Detecting Edges from Non-uniform Fourier Data Using Fourier Frames

Edge detection plays an important role in identifying regions of interest in an underlying signal or image. In some applications, such as magnetic resonance imaging (MRI) or synthetic aperture radar (SAR), data are sampled in the Fourier domain. Many algorithms have been developed to efficiently extract edges of images when uniform Fourier data are acquired. However, in cases where the data are sampled non-uniformly, such as in non-Cartesian MRI or SAR, standard inverse Fourier transformation techniques are no longer suitable. Methods exist for handling these types of sampling patterns, but are often ill-equipped for cases where data are highly non-uniform or when the data are corrupted or otherwise not usable in certain parts of the frequency domain. This investigation further develops an existing approach to discontinuity detection, and involves the use of concentration factors. Previous research shows that the concentration factor technique can successfully determine jump discontinuities in non-uniform data. However, as the distribution diverges further away from uniformity so does the efficacy of the identification. Thus we propose a method that employs the finite Fourier approximation to specifically tailor the design of concentration factors. We also adapt the algorithm to incorporate appropriate smoothness assumptions in the piecewise smooth regions of the function. Numerical results indicate that our new design method produces concentration factors which can more precisely identify jump locations than those previously developed in both one and two dimensions.     

A Model-Theoretic Approach for Recovering Consistent Data from Inconsistent Knowledge Bases

One of the most significant drawbacks of classical logic is its being useless in the presence of an inconsistency. Nevertheless, the classical calculus is a very convenient framework to work with. In this work we propose means for drawing conclusions from systems that are based on classical logic, although the information might be inconsistent. The idea is to detect those parts of the knowledge base that cause the inconsistency, and isolate the parts that are recoverable. We do this by temporarily switching into Ginsberg/Fitting multivalued framework of bilattices (which is a common framework for logic programming and nonmonotonic reasoning). Our method is conservative in the sense that it considers the contradictory data as useless and regards all the remaining information unaffected. The resulting logic is nonmonotonic, paraconsistent, and a plausibility logic in the sense of Lehmann.     

Image Reconstruction from Fourier Data Using Sparsity of Edges

Data of piecewise smooth images are sometimes acquired as Fourier samples. Standard reconstruction techniques yield the Gibbs phenomenon, causing spurious oscillations at jump discontinuities and an overall reduced rate of convergence to first order away from the jumps. Filtering is an inexpensive way to improve the rate of convergence away from the discontinuities, but it has the adverse side effect of blurring the approximation at the jump locations. On the flip side, high resolution post processing algorithms are often computationally cost prohibitive and also require explicit knowledge of all jump locations. Recent convex optimization algorithms using \(l^1\) regularization exploit the expected sparsity of some features of the image. Wavelets or finite differences are often used to generate the corresponding sparsifying transform and work well for piecewise constant images. They are less useful when there is more variation in the image, however. In this paper we develop a convex optimization algorithm that exploits the sparsity in the edges of the underlying image. We use the polynomial annihilation edge detection method to generate the corresponding sparsifying transform. Our method successfully reduces the Gibbs phenomenon with only minimal blurring at the discontinuities while retaining a high rate of convergence in smooth regions.     

利用专题指数改善沙漠化土地遥感分类精度

以民勤绿洲及周边区域ETM+数据为例,分析光谱变换专题指数和纹理特征变量的参与对沙漠化土地分类精度的影响,以及不同分类器对两者的响应。原始数据中单独加入专题指数,并不一定直接提高总体分类精度,在同时加入纹理变量的情况下,专题指数的作用才得以充分体现;最大似然法和人工神经网络法分类器对输入变量的响应有所不同,前者在3类数据同时参与时效果最佳,而后者在剔除原始数据时取得最高总体分类精度。实验表明:光谱变换专题指数能够提高沙漠化土地分类精度,但必须慎重选择分类器和分类变量。     

FAT32分区DBR故障的数据恢复解决方案

该文针对FAT32文件系统DBR损坏造成分区无法正常打开的故障,提出手工重建DBR及先备份再格式化恢复分区的解决方案。实践证明,两种解决方案对解决DBR损坏的故障都是有效的。     

基于康普顿散射的能谱数据重建电子密度图像

提出一种基于能谱和行扫描的康普顿散射成像方法。该方法通过逐行扫描，把一个较大的图像重建问题分解成几个独立的小而容易解决的问题进行重建。对于正向方程中源于非扫描行的衰减作用，利用已重建行的像素值来计算；对源于扫描行自身的衰减作用，用逐步近似(SAP)的方法来计算。为了减小说差在不同扫描行之间的传播，利用途射数据对重建结果进行校正。实验证明，该方法速度快、可靠性高，易于实现。     

