage and inverse transformation. In this way, the collaborative filtering provides estimates for each volume stacked in the group, which are then returned and adaptively aggregated to their original positions in the video. The proposed filtering procedure addresses several video processing applications, such as denoising, deblocking, and enhancement of both grayscale and color data. Experimental results prove the effectiveness of our method in terms of both subjective and objective visual quality, and show that it outperforms the state of the art in video denoising.     

Space-frequency quantization for image compression with directionlets.

The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions, called directionlets. In this paper, we show how to design and implement a novel efficient space-frequency quantization (SFQ) compression algorithm using directionlets. Our new compression method outperforms the standard SFQ in a rate-distortion sense, both in terms of mean-square error and visual quality, especially in the low-rate compression regime. We also show that our compression method, does not increase the order of computational complexity as compared to the standard SFQ algorithm.     

Operational rate-distortion modeling for wavelet video coders

Based on our statistical investigation of a typical three-dimensional (3-D) wavelet codec, we present a unified mathematical model to describe its operational rate-distortion (RD) behavior. The quantization distortion of the reconstructed video frames is assessed by tracking the quantization noise along the 3-D wavelet decomposition trees. The coding bit-rate is estimated for a class of embedded video coders. Experimental results show that the model captures sequence characteristics accurately and reveals the relationship between wavelet decomposition levels and the overall RD performance. After being trained with offline RD data, the model enables accurate prediction of real RD performance of video codecs and therefore can enable optimal RD adaptation of the encoding parameters according to various network conditions.     

Spatiotemporal selective extrapolation for 3-D signals and its applications in video communications.

In this paper, we derive a spatiotemporal extrapolation method for 3-D discrete signals. Extending a discrete signal beyond a limited number of known samples is commonly referred to as discrete signal extrapolation. Extrapolation problems arise in many applications in video communications. Transmission errors in video communications may cause data losses which are concealed by extrapolating the surrounding video signal into the missing area. The same principle is applied for TV logo removal. Prediction in hybrid video coding is also interpreted as an extrapolation problem. Conventionally, the unknown areas in the video sequence are estimated from either the spatial or temporal surrounding. Our approach considers the spatiotemporal signal including the missing area in a volume and replaces the unknown samples by extrapolating the surrounding signal from spatial, as well as temporal direction. By exploiting spatial and temporal correlations at the same time, it is possible to inherently compensate motion. Deviations in luminance occurring from frame to frame can be compensated, too.     

Lossless video sequence compression using adaptive prediction.

We present an adaptive lossless video compression algorithm based on predictive coding. The proposed algorithm exploits temporal, spatial, and spectral redundancies in a backward adaptive fashion with extremely low side information. The computational complexity is further reduced by using a caching strategy. We also study the relationship between the operational domain for the coder (wavelet or spatial) and the amount of temporal and spatial redundancy in the sequence being encoded. Experimental results show that the proposed scheme provides significant improvements in compression efficiencies.     

Three-dimensional video compression using subband/wavelet transformwith lower buffering requirements

Three-dimensional (3-D) video compression using wavelets decomposition along the temporal axis dictates that a number of video frames must be buffered to allow for the temporal decomposition. Buffering of frames allows for the temporal correlation to be made use of, and the larger the buffer the more effective the decomposition. One problem inherent in such a set up in interactive applications such as video conferencing, is that buffering translates into a corresponding time delay. We show that 3-D coding of such image sequences can be achieved in the true sense of temporal direction decomposition but with much less buffering requirements. For a practical coder, this can be achieved by introducing an approximation to the way the transform coefficients are encoded. Applying wavelet decomposition using some types of filters may introduce edge errors, which become more prominent in short signal segments. We also present a solution to this problem for the Daubechies (1988) family of filters.     

An efficient content-adaptive motion-compensated 3-D DWT with enhanced spatial and temporal scalability.

We propose a novel, content adaptive method for motion-compensated three-dimensional wavelet transformation (MC 3-D DWT) of video. The proposed method overcomes problems of ghosting and nonaligned aliasing artifacts which can arise in regions of motion model failure, when the video is reconstructed at reduced temporal or spatial resolutions. Previous MC 3-D DWT structures either take the form of MC temporal DWT followed by a spatial transform ("t+2D"), or perform the spatial transform first ("2D + t"), limiting the spatial frequencies which can be jointly compensated in the temporal transform, and hence limiting the compression efficiency. When the motion model fails, the "t + 2D" structure causes nonaligned aliasing artifacts in reduced spatial resolution sequences. Essentially, the proposed transform continuously adapts itself between the "t + 2D" and "2D + t" structures, based on information available within the compressed bit stream. Ghosting artifacts may also appear in reduced frame-rate sequences due to temporal low-pass filtering along invalid motion trajectories. To avoid the ghosting artifacts, we continuously select between different low-pass temporal filters, based on the estimated accuracy of the motion model. Experimental results indicate that the proposed adaptive transform preserves high compression efficiency while substantially improving the quality of reduced spatial and temporal resolution sequences.     

