Statistical distributions of DCT coefficients and their application to an interframe compression algorithm for 3-D medical images

Displacement estimated interframe (DEI) coding, a coding scheme for 3-D medical image data sets such as X-ray computed tomography (CT) or magnetic resonance (MR) images, is presented. To take advantage of the correlation between contiguous slices, a displacement-compensated difference image based on the previous image is encoded. The best fitting distribution functions for the discrete cosine transform (DCT) coefficients obtained from displacement compensated difference images are determined and used in allocating bits and optimizing quantizers for the coefficients. The DEI scheme is compared with 2-D block discrete cosine transform (DCT) as well as a full-frame DCT using the bit allocation technique of S. Lo and H.K. Huang (1985). For X-ray CT head images, the present bit allocation and quantizer design, using an appropriate distribution model, resulted in a 13-dB improvement in the SNR compared to the full-frame DCT using the bit allocation technique. For an image set with 5-mm slice thickness, the DEI method gave about 5% improvement in the compression ratio on average and less blockiness at the same distortion. The performance gain increases to about 10% when the slice thickness decreases to 3 mm.     

Multiresolution Image Representation Using Combined 2-D and 1-D Directional Filter Banks

In this paper, effective multiresolution image representations using a combination of 2-D filter bank (FB) and directional wavelet transform (WT) are presented. The proposed methods yield simple implementation and low computation costs compared to previous 1-D and 2-D FB combinations or adaptive directional WT methods. Furthermore, they are nonredundant transforms and realize quad-tree like multiresolution representations. In applications on nonlinear approximation, image coding, and denoising, the proposed filter banks show visual quality improvements and have higher PSNR than the conventional separable WT or the contourlet.     

纯二维全相位滤波器组及其在图像压缩中的应用

基于全相位理论,设计了3种纯二维全相位滤波器组(ADFB).这些滤波器组可以直接对图像进行纯二维分解和重构,若忽略滤波器的有限精度问题,系统是全重建的.为了减小运算量,纯二维ADFB采用提升格式实现.仿真试验表明,纯二维ADFB具有良好的数据压缩特性.在压缩率相同的情况下,尤其是IDCT-AFB7.7比Daubechies9/7小波重建图像的峰值信噪比(PSNR)最多小0.7 dB,这与采用的适合于可分离二维小波变换的四叉树SPIHT编码方案有关,若采用二叉树SPIHT编码,会使压缩效果得到改善.     

Multispectral code excited linear prediction coding and itsapplication in magnetic resonance images

This paper reports a multispectral code excited linear prediction (MCELP) method for the compression of multispectral images. Different linear prediction models and adaptation schemes have been compared. The method that uses a forward adaptive autoregressive (AR) model has been proven to achieve a good compromise between performance, complexity, and robustness. This approach is referred to as the MFCELP method. Given a set of multispectral images, the linear predictive coefficients are updated over nonoverlapping three-dimensional (3-D) macroblocks. Each macroblock is further divided into several 3-D micro-blocks, and the best excitation signal for each microblock is determined through an analysis-by-synthesis procedure. The MFCELP method has been applied to multispectral magnetic resonance (MR) images. To satisfy the high quality requirement for medical images, the error between the original image set and the synthesized one is further specified using a vector quantizer. This method has been applied to images from 26 clinical MR neuro studies (20 slices/study, three spectral bands/slice, 256x256 pixels/band, 12 b/pixel). The MFCELP method provides a significant visual improvement over the discrete cosine transform (DCT) based Joint Photographers Expert Group (JPEG) method, the wavelet transform based embedded zero-tree wavelet (EZW) coding method, and the vector tree (VT) coding method, as well as the multispectral segmented autoregressive moving average (MSARMA) method we developed previously.     

On two-channel filter banks with directional vanishing moments.

The contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform. One way to guarantee good approximation behavior is to let the directional filters in the contourlet filter bank have sharp frequency response. This requires filters with large support size. We seek to isolate the key filter property that ensures good approximation. In this direction, we propose filters with directional vanishing moments (DVM). These filters, we show, annihilate information along a given direction. We study two-channel filter banks with DVM filters. We provide conditions under which the design of DVM filter banks is possible. A complete characterization of the product filter is, thus, obtained. We propose a design framework that avoids 2-D factorization using the mapping technique. The filters designed, when used in the contourlet transform, exhibit nonlinear approximation comparable to the conventional filters while being shorter and, therefore, providing better visual quality with less ringing artifacts. Furthermore, experiments show that the proposed filters outperform the conventional ones in image approximation and denoising.     

Semantic image retrieval in magnetic resonance brain volumes

Practitioners in the area of neurology often need to retrieve multimodal magnetic resonance (MR) images of the brain to study disease progression and to correlate observations across multiple subjects. In this paper, a novel technique for retrieving 2-D MR images (slices) in 3-D brain volumes is proposed. Given a 2-D MR query slice, the technique identifies the 3-D volume among multiple subjects in the database, associates the query slice with a specific region of the brain, and retrieves the matching slice within this region in the identified volumes. The proposed technique is capable of retrieving an image in multimodal and noisy scenarios. In this study, support vector machines (SVM) are used for identifying 3-D MR volume and for performing semantic classification of the human brain into various semantic regions. In order to achieve reliable image retrieval performance in the presence of misalignments, an image registration-based retrieval framework is developed. The proposed retrieval technique is tested on various modalities. The test results reveal superior robustness performance with respect to accuracy, speed, and multimodality.     

基于非下采样三通道不可分对称小波的多光谱图像融合

针对IHS变换融合方法不能保持好的光谱信息,张量积小波变换融合方法生成的融合结果图像空间分辨率偏低、且易产生方块效应等不足.提出了一种基于三通道不可分对称小波的多光谱图像融合方法.利用矩阵扩充的方法,给出了三通道不可分对称小波滤波器组的构造方法,用所构造的不可分小波滤波器组分别对多光谱图像的亮度分量和全色图像作非下采样...     

Synthesis filter bank optimization in two-dimensional separablesubband coding systems

Subband coding is a popular and well established technique used in visual communications, such as image and video transmission. In the absence of quantization and transmission errors, the analysis and synthesis filters in a subband coding scheme can be designed to obtain perfect reconstruction of the input signal, but this is no longer the optimal solution in the presence of quantization of the subband coefficients. We presuppose the use of a two-dimensional (2-D) separable subband scheme and we address the problem of designing, for a given analysis filter bank and assuming uniform quantization of the subband coefficients, the set of row and column synthesis filters that minimize the mean squared reconstruction error at the output of the subband system. Since the corresponding optimization problem is inherently nonlinear, we propose a suboptimal solution that extends a one-dimensional (l-D) optimal filter design procedure, already presented in the literature, to a 2-D separable synthesis filter bank. The separable 2-D extension is not trivial, since the processing in one direction, e.g., the rows, alters the statistics of the signals for the design of the filters in the other direction, e.g., the columns. To further simplify the filter design, we propose to model the input image as a 2-D separable Markov process plus an additive white component. Several design examples using both synthetic signals and real world images are presented, showing that the filters designed using the proposed technique can give a significant gain with respect to the perfect reconstruction solution, especially when the dither technique is used for quantization. The simulation results also show that the proposed image model can be conveniently used in the synthesis filter design procedure.     

