Image analysis by Gaussian-Hermite moments

Orthogonal moments are powerful tools in pattern recognition and image processing applications. In this paper, the Gaussian-Hermite moments based on a set of orthonormal weighted Hermite polynomials are extensively studied. The rotation and translation invariants of Gaussian-Hermite moments are derived algebraically. It is proved that the construction forms of geometric moment invariants are valid for building the Gaussian-Hermite moment invariants. The paper also discusses the computational aspects of Gaussian-Hermite moment, including the recurrence relation and symmetrical property. Just as the other orthogonal moments, an image can be easily reconstructed from its Gaussian-Hermite moments thanks to the orthogonality of the basis functions. Some reconstruction tests with binary and gray-level images (without and with noise) were performed and the obtained results show that the reconstruction quality from Gaussian-Hermite moments is better than that from known Legendre, discrete Tchebichef and Krawtchouk moments. This means Gaussian-Hermite moment has higher image representation ability. The peculiarity of image reconstruction algorithm from Gaussian-Hermite moments is also discussed in the paper. The paper offers an example of classification using Gaussian-Hermite moment invariants as pattern feature and the result demonstrates that Gaussian-Hermite moment invariants perform significantly better than Hu's moment invariants under both noise-free and noisy conditions.     

微波辐射计的SIR图像重建算法

提出了图像重建可以提高微波辐射计分辨率,并对图像重建的SIR算法原理进行了研究;从采样间隔和迭代次数两方面分别对图像含噪声和不含噪声两种情况进行仿真验证.结果表明,SIR算法是一种有效的图像重建算法.     

A moment-based variational approach to tomographic reconstruction

We describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood (ML) estimates of its orthogonal moments. We show how these estimated moments and their (correlated) error statistics can be computed directly, and in a linear fashion from given noisy and possibly sparse projection data. Moreover, thanks to the consistency properties of the Radon transform, this two-step approach (moment estimation followed by image reconstruction) can be viewed as a statistically optimal procedure. Furthermore, by focusing on the important role played by the moments of projection data, we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments. Taking advantage of this connection, our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data. We show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem. We show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back-projection (FBP) algorithm.     

Electrical impedance tomography: regularized imaging and contrast detection

Dynamic electrical impedance tomography (EIT) images changes in the conductivity distribution of a medium from low frequency electrical measurements made at electrodes on the medium surface. Reconstruction of the conductivity distribution is an under-determined and ill-posed problem, typically requiring either simplifying assumptions or regularization based on a priori knowledge. This paper presents a maximum a posteriori (MAP) approach to linearized image reconstruction using knowledge of the noise variance of the measurements and the covariance of the conductivity distribution. This approach has the advantage of an intuitive interpretation of the algorithm parameters as well as fast (near real time) image reconstruction. In order to compare this approach to existing algorithms, the authors develop figures of merit to measure the reconstructed image resolution, the noise amplification of the image reconstruction, and the fidelity of positioning in the image. Finally, the authors develop a communications systems approach to calculate the probability of detection of a conductivity contrast in the reconstructed image as a function of the measurement noise and the reconstruction algorithm used.     

Electronic Noise Modeling in Statistical Iterative Reconstruction

We consider electronic noise modeling in tomographic image reconstruction when the measured signal is the sum of a Gaussian distributed electronic noise component and another random variable whose log-likelihood function satisfies a certain linearity condition. Examples of such likelihood functions include the Poisson distribution and an exponential dispersion (ED) model that can approximate the signal statistics in integration mode X-ray detectors. We formulate the image reconstruction problem as a maximum-likelihood estimation problem. Using an expectation-maximization approach, we demonstrate that a reconstruction algorithm can be obtained following a simple substitution rule from the one previously derived without electronic noise considerations. To illustrate the applicability of the substitution rule, we present examples of a fully iterative reconstruction algorithm and a sinogram smoothing algorithm both in transmission CT reconstruction when the measured signal contains additive electronic noise. Our simulation studies show the potential usefulness of accurate electronic noise modeling in low-dose CT applications.      

Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations

The maximum-likelihood (ML) expectation-maximization (EM) [ML-EM] algorithm is being widely used for image reconstruction in positron emission tomography. The algorithm is strictly valid if the data are Poisson distributed. However, it is also often applied to processed sinograms that do not meet this requirement. This may sometimes lead to suboptimal results: streak artifacts appear and the algorithm converges toward a lower likelihood value. As a remedy, we propose two simple pixel-by-pixel methods [noise equivalent counts (NEC)-scaling and NEC-shifting] in order to transform arbitrary sinogram noise into noise which is approximately Poisson distributed (the first and second moments of the distribution match those of the Poisson distribution). The convergence speed associated with both transformation methods is compared, and the NEC-scaling method is validated with both simulations and clinical data. These new methods extend the ML-EM algorithm to a general purpose nonnegative reconstruction algorithm.     

广义雅可比-傅立叶矩

图像正交矩具有数值稳定和方便重构等优点,雅 可比-傅立叶矩(JFM)是传统正交矩的推广,然而其定义中 的径向函数仅是整数阶多项式。本文改造JFM的径向函数,提出广义JFM,其定 义中的径向函数既可以是分数阶的多项式,也可以是更一般的函数,JFM仅是这种构造的特 例,并且证明了所提广义JFM的正交性和旋转不变性。数值实验也表明,利用所 提方法可构造出重构性能好、抗噪性能强的图像正交矩。     

Reconstructing polygons from moments with connections to arrayprocessing

We establish a set of results showing that the vertices of any simply connected planar polygonal region can be reconstructed from a finite number of its complex moments. These results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory, where in the former, it is of interest to estimate the shape of an object from a finite number of its projections, whereas in the latter, the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points. We show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem, and taking advantage of this relationship, we derive and illustrate several new algorithms for the reconstruction of the vertices of simply connected polygons from moments     

一种新的Pseudo-Zernike矩的快速算法

Zernike矩因具有正交性和旋转不变性而广泛应用于模式识别、图像分析等领域.Pseudo-Zernike 矩具有与Zernike 矩相似的性质,但它较Zernike 矩具有更好的抗噪声性.由于pseudo-Zernike矩的复杂性,相关的快速算法的研究尚未得到很好的解决.本文根据pseudo-Zernike矩自身的特点,推导了一种快速有效的计算方法.     

基于线性混合模型的高光谱图像分布式压缩感知

为了实现高光谱图像的有效压缩采样与重构,对分布式压缩采样的高光谱数据应用线性混合模型进行重构.首先,在图像采集阶段,针对高光谱图像的空谱特性,应用分布式压缩采样策略对高光谱数据进行采集;在数据重构阶段,应用高光谱图像的线性混合模型假设,先对压缩数据进行端元数目的估计,再利用估计的端元数来估计丰度矩阵,根据端元特征信号的稀疏性质提取端元矩阵,从而重构出原始的高光谱数据,抛弃了压缩感知重构算法中高计算复杂性的欠定问题求解.实验结果表明:在压缩采样数据为总数据的20％时,重构的平均信噪比比压缩投影主成分分析算法提高了15 dB以上,同时该方法还便于获得端元和丰度信息.所设计的压缩感知方案采样方式简单,重构速度快、精度高,可应用于星载或机载的高光谱压缩感知成像.     

Modeling for edge detection problems in blurred noisy images

The aim of this paper is to provide a theoretical set up and a mathematical model for the problem of image reconstruction. The original image belongs to a family of two-dimensional (2-D) possibly discontinuous functions, but is blurred by a Gaussian point spread function introduced by the measurement device. In addition, the blurred image is corrupted by an additive noise. We propose a preprocessing of data which enhances the contribution of the signal discontinuous component over that one of the regular part, while damping down the effect of noise. In particular we suggest to convolute data with a kernel defined as the second order derivative of a Gaussian spread function. Finally, the image reconstruction is embedded in an optimal problem framework. Now convexity and compactness properties for the admissible set play a fundamental role. We provide an instance of a class of admissible sets which is relevant from an application point of view while featuring the desired properties.     

Interpolation of missing data in image sequences

This paper presents a number of model based interpolation schemes tailored to the problem of interpolating missing regions in image sequences. These missing regions may be of arbitrary size and of random, but known, location. This problem occurs regularly with archived film material. The film is abraded or obscured in patches, giving rise to bright and dark flashes, known as "dirt and sparkle" in the motion picture industry. Both 3-D autoregressive models and 3-D Markov random fields are considered in the formulation of the different reconstruction processes. The models act along motion directions estimated using a multiresolution block matching scheme. It is possible to address this sort of impulsive noise suppression problem with median filters, and comparisons with earlier work using multilevel median filters are performed. These comparisons demonstrate the higher reconstruction fidelity of the new interpolators.     

