Multigrid tomographic inversion with variable resolution data and image spaces.

A multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed. Since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements, the proposed algorithm further reduces the computation relative to conventional multigrid approaches, which change only the image space resolution at coarse scales. The advantage is particularly important for data-rich applications, where data resolutions may differ for different scales. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography with a generalized Gaussian Markov random field image prior are presented, both with a Poisson noise model and with a quadratic data term. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent method and a multigrid method with fixed-data resolution.     

Solution of inverse problems in image processing by waveletexpansion

We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results.     

Analysis of Millimeter Wave Scattering by an Electrically Large Metallic Grating Using Wavelet-Based Algebraic Multigrid Preconditioned CG Method

An effective wavelet based multigrid preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using wavelet transformation we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the new improvement for the conjugate gradient (CG) method. Numerical results show that our developed wavelet based multigrid preconditioned CG method can reach large improvement of computational complexity. Due to the automaticity of wavelet transformation, this method is potential to be a block box solver without physical background.     

利用基追踪算法实现图像压缩感知重建研究

压缩感知理论突破了奈奎斯特采样频率的限制,利用该理论研究和实现了二维图像的压缩采样和重建。该方案利用小波变换实现图像稀疏化,利用标准伪随机数均匀分布和二维中心傅里叶变换生成随机测量矩阵,并对小波变换后的高频子带进行加权采样,用改进的基追踪算法实现二维图像压缩感知重建。仿真实验结果表明,该方案重建图像的客观评价PSNR效果较好。     

Analysis of electromagnetic scattering from conducting bodies ofrevolution using orthogonal wavelet expansions

The wavelet expansion method has been extended to study the electromagnetic scattering from conducting bodies of revolution. The magnetic field integral equation (MFIE) is solved by this approach. By expanding the induced surface currents in terms of Fourier series of uncoupled azimuthal cylindrical modes, a simplified MFIE is attained for each unknown mode current that varies along the curved profile of the scatterer. By applying the boundary element method (BEM), the curved profile is mapped into the definition domain of the orthogonal wavelets on the interval. The unknown mode currents are then expressed using multiscale wavelet expansions. The simplified MFIE is converted into a sparse, multilevel matrix equation by the Galerkin method. Numerical examples are provided to illustrate the merits of this wavelet approach     

Mexico 草帽小波与电离层CT反演

电离层ＣＴ技术中由于数据采集系统的几何结构存在局限性,致使探测所得数据不导致其成为不完全数据重建问题。投影中的采样点不均匀,且由投影谱通过Ｆｏｕｒｉｅｒ中心切片原理组合而得的二维谱平面不完全可知,若要用变换方法重建成象,需要对其进行估计。     

基于正交小波变换的图像去噪算法研究

提出了一种基于正交小波变换的图像去噪方法,首先利用离散小波对图像信号按Mallat算法进行分解,然后采用软闽值与小波重构的算法进行去噪。深入研究了小波变换中的图像分解与重构的Mallat算法,详细介绍了正交小波变换中阈值的选取,并进行了实验研究。实验结果表明,该方法可以有效去除噪声,并保留了图像细节部分的有用信息。     

Multiresolution reconstruction in fan-beam tomography

In this paper, a new multiresolution reconstruction approach for fan-beam tomography is established. The theoretical development assumes radial wavelets. An approximate reconstruction formula based on a near-radial quincunx multiresolution scheme is proposed. This multiresolution algorithm allows to compute both the quincunx approximation and detail coefficients of an image from its fan-beam projections. Simulations on mathematical phantoms show that wavelet decomposition is acceptable for small beam angles but deteriorates at high angles. The main applications of the method are denoising and wavelet-based image analysis.     

Computer-aided tumor detection in endoscopic video using color wavelet features

We present an approach to the detection of tumors in colonoscopic video. It is based on a new color feature extraction scheme to represent the different regions in the frame sequence. This scheme is built on the wavelet decomposition. The features named as color wavelet covariance (CWC) are based on the covariances of second-order textural measures and an optimum subset of them is proposed after the application of a selection algorithm. The proposed approach is supported by a linear discriminant analysis (LDA) procedure for the characterization of the image regions along the video frames. The whole methodology has been applied on real data sets of color colonoscopic videos. The performance in the detection of abnormal colonic regions corresponding to adenomatous polyps has been estimated high, reaching 97% specificity and 90% sensitivity.     

On the use of wavelet expansions in the method of moments [EMscattering]

An approach which incorporates the theory of wavelet transforms in method-of-moments solutions for electromagnetic wave interaction problems is presented. The unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function, which is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer. The approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths. Using a Galerkin method and subsequently applying a threshold procedure, the moment-method matrix is rendered sparsely populated. The structure of the matrix reveals the localized scale-fitting distribution long before the matrix equation is solved. The performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double-slot aperture     

一种像素级多算子红外与可见光图像融合方法

给出了一种新的基于多尺度分解的像素级图像融合方法。该方法利用小波变换对每一图像进行多尺度分解,按照不同的融合规则,采用多种融合算子去构造融合图像对应的各小波系数,再根据融合图像的各小波系数重构融合图像。该方法被成功地用于红外与可见光图像的融合处理。实验结果表明该融合方法十分有效,获得的融合图像更符合人们的视觉特性、更有利于机器视觉。     

Nonlinear multigrid algorithms for Bayesian optical diffusiontomography

Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional (3-D) imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality     

双正交小波提升系数的递推算法与实现

根据双正交小波提升格式的特点,为了得到快速提升小波变换的系数,提出求解提升系数的递推算法。该方法基于前向小波变换的预测和更新过程的递推式,与给定双正交小波滤波器比较系数,求得小波提升系数和尺度系数。实例证明,无论是先预测后更新的提升格式,还是先更新后预测的提升格式,均可用此法求解提升系数。在Matlab7.0平台上,用递推算法编程实现db5.3小波转换成提升格式,完成图像的三级分解。     

A general framework for nonlinear multigrid inversion.