变采样率的磁共振图像分块压缩感知

提出一种磁共振(MR)图像的变采样率分块压缩感知(BCS,block-based compressed sensing)方法;根据MR图像细节丰富、纹理复杂的特点 ,引入对图像高 维奇异结构具有良好稀疏表示能力的Tetrolet变换,同时考虑到MR图像各切片间的时空相 关性,将相邻时序的MR切片组成图片组(GOP),通过计算参考图片与相邻切片的差异,并对 参考 图片及差异图进行不重叠分块,根据图像块内容变化的快慢自适应分配采样率,获取测量数 据,采用平滑投影Landweber(SPL,smooth projected Landweber)算法实现GOP的高质 量压缩感知(CS)重构。实验结果表明,Tetrolet 变换适用于MR图像的稀疏表示,相较于采用离散余弦变换(DCT)及双树小波变换(DWT)的方法 ,本文的重构图 像的PSNR平均提高了0.92dB与2.06dB;而且对于不同的GOP,采用变采样率方案时, 重构图像的质量均优于固定采样率时所得到的结果,为MR图像的CS提供了一种可行 的解决方案。     

A comparison of hardware implementations of the biorthogonal 9/7 DWT: convolution versus lifting

The filter bank approach for computing the discrete wavelet transform (DWT), which we call the convolution method, can employ either a nonpolyphase or polyphase structure. This work compares filter banks with an alternative polyphase structure for calculating the DWT-the lifting method. We look at the traditional lifting structure and a recently proposed "flipping" structure for implementing lifting. All filter bank structures are implemented on an Altera field-programmable gate array. The quantization of the coefficients (for implementation in fixed-point hardware) plays a crucial role in the performance of all structures, affecting both image compression quality and hardware metrics. We design several quantization methods and compare the best design for each approach: the nonpolyphase filter bank, the polyphase filter bank, the lifting and flipping structures. The results indicate that for the same image compression performance, the flipping structure gives the smallest and fastest, low-power hardware.     

Adaptive Nonseparable Wavelet Transform via Lifting and its Application to Content-Based Image Retrieval

We present in this paper a novel way to adapt a multidimensional wavelet filter bank, based on the nonseparable lifting scheme framework, to any specific problem. It allows the design of filter banks with a desired number of degrees of freedom, while controlling the number of vanishing moments of the primal wavelet (mathtilde N? moments) and of the dual wavelet ( N? moments). The prediction and update filters, in the lifting scheme based filter banks, are defined as Neville filters of order mathtilde N? and N? , respectively. However, in order to introduce some degrees of freedom in the design, these filters are not defined as the simplest Neville filters. The proposed method is convenient: the same algorithm is used whatever the dimensionality of the signal, and whatever the lattice used. The method is applied to content-based image retrieval (CBIR): an image signature is derived from this new adaptive nonseparable wavelet transform. The method is evaluated on four image databases and compared to a similar CBIR system, based on an adaptive separable wavelet transform. The mean precision at five of the nonseparable wavelet based system is notably higher on three out of the four databases, and comparable on the other one. The proposed method also compares favorably with the dual-tree complex wavelet transform, an overcomplete nonseparable wavelet transform.     

基于采样二通道不可分小波的多光谱图像融合

针对基于非下采样不可分小波图像融合方法空间分辨率不高、基于张量积小波融合方法会出现方块效应的不足,提出了一种基于伸缩矩阵为[1,1;1,-1]的二通道采样不可分小波的多光谱图像和全色图像融合方法.利用矩阵扩充方法,构造了一组新的不可分低通滤波器和高通滤波器组,利用所设计滤波器组分别对多光谱图像的亮度分量和全色图像作下采样的多尺度不可分小波分解,分别对分解后的低频子图像和高频子图像按不同的融合规则进行融合.实验结果表明,其保持光谱信息的能力和保持空间分辨率信息的能力比基于IHS变换融合方法、基于DWT的融合方法、基于IHS-DWT的融合方法、基于IHS-Contourlet变换的融合方法、基于IHS-Curvelet变换的融合方法、SRF方法都强,与基于非下采样的二通道不可分正交小波和不可分双正交小波融合方法相比,该方法能保持较好的整体光谱信息和较高的空间分辨率信息.     

Moving window-based double Haar wavelet transform for image processing.

