On the validity of hypothesis testing for feasibility of image reconstructions

Feasible images have been defined as those images that could have generated the original data by the statistical process that governs the measurement. In the case of emission tomography, the statistical process of emission is Poisson and it is known that feasible images resulting from the maximum likelihood estimator (MLE) and Bayesian methods with entropy priors can be of high quality. Tests for feasibility have been described that are based on one critical assumption: the image that is being tested is independent of the data, even though the reconstruction algorithm has used those data in order to obtain the image. This fact could render the procedure unacceptable unless it is shown that its effects on the results of the tests are negligible. Experimental evidence is presented showing that images reconstructed by the MLE and stopped before convergence do indeed behave as if independent of the data. The results justify the use of hypothesis testing in practice, although they leave the problem of analytical proof still open.     

Model-based reconstruction of multiple circular and ellipticalobjects from a limited number of projections

We consider tomographic image reconstruction from a limited number of noisy projections. An efficient algorithm based on maximum likelihood estimation (MLE) is developed to reconstruct images of multiple discs with unknown locations and radii. The algorithm is successfully applied to images with signal-to-noise ratio (SNR) as low as 0 dB, using as few as 16 projections, and containing as many as twelve discs with widely varying radii. Experimental results show that our approach significantly outperforms conventional convolution back projection. The algorithm is successfully extended to the multiple ellipse case.     

Improved iterative image reconstruction with automatic noise artifact suppression

A method for stabilizing iterative image reconstruction techniques has been developed for improving the image quality of position emission tomography. A damping matrix is introduced, which suppresses noisy correction on a pixel-by-pixel basis, depending on the statistical precision of the iterative correction. The precision is evaluated by comparing a certain number of correction submatrices, each of which is formed from a subset of the projection data. Simulation studies showed that statistical noise is effectively suppressed, while the image of the source object is reconstructed with high resolution, as long as the signal level is higher than the local noise level. In the application to the MLE (maximum likelihood estimator), the minimum RMS error of the image was reduced to 84% for 500 k total counts, and the RMS error increased more slowly with further iterations as compared with the simple MLE. The method was also applied to the FIR (filtered iterative reconstruction) algorithm, and the images were found to be better than those obtained by the convolution backprojection method.     

Feature extraction techniques for exploratory visualization ofvector-valued imagery

This paper addresses the exploratory visualization of multispectral image data. In such data, each component of the vector pixel corresponds to a different imaging modality or a different combination of imaging parameters, and may provide different levels of contrast sensitivity between different regions of the underlying image. We address the problem of presenting this multidimensional data to human observers by synthesizing a display matched to their visual capabilities. Specifically, we seek to determine a data-adaptive linear projection of the vector data to one dimension that produces a grayscale image providing maximum discrimination between the different regions of the underlying object. The approach is equivalent to the extraction of the best linear feature of the vector field. Several new feature-extraction criteria that take into account both the spatial and multivariate structures of the data are proposed and illustrated by simulations on test images.     

An adaptive Gaussian model for satellite image deblurring

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose here to use an inhomogeneous model. We use the maximum likelihood estimator (MLE) to estimate its parameters and we show that the MLE computed on the corrupted image is not suitable for image deconvolution because it is not robust to noise. We then show that the estimation is correct only if it is made from the original image. Since this image is unknown, we need to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, a hybrid method is first used to estimate the space-variant parameters from this image and then to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures, and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.     

Feasible images and practical stopping rules for iterative algorithms in emission tomography

The discussion of the causes of image deterioration in the maximum-likelihood estimator (MLE) method of tomographic image reconstruction, initiated with the publication of a stopping rule for that iterative process (E. Veklerov and J. Llacer, 1987) is continued. The concept of a feasible image is introduced, which is a result of a reconstruction that, if it were a radiation field, could have generated the initial projection data by the Poisson process that governs radioactive decay. From the premise that the result of a reconstruction should be feasible, the shape and characteristics of the region of feasibility in projection space are examined. With a new rule, reconstructions from real data can be tested for feasibility. Results of the tests and reconstructed images for the Hoffman brain phantom are shown. A comparative examination of the current methods of dealing with MLE image deterioration is included.     

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.     

Resolution enhancement of tomographic images using the row action projection method

The row action projection (RAP) method is used to increase the spatial resolution of images reconstructed via the filtered back projection (FBP) algorithm. An implementation of RAP is introduced which is computationally efficient and facilitates local adaptation of the projection operators. The local mean value as well as minimum and maximum bounds are used as constraints. The method is proposed to provide zoom-in capability, which yields a high-resolution estimate of a specified region of the image. Computer simulations demonstrate the new method to be very effective in recovering high-order spectral components of designated regions of the reconstructed image.     