Spatially adaptive high-resolution image reconstruction of DCT-based compressed images

The problem of recovering a high-resolution image from a sequence of low-resolution DCT-based compressed observations is considered in this paper. The introduction of compression complicates the recovery problem. We analyze the DCT quantization noise and propose to model it in the spatial domain as a colored Gaussian process. This allows us to estimate the quantization noise at low bit-rates without explicit knowledge of the original image frame, and we propose a method that simultaneously estimates the quantization noise along with the high-resolution data. We also incorporate a nonstationary image prior model to address blocking and ringing artifacts while still preserving edges. To facilitate the simultaneous estimate, we employ a regularization functional to determine the regularization parameter without any prior knowledge of the reconstruction procedure. The smoothing functional to be minimized is then formulated to have a global minimizer in spite of its nonlinearity by enforcing convergence and convexity requirements. Experiments illustrate the benefit of the proposed method when compared to traditional high-resolution image reconstruction methods. Quantitative and qualitative comparisons are provided.     

Filtering of medical ultrasonic images based on a modified anistropic diffusion equation

Speckle noise reduction is a key problem of the image analysis of medical UltraSound images. In this paper, two important improvements have been developed to a fast anisotropic diffusion algorithm for speckle noise reduction. The Gaussian filter is firstly used before gradient calculation, and then the adaptive algorithm of the factor k is proposed. Numerous experimental results show that the proposed model is superior to other methods in noise removal, fidelity and edge preservation. It is suitable for the preprocessing of a great number of medical UltraSound images, such as three dimen- sional reconstruction.     

具有空间反馈噪声形成的自适应预测图象编码方法

本文提出一种基于人的视觉特性的自适应预测图象编码方法(APICM),该方法核心是通过引入噪声反馈滤波器实现噪声重新分布,以抑制图象敏感区频带内的重构噪声.同时,在不灵敏频带内(如图象边缘区)引入一定噪声以达到整个恢复图象的噪声平滑.因而,可以用更粗(量化电平更少)的非均匀量化器实现.此方法不仅设计复杂度低,且性能比传统的DPCM方法好.     

基于梯度重建与形态学分水岭算法的图像分割

由于分水岭算法存在着过分割的问题,文章提出了一个有效解决该问题的方法。首先,在图像预处理过程中先对图像进行形态学滤波,消除部分噪声;其次,采用形态学求梯度的方法得到原始图像的梯度图并对其进行开闭重建,在保留区域重要轮廓的同时去除噪声和图像细节;第三,对重建后的梯度图像进行基于标记约束的分水岭分割。试验结果表明：该方法能够很好地抑制过分割,同时通过结构元素的选择而具备一定的灵活性,整个过程无需进行合并处理,从而降低了分割的复杂性。     

Incremental variations of image moments for nonlinear image registration

In this paper, we use image moments to solve the problem of estimating deformation fields given a pair of images as input. We use a single family of polynomials to parameterize the deformation field and to define image moments. In this way, variations in image moments can be represented by a set of linear equations. We solve these equations iteratively for the deformation parameters between two shapes. Our approach improves existing moment-based registration methods in both robustness to noise and convergence rate. In addition, our method does not rely on solving the correspondence problem. We have extensively tested our new method on both synthetically deformed MPEG-7 shapes and real-world biomedical images.     

Super resolution image reconstruction through bregman iteration using morphologic regularization

Multiscale morphological operators are studied extensively in the literature for image processing and feature extraction purposes. In this paper, we model a nonlinear regularization method based on multiscale morphology for edge-preserving super resolution (SR) image reconstruction. We formulate SR image reconstruction as a deblurring problem and then solve the inverse problem using Bregman iterations. The proposed algorithm can suppress inherent noise generated during low-resolution image formation as well as during SR image estimation efficiently. Experimental results show the effectiveness of the proposed regularization and reconstruction method for SR image.     

红外成像系统图像处理与重建过程分析

一个完整的红外成像系统包含许多个子系统,每个子系统处理的信息不同。讨论了扫描图像的处理及重建过程,分析了用单点校正法、两点校正方法消除固定图形噪声的特点,讨论了将参考黑体加入扫描系统对系统的改良效果。最后系统地总结了图像处理和重建过程。