Image denoising is a lively research field. The classical nonlinear filters used for image denoising, such as median filter, are based on a local analysis of the pixels within a moving window. Recently, the research of image denoising has been focused on the wavelet domain. Compared to the classical nonlinear filters, it is based on a global multiscale analysis of images. Apparently, the wavelet transform can be embedded in a moving window. Thus, a moving window-based local multiscale analysis is obtained. In this paper, based on the Haar wavelet, a class of nonorthogonal multi-channel filter bank with its corresponding wavelet shrinkage called Lee shrinkage is derived. As a special case of this filter bank, the double Haar wavelet transform is introduced. Examples show that it is suitable for a moving window-based local multiscale analysis used for image denoising, edge detection, and edge enhancement.     

Nonlinear filtering approach to 3-D gray-scale image interpolation

Three-dimensional (3-D) images are now common in radiology. A 3-D image is formed by stacking a contiguous sequence of two-dimensional cross-sectional images, or slices. Typically, the spacing between known slices is greater than the spacing between known points on a slice. Many visualization and image-analysis tasks, however, require the 3-D image to have equal sample spacing in all directions. To meet this requirement, one applies an interpolation technique to the known 3-D image to generate a new uniformly sampled 3-D image. The authors propose a nonlinear-filter-based approach to gray-scale interpolation of 3-D images. The method, referred to as column-fitting interpolation, is reminiscent of the maximum-homogeneity filter used for image enhancement. The authors also draw upon the paradigm of relaxation labeling to devise an improved column-fitting interpolator. Both methods are typically more effective than traditional gray-scale interpolation techniques.     

Perceptual Audio Coding Using Sinusoidal/Optimum Wavelet Representation

A perceptual audio coder, in which each audio segment is adaptively analyzed using either a sinusoidal or an optimum wavelet basis according to the time-varying characteristics of the audio signals, has been constructed. The basis optimization is achieved by a novel switched filter bank scheme, which switches between a uniform filter bank structure (discrete cosine transform) and a non-uniform filter bank structure (discrete wavelet transform). A major artifact of the International ISO/Moving Pictures Experts Group (MPEG) audio coding standard (MPEG-I layers 1 and 2) known as pre-echo distortion which uses a uniform filter bank structure for audio signal analysis, is almost eliminated in the proposed coder. A perceptual masking model implemented using a high-resolution wavelet packet filter bank with 27 subbands, closely mimicking the critical bands of the human auditory system, is employed in this audio coder. The resulting scheme is a variable bit-rate audio coder, which provides compression ratios comparable to MPEG-I layers 1 and 2 with almost transparent quality.     

Spiral interpolation algorithms for multislice spiral CT--part II: measurement and evaluation of slice sensitivity profiles and noise at a clinical multislice system

The recently introduced multislice data acquisition for computed tomography (CT) is based on multirow detector design, increased rotation speed, and advanced z-interpolation and z-filtering algorithms. We evaluated slice sensitivity profiles (SSPs) and noise of a clinical multislice spiral CT (MSCT) scanner with M = 4 simultaneously acquired slices and adaptive axial interpolator (AAI) reconstruction software. SSPs were measured with a small gold disk of 50 microm thickness and 2-mm diameter located at the center of rotation (COR) and 100 mm off center. The standard deviation of CT values within a 20-cm water phantom was used as a measure of image noise. With a detector slice collimation of S = 1.0 mm, we varied spiral pitch p from 0.25 to 2.0 in steps of 0.025. Nominal reconstructed slice thicknesses were 1.25, 1.5, and 2.0 mm. For all possible pitch values, we found the full-width at half maximum (FWHM) of the respective sensitivity profile at the COR equivalent to the selected nominal slice thickness. The profiles at 100 mm off center are broadened less than 7 % on the average compared with the FWHM at the COR. In addition, variation of the full-width at tenth maximum (FWTM) at the COR was below 10% for p < or = 1.75. Within this range, image noise varied less than 10% with respect to the mean noise level. The slight increase in measured slice-width above p = 1.75 for nominal slice-widths of 1.25 and 1.50 mm is accompanied by a decrease of noise according to the inverse square root relationship. The MSCT system that we scrutinized provides reconstructed slice-widths and image noise, which can be regarded as constant within a wide range of table speeds. With respect to this, MSCT is superior to single-slice spiral CT. These facts can be made use of when defining and optimizing clinical protocols: the spiral pitch can be selected almost freely, and scan protocols can follow the diagnostic requirements without technical restrictions. In summary, MSCT offers constant image quality while scan times are reduced drastically. Volume scans with three-dimensional (3-D) isotropic resolution are routinely feasible for complete anatomical regions.     