三维小波变换结合运动补偿的视频编码器

对三雏小波变换结合运动补偿的视频压缩算法提出了改进方案。针对运动补偿提升（MCLIFT）框架的弱点,结合MPEG的特点,采用新的帧结构对视频序列进行帧间滤波去除时间冗余,再对每个帧在空间上进行小波分解并用SPIHT算法对小波系数进行编码。实验表明,此方法继承了MCLIFT框架的优点,同时又减少了时延和所需的帧缓存,而且这种与MPEG相似的帧结构能进一步降低码率,提高压缩比。     

Motion compensated lossy-to-lossless compression of 4-D medical images using integer wavelet transforms.

This paper proposes a method for progressive lossy-to-lossless compression of four-dimensional (4-D) medical images (sequences of volumetric images over time) by using a combination of three-dimensional (3-D) integer wavelet transform (IWT) and 3-D motion compensation. A 3-D extension of the set-partitioning in hierarchical trees (SPIHT) algorithm is employed for coding the wavelet coefficients. To effectively exploit the redundancy between consecutive 3-D images, the concepts of key and residual frames from video coding is used. A fast 3-D cube matching algorithm is employed to do motion estimation. The key and the residual volumes are then coded using 3-D IWT and the modified 3-D SPIHT. The experimental results presented in this paper show that our proposed compression scheme achieves better lossy and lossless compression performance on 4-D medical images when compared with JPEG-2000 and volumetric compression based on 3-D SPIHT.     

A compression method for a massive image data set in image-based rendering

In image-based rendering with adjustable illumination, the data set contains a large number of pre-captured images under different sampling lighting directions. Instead of individually compressing each pre-captured image, we propose a two-level compression method. Firstly, we use a few spherical harmonic (SH) coefficients to represent the plenoptic property of each pixel. The classical discrete summation method for extracting SH coefficient requires that the sampling lighting directions should be uniformly distributed on the whole spherical surface. It cannot handle the case that the sampling lighting directions are irregularly distributed. A constrained least-squares algorithm is proposed to handle this case. Afterwards, embedded zero-tree wavelet coding is used for removing the spatial redundancy in SH coefficients. Simulation results show our approach is much superior to the JPEG, JPEG2000, MPEG2, and 4D wavelet compression method. The way to allow users to interactively control the lighting condition of a scene is also discussed.     

Sparse geometric image representations with bandelets.

This paper introduces a new class of bases, called bandelet bases, which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow. This geometric flow indicates directions in which the image gray levels have regular variations. The image decomposition in a bandelet basis is implemented with a fast subband-filtering algorithm. Bandelet bases lead to optimal approximation rates for geometrically regular images. For image compression and noise removal applications, the geometric flow is optimized with fast algorithms so that the resulting bandelet basis produces minimum distortion. Comparisons are made with wavelet image compression and noise-removal algorithms.     

Coherent 3-D echo detection for ultrasonic imaging

The purpose of the present paper is to present an ultrasonic processing set-up by which three-dimensional (3-D) echo location can be computed more efficiently than by other one-dimensional (1-D) methods. This set-up contains three successive tasks. The first one deals with a model for representing echoes. This model is based on a generic wavelet, which is a cosine function with variable amplitude and phase. To estimate the wavelet, we propose to use a spline representation of its complex envelope in order to reduce amplitude and phase dimension. The second task deals with 1-D detection and is conducted within a Bayesian framework. Using an Ascan decomposition on a family of wavelets resulting from the first task, we propose a specific procedure to carry on constrained least-squares in order to alleviate the bias inherent to this criterion. The third task deals with the spatial regularization of the detected echo location field resulting from the second task. We propose a Bayes-Markov model for removing isolated wrong detections and simultaneously improving, under regularization constraint, the spatial location of the detected echoes. In fact, this model deals with the general problem of nonorganized point approximation. All the proposed techniques are illustrated on real ultrasonic data.     