Edge Detection from Non-Uniform Fourier Data Using the Convolutional Gridding Algorithm

Detecting edges in images from a finite sampling of Fourier data is important in a variety of applications. For example, internal edge information can be used to identify tissue boundaries of the brain in a magnetic resonance imaging (MRI) scan, which is an essential part of clinical diagnosis. Likewise, it can also be used to identify targets from synthetic aperture radar data. Edge information is also critical in determining regions of smoothness so that high resolution reconstruction algorithms, i.e. those that do not “smear over” the internal boundaries of an image, can be applied. In some applications, such as MRI, the sampling patterns may be designed to oversample the low frequency while more sparsely sampling the high frequency modes. This type of non-uniform sampling creates additional difficulties in processing the image. In particular, there is no fast reconstruction algorithm, since the FFT is not applicable. However, interpolating such highly non-uniform Fourier data to the uniform coefficients (so that the FFT can be employed) may introduce large errors in the high frequency modes, which is especially problematic for edge detection. Convolutional gridding, also referred to as the non-uniform FFT, is a forward method that uses a convolution process to obtain uniform Fourier data so that the FFT can be directly applied to recover the underlying image. Carefully chosen parameters ensure that the algorithm retains accuracy in the high frequency coefficients. Similarly, the convolutional gridding edge detection algorithm developed in this paper provides an efficient and robust way to calculate edges. We demonstrate our technique in one and two dimensional examples.     

Aster数据的DEM生产及精度评价

利用贵州省黎平县ASTER 15m的立体影像像对进行DEM生产并对其精度进行评价。研究结果表明：ASTER数据提取DEM是可行的；地面控制点(GCPs)的精度、分布和数量是决定提取DEM数据精度的关键；控制点数目较多，分布均匀时可以大大提高DEM提取的精度。     

Representation of High Resolution Images from Low Sampled Fourier Data: Applications to Dynamic MRI

In this work we propose the use of B-spline functions for the parametric representation of high resolution images from low sampled data in the Fourier domain. Traditionally, exponential basis functions are employed in this situation, but they produce artifacts and amplify the noise on the data. We present the method in an algorithmic form and carefully consider the problem of solving the ill-conditioned linear system arising from the method by an efficient regularization method. Two applications of the proposed method to dynamic Magnetic Resonance images are considered. Dynamic Magnetic Resonance acquires a time series of images of the same slice of the body; in order to fasten the acquisition, the data are low sampled in the Fourier space. Numerical experiments have been performed both on simulated and real Magnetic Resonance data. They show that the B-splines reduce the artifacts and the noise in the representation of high resolution Magnetic Resonance images from low sampled data. This work was supported by the Italian MIUR project Inverse Problems in Medical Imaging 2004–2006 (grant no 2004015818). Germana Landi received the BS degree in Mathematics from the University of Bologna in 1997 and the Ph.D. degree in Computational Mathematics from the University of Padova in 2000. She is currently a postdoctoral researcher in Numerical Analysis at the Department of Mathematics of the University of Bologna. Her research interests include medical imaging and inverse ill-posed problems. Elena Loli Piccolomini received the BS degree in Mathematics from the University of Bologna in 1988. She is an associate professor in Numerical Analysis at the Department of Mathematics of the University of Bologna. Her research interests include numerical methods for the regularization of discrete ill-posed problems with application to medical imaging (MR, TAC, SPECT, PET).     

Blind System Identification Using Normalized Fourier Coefficient Gradient Vectors Obtained from Time-Frequency Entropy-Based Blind Clustering of Data Wavelets

A method for the blind identification of spatially varying transfer functions found in various remote sensing applications such as medical imagery, radar, sonar, and seismology is described. The techniques proposed herein are based on model matching of Fourier coefficient sensitivity vectors of a known transfer function, which can be nonlinear in the parameters, with a set of eigenvectors obtained from data covariance matrices. One distinction between this technique and usual channel subspace methods is that no FIR structure for the individual transfer functions is assumed. Instead we assume that the frequency response as a function of the parameters is known as is often the case in wave transmission problems. A channel identification procedure based on subspace matching is proposed. The procedure matches the eigenvectors of the signal deviation covariance matrix to a set of scaled and energy-normalized sensitivity vectors. For the case where neither the number of channels, the model parameters of each channel nor the membership assignment of data traces to the channels is known, we propose a novel preliminary clustering process. By separating the data into clusters of modest variability such that the measurements are linear with the parameters, we are able to deduce all of the above. The clustering is based on feature vectors obtained from a time-frequency entropy measure, also a novelty of our paper. To support the theory developed, we include parameter estimation results based on simulated data backscattered from a synthetic multi-layer structure.