Optimal design of high-performance separable wavelet filter banks for image coding

An optimization-based method is proposed for the design of high-performance separable wavelet filter banks for image coding. This method yields linear-phase perfect-reconstruction systems with high coding gain, good frequency selectivity, and certain prescribed vanishing-moment properties. Several filter banks designed with the proposed method are presented and shown to work extremely well for image coding, outperforming the well-known 9/7 filter bank from JPEG 2000 in most cases. With the proposed design method, the coding gain can be maximized with respect to the separable or isotropic image model, or jointly with respect to both models. The joint case, which is shown to be equivalent to the isotropic case, is experimentally demonstrated to lead to filter banks with better average coding performance than the separable case.During the development of the proposed design method, filter banks from a certain popular separable two-dimensional (2D) wavelet class (to which our optimal designs belong) were observed to always have a higher coding gain with respect to the separable image model than with respect to the isotropic one. This behavior is examined in detail, leading to the conclusion that, for filter banks belonging to the above class, it is highly improbable (if not impossible) for the isotropic coding gain to exceed the separable coding gain.     

基于二维提升结构的SAR相干斑噪声抑制

针对SAR图像提出了一种新的二维提升变换斑点噪声抑制方法.这种方法利用提升结构构造的双正交小波所具有的良好的逼近和重构性能,以及平滑面区域的特性而实现.仿真时将阈值去噪环节加入变换中.仿真结果表明,本文提出的二维提升变换方法在充分抑制图像斑点噪声的同时,能很好地保持均匀区域内的辐射特性,图像中的边缘、细小特征和点目标,以及图像的纹理特征,克服了传统降噪方法的不足,具有较好的视觉效果.     

Edge-preserving image compression using adaptive lifting wavelet transform

In this paper, a novel 2-D adaptive lifting wavelet transform is presented. The proposed algorithm is designed to further reduce the high-frequency energy of wavelet transform, improve the image compression efficiency and preserve the edge or texture of original images more effectively. In this paper, a new optional direction set, covering the surrounding integer pixels and sub-pixels, is designed. Hence, our algorithm adapts far better to the image orientation features in local image blocks. To obtain the computationally efficient and coding performance, the complete processes of 2-D adaptive lifting wavelet transform is introduced and implemented. Compared with the traditional lifting-based wavelet transform, the adaptive directional lifting and the direction-adaptive discrete wavelet transform, the new structure reduces the high-frequency wavelet coefficients more effectively, and the texture structures of the reconstructed images are more refined and clear than that of the other methods. The peak signal-to-noise ratio and the subjective quality of the reconstructed images are significantly improved.     

基于二维APDCSF的列率子带特征编码方法

提出了一种子带编码的新方法。该方法利用二维全相位离散反余弦列率滤波器（APDCSF）对图像进行子带分解;对于低频子带图像采用直接斜交多重亚采样和基于全相位离散反余弦列牢滤波器（APDICsF）的多重旋转内插恢复．而对高频子带图像利用直方图自动阈值化提取如边缘和线等特征的图像元;根据各个子带的图像元的特征分别进行编码压缩,解压缩后利用凸集投影重建原始图像。该方法消除了传统的离散余弦变换（DCT）编码的方块化效应,与基于小波变换的子带特征编码方法相比,计算复杂度小,压缩率高,主观视觉性能好,对于灰阶图像可达到0．1～0．3bpp,特别适用于低比特率图像压缩。