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. In this paper, we propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.     

Incorporation of correlated structural images in PET image reconstruction

Reports on a new method in which spatially correlated magnetic resonance (MR) or X-ray computed tomography (CT) images are employed as a source of prior information in the Bayesian reconstruction of positron emission tomography (PET) images. This new method incorporates the correlated structural images as anatomic templates which can be used for extracting information about boundaries that separate regions exhibiting different tissue characteristics. In order to avoid the possible introduction of artifacts caused by discrepancies between functional and anatomic boundaries, the authors propose a new method called the "weighted line site" method, in which a prior structural image is employed in a modified updating scheme for the boundary variable used in the iterative Bayesian reconstruction. This modified scheme is based on the joint probability of structural and functional boundaries. As to the structural information provided by CT or MR images, only those which have high joint probability with the corresponding PET data are used; whereas other boundary information that is not supported by the PET image is suppressed. The new method has been validated by computer simulation and phantom studies. The results of these validation studies indicate that this new method offers significant improvements in image quality when compared to other reconstruction algorithms, including the filtered backprojection method and the maximum likelihood approach, as well as the Bayesian method without the use of the prior boundary information.     

Multi-spectral and hyperspectral image fusion using 3-D wavelet transform

Image fusion is performed between one band of multi-spectral image and two bands of hyperspectral image to produce fused image with the same spatial resolution as source multi-spectral image and the same spectral resolution as source hyperspeetral image. According to the characteristics and 3-Dimensional （3-D） feature analysis of multi-spectral and hyperspectral image data volume, the new fusion approach using 3-D wavelet based method is proposed. This approach is composed of four major procedures： Spatial and spectral resampling, 3-D wavelet transform, wavelet coefficient integration and 3-D inverse wavelet transform. Especially, a novel method, Ratio Image Based Spectral Resampling （RIBSR）method, is proposed to accomplish data resampling in spectral domain by utilizing the property of ratio image. And a new fusion rule, Average and Substitution （A＆S） rule, is employed as the fusion rule to accomplish wavelet coefficient integration. Experimental results illustrate that the fusion approach using 3-D wavelet transform can utilize both spatial and spectral characteristics of source images more adequately and produce fused image with higher quality and fewer artifacts than fusion approach using 2-D wavelet transform. It is also revealed that RIBSR method is capable of interpolating the missing data more effectively and correctly, and A＆S rule can integrate coefficients of source images in 3-D wavelet domain to preserve both spatial and spectral features of source images more properly.     

小波域多角度轮廓模板变分模型的单幅图像超分辨率重建

近年来图像超分辨率重建技术因其可以提高图像的识别精度和识别能力而受到重视,其中一个难点问题是如何保证图像边缘纹理区域的重建质量.本文提出一种基于小波域的单幅图像超分辨率重建方法,首先对输入图像进行非下采样小波变换,根据小波变换的多方向性提出三类多角度模板,并采用TV模型估计各子带轮廓,确定其所属的最优方向,然后利用多角度模板来对各个子带进行双三次B样条插值,最后进行非下采样小波反变换.该方法使重建后图像的边缘、纹理信息更加精细,克服了诸如双线性插值法与双三次插值法等传统插值重建所产生的边缘模糊与边缘锯齿化,以及纹理区域失真等不足,在一定程度上提高了重建图像的质量.该方法可用于图像监控、遥感影像分析和医学图像处理等领域.大量的仿真实验验证了所提出方法的有效性.     

一种基于多字典学习的图像分割模糊方法

本文提出一种基于多字典学习的图像分割模糊模型和算法.在模型中,结合多字典学习和模糊方法,考虑了分割区域内部的一致性和边界的正则性：一方面使用区域块均值和带有类标的结构字典重构图像块,利用重构误差和l2正则能量共同度量分割区域内部的一致性,该度量能够刻画图像不同区域的灰度信息和纹理模式;另一方面采用小波系数稀疏正则保持分割区域边界的几何结构.基于交替方向乘子法和字典学习方法给出新模型的快速求解算法.在该算法中,除了小波阈值,每一步都是显示表达式,因此简单易用.一系列实验结果验证了本文算法的有效性.     

Ordering for embedded coding of wavelet image data based on arbitrary scalar quantization schemes.

Many modern wavelet quantization schemes specify wavelet coefficient step sizes as continuous functions of an input step-size selection criterion; rate control is achieved by selecting an appropriate set of step sizes. In embedded wavelet coders, however, rate control is achieved simply by truncating the coded bit stream at the desired rate. The order in which wavelet data are coded implicitly controls quantization step sizes applied to create the reconstructed image. Since these step sizes are effectively discontinuous, piecewise-constant functions of rate, this paper examines the problem of designing a coding order for such a coder, guided by a quantization scheme where step sizes evolve continuously with rate. In particular, it formulates an optimization problem that minimizes the average relative difference between the piecewise-constant implicit step sizes associated with a layered coding strategy and the smooth step sizes given by a quantization scheme. The solution to this problem implies a coding order. Elegant, near-optimal solutions are presented to optimize step sizes over a variety of regions of rates, either continuous or discrete. This method can be used to create layers of coded data using any scalar quantization scheme combined with any wavelet bit-plane coder. It is illustrated using a variety of state-of-the-art coders and quantization schemes. In addition, the proposed method is verified with objective and subjective testing.