Regularized image reconstruction algorithms for dual-isotope myocardial perfusion SPECT (MPS) imaging using a cross-tracer prior

In simultaneous dual-isotope myocardial perfusion SPECT (MPS) imaging, data are simultaneously acquired to determine the distributions of two radioactive isotopes. The goal of this work was to develop penalized maximum likelihood (PML) algorithms for a novel cross-tracer prior that exploits the fact that the two images reconstructed from simultaneous dual-isotope MPS projection data are perfectly registered in space. We first formulated the simultaneous dual-isotope MPS reconstruction problem as a joint estimation problem. A cross-tracer prior that couples voxel values on both images was then proposed. We developed an iterative algorithm to reconstruct the MPS images that converges to the maximum a posteriori solution for this prior based on separable surrogate functions. To accelerate the convergence, we developed a fast algorithm for the cross-tracer prior based on the complete data OS-EM (COSEM) framework. The proposed algorithm was compared qualitatively and quantitatively to a single-tracer version of the prior that did not include the cross-tracer term. Quantitative evaluations included comparisons of mean and standard deviation images as well as assessment of image fidelity using the mean square error. We also evaluated the cross tracer prior using a three-class observer study with respect to the three-class MPS diagnostic task, i.e., classifying patients as having either no defect, reversible defect, or fixed defects. For this study, a comparison with conventional ordered subsets-expectation maximization (OS-EM) reconstruction with postfiltering was performed. The comparisons to the single-tracer prior demonstrated similar resolution for areas of the image with large intensity changes and reduced noise in uniform regions. The cross-tracer prior was also superior to the single-tracer version in terms of restoring image fidelity. Results of the three-class observer study showed that the proposed cross-tracer prior and the convergent algorithms improved the image quality of dual-isotope MPS images compared to OS-EM.     

一种结合空谱聚类的高光谱图像快速压缩算法

对高光谱图像进行快速压缩已经成为了高光谱遥感领域的研究热点.针对现有的高光谱图像数据量大和压缩所需运算量大的问题,提出了一种基于频段聚类+主成分分析(PCA)与空间分类相结合的高光谱图像快速压缩算法.首先利用最大相关度频段聚类算法(MCBC)将频段聚类,接着将每一类频段用PCA压缩,然后将压缩后的图像利用聚类信号子空间投影(CSSP)算法进行图像分类,最后在每一类内利用LBG(Linde Buzo Gray)算法通过矢量量化快速完成高光谱图像的编码.在不同的压缩比下进行实验,结果表明提出的高光谱图像压缩算法能在保证良好的图像恢复质量的前提下,大幅度降低运算复杂度,实现高光谱图像的快速压缩.     

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.     

Image reconstruction by conditional entropy maximisation for PET system

The authors show that the conditional entropy maximisation algorithm is a generalised version of the maximum likelihood algorithm for positron emission tomography (PET). Promising properties of the conditional entropy maximisation algorithm are as follows: an assumption is made that the entropy of the information content of the data should be maximised; it is a consistent way of selecting an image from the very many images that fit the measurement data; this approach takes care of the positivity of the reconstructed image pixels, since entropy does not exist for negative image pixel values; and inclusion of prior distribution knowledge in the reconstruction process is possible. Simulated experiments performed on a PET system have shown that the quality of the reconstructed image using the entropy maximisation method is good. A Gibbs distribution is used to incorporate prior knowledge into the reconstruction process. The mean squared error (MSE) of the reconstructed images shows a sharp new dip, confirming improved image reconstruction. The entropy maximisation method is an alternative approach to maximum likelihood (ML) and maximum a posteriori (MAP) methodologies.     

Controlling Familywise Error Rate for Matched Subspace Detection in Dynamic FDG PET

Detection of small lesions in fluorodeoxyglucose (FDG) positron emission tomography (PET) is limited by image resolution and low signal to noise ratio. We have previously described a matched subspace detection method that uses the time activity curve to distinguish tumors from background in dynamic FDG PET. Applying this algorithm on a voxel by voxel basis throughout the dynamic image produces a test statistic image or ldquomaprdquo which on thresholding indicates the potential locations of secondary or metastatic tumors. In this paper, we describe a thresholding method that controls familywise error rate (FWER) for the matched subspace detection statistical map. The method involves three steps. First, the PET image is segmented into several homogeneous regions. Then, the statistical map is normalized to a zero mean unit variance Gaussian random field. Finally, the images are thresholded at a fixed FWER by estimating their spatial smoothness and applying a random field theory maximum statistic approach. We evaluate this thresholding method using digital phantoms generated from clinical dynamic images. We also present an application of the proposed approach to clinical PET data from a breast cancer patient with metastatic disease.     