基于几何方向的图像压缩算法

标准二维小波仅沿图像水平和垂直两个方向变换,图像稀疏化表示有待改进完善.文中提出了一种基于方向波变换( Directionlet)的图像压缩算法:通过八叉树分割算法对图像自适应分块;块内最优逼近凡何方向构成Directionlet变换的采样矩阵;块区域进行Directionlet变换,变换系数和方向信息分别编码.沿图像...     

二维电能质量数据压缩

近年来,大量电能质量监测点的建立,使得电能质量数据增加,为处理大量的电能质量监测数据,提出了一种基于方向小波变换的电能质量数据压缩方法.将一维的电能质量数据转换成二维的数据,得到经过此变换分解的二维数据的小波系数,再将这些小波系数应用图像压缩中的SPIHT（多级树集合分裂）编码算法,压缩二维表示的电能质量数据.实验结果表明,此方法具有压缩率高、速度快,控制压缩比和特征不变的特点,有利于根据网络的状况调节传输的数据量.     

A 2-D ECG compression method based on wavelet transform and modified SPIHT

A two-dimensional (2-D) wavelet-based electrocardiogram (ECG) data compression method is presented which employs a modified set partitioning in hierarchical trees (SPIHT) algorithm. This modified SPIHT algorithm utilizes further the redundancy among medium- and high-frequency subbands of the wavelet coefficients and the proposed 2-D approach utilizes the fact that ECG signals generally show redundancy between adjacent beats and between adjacent samples. An ECG signal is cut and aligned to form a 2-D data array, and then 2-D wavelet transform and the modified SPIHT can be applied. Records selected from the MIT-BIH arrhythmia database are tested. The experimental results show that the proposed method achieves high compression ratio with relatively low distortion and is effective for various kinds of ECG morphologies.     

Lifting-based invertible motion adaptive transform (LIMAT) framework for highly scalable video compression

We propose a new framework for highly scalable video compression, using a lifting-based invertible motion adaptive transform (LIMAT). We use motion-compensated lifting steps to implement the temporal wavelet transform, which preserves invertibility, regardless of the motion model. By contrast, the invertibility requirement has restricted previous approaches to either block-based or global motion compensation. We show that the proposed framework effectively applies the temporal wavelet transform along a set of motion trajectories. An implementation demonstrates high coding gain from a finely embedded, scalable compressed bit-stream. Results also demonstrate the effectiveness of temporal wavelet kernels other than the simple Haar, and the benefits of complex motion modeling, using a deformable triangular mesh. These advances are either incompatible or difficult to achieve with previously proposed strategies for scalable video compression. Video sequences reconstructed at reduced frame-rates, from subsets of the compressed bit-stream, demonstrate the visually pleasing properties expected from low-pass filtering along the motion trajectories. The paper also describes a compact representation for the motion parameters, having motion overhead comparable to that of motion-compensated predictive coders. Our experimental results compare favorably to others reported in the literature, however, our principal objective is to motivate a new framework for highly scalable video compression.     

Semi-regular representation and progressive compression of 3-D dynamic mesh sequences.

We propose an algorithm that represents three-dimensional dynamic objects with a semi-regular mesh sequence and compresses the sequence using the spatiotemporal wavelet transform. Given an irregular mesh sequence, we construct a semi-regular mesh structure for the first frame and then map it to subsequent frames based on the hierarchical motion estimation. The regular structure of the resulting mesh sequence facilitates the application of advanced coding schemes and other signal processing techniques. To encode the mesh sequence compactly, we develop an embedded coding scheme, which supports signal-to-noise ratio and temporal scalability modes. Simulation results demonstrate that the proposed algorithm provides significantly better compression performance than the static mesh coder, which encodes each frame independently.     

An algorithm for coding video signal based on 3-D wavelet transformation

This paper presents an algorithm for coding video signal based on 3-D wavelet transformation. When the frame order t of a video signal is replaced by order 2, the video signal can be looked as a block in 3-D space. After splitting the block into smaller sub-blocks, imitate the method of 2-D wavelet transformation for images, we can transform the sub-blocks with 3-D wavelet. Most of video signal energy is in the decomposed low-frequency sub-bands. These sub-bands affect the visual quality of the video signal most. Quantizing different sub-bands with different precision and then entropy encoding each sub-band, we can eliminate inter- and intra-frame redundancy of the video signal and compress data. Our simulation experiments show that this algorithm can achieve very good result.