基于最佳线性估计的快速压缩感知图像重建算法

针对目前存在的压缩感知(CS)重建算法计算复杂度过高的问题,该文提出一种基于最佳线性估计的快速CS图像重建算法。该算法在编码端进行分块自适应CS随机测量,在解码端根据图像块不同的统计特性,估计出统计自相关函数矩阵,进而构造出最佳线性算子用于重建出各个图像块。由于该算法用线性投影的方式替代了传统CS重建算法的非线性迭代过程,使得其大大缩短了图像重建时间。仿真实验结果表明,对于纹理细节不复杂的图像,所提出的算法并没有因为其计算复杂度的减少而影响到重建质量,仍优于目前流行的CS重建算法。     

结合文字核心区域和扩展生长的藏文古籍文本行切分

藏文古籍文档图像中相邻文本行之间通常存在黏连和重叠的情况,这使得文本行切分成为一项艰巨的任务.因此,提出了一种结合文字核心区域和扩展生长的藏文古籍文档图像的行切分方法.首先,根据二值藏文古籍文档图像中连通域的面积和真圆度去除非音节点,获得音节点图像.其次,通过水平投影音节点图像和垂直投影二值原图,得到文本行基线所处的范...     

基于最大值投影和快速配准的空间小目标检测

天基观测平台下弱小目标的检测是分析空间安全的重要研究内容。由于空间中存在大量外观与目标相似的恒星导致可利用空间分布信息缺乏;观测平台的不规则性运动导致帧间成像差异,都使得开发自动快速处理算法的难度增加。在分析星空图像模型的基础上,提出了一种基于三角形匹配和最大值投影的小目标检测方法。首先通过特征三角形对序列图像进行配准,并采用星点坐标矩阵的方法减小计算量。然后针对序列帧所有图像,采用最大值投影变换的方法,检测运动的小目标。最后通过200帧观测图像对算法进行验证,实验表明该方法能实时、准确地对目标进行检测,同时可以精确地定位目标质心。     

Suppression of Metal Artifacts in CT Using a Reconstruction Procedure That Combines MAP and Projection Completion

Metal implants such as hip prostheses and dental fillings produce streak and star artifacts in the reconstructed computed tomography (CT) images. Due to these artifacts, the CT image may not be diagnostically usable. A new reconstruction procedure is proposed that reduces the streak artifacts and that might improve the diagnostic value of the CT images. The procedure starts with a maximum a posteriori (MAP) reconstruction using an iterative reconstruction algorithm and a multimodal prior. This produces an artifact-free constrained image. This constrained image is the basis for an image-based projection completion procedure. The algorithm was validated on simulations, phantom and patient data, and compared with other metal artifact reduction algorithms.      

Dual information hiding algorithm based on the regularity of 3D mesh model

An adaptive thresholds algorithm is proposed in this letter, which is used to determine the global optimal thresholds for multi-bit quanta image sensor (MB-QIS). Firstly, the senor model of MB-QIS is set up. Then global optimal thresholds theory is analyzed and a thresholds optimization algorithm based on the binary search is designed to determine the optimal global thresholds. Finally, the high dynamic range (HDR) images are reconstructed by the non-iterative maximum likelihood estimation (MLE) image reconstruction method. The results of simulation prove that HDR imaging of MB-QIS is realized by the proposed method effectively.     

基于记忆分子动理论优化算法的多目标截面投影Otsu图像分割

传统截面投影Otsu法后处理过程中的阈值Q为预先设定的常量,对含噪程度不同的图像普适性较差。该文提出一种基于记忆分子动理论优化算法的多目标截面投影Otsu法。该方法将阈值Q作为变量,结合分割阈值T,基于最大类间方差和最大峰值信噪比准则建立多目标图像分割模型,以兼顾图像分割的准确性和抗噪性;为免阈值增加而影响算法效率,将人工记忆原理引入分子动理论优化算法,设计了一种基于记忆分子动理论优化算法的多目标图像分割模型求解方法。实验表明:该方法分割准确、抗噪性强、鲁棒性好,对含不同噪声的图像更具普适性。     

基于模型的单幅高分辨SAR图像建筑物高度反演方法

高分辨合成孔径雷达(SAR)图像的丰富使得建筑物三维信息获取成为城区遥感的一项重要研究课题.针对单幅SAR图像建筑物的高度估计问题,提出了一种基于模型的高度反演方法.该方法遵循假设检验的思路,通过正交投影模型实现模型假设的快速生成,并设计了基于分割的似然函数,利用模拟退火算法在高维模型假设空间中搜索最优解.基于模拟和实测机载SAR图像的实验验证了算法的有效性.