一种非均匀采样信号重构方法

针对周期性非均匀采样信号,推导了其频谱和均匀采样序列频谱之间的关系,并基于此给出了一种信号重构方法。仿真结果验证了该方法的可行性。     

Reconstruction of emission tomography data using origin ensembles

A new statistical reconstruction method based on origin ensembles (OE) for emission tomography (ET) is examined. Using a probability density function (pdf) derived from first principles, an ensemble expectation of numbers of detected event origins per voxel is determined. These numbers divided by sensitivities of voxels and acquisition time provide OE estimates of the voxel activities. The OE expectations are shown to be the same as expectations calculated using the complete-data space. The properties of the OE estimate are examined. It is shown that OE estimate approximates maximum likelihood (ML) estimate for conditions usually achieved in practical applications in emission tomography. Three numerical experiments with increasing complexity are used to validate theoretical findings and demonstrate similarities of ML and OE estimates. Recommendations for achieving improved accuracy and speed of OE reconstructions are provided.     

Reconstruction of fluorescence molecular tomography using a neighborhood regularization

In fluorescence molecular tomography, the highly scattering property of biological tissues leads to an ill-posed inverse problem and reduces the accuracy of detection and localization of fluorescent targets. Regularization technique is usually utilized to obtain a stable solution. Conventional Tikhonov regularization is based on singular value decomposition (SVD) and L-curve strategy, which attempts to find a tradeoff between the residual norm and image norm. It is computationally demanding and may fail when there is no optimal turning point in the L-curve plot. In this letter, a neighborhood regularization method is presented. It achieves a reliable solution by computing the geometric mean of multiple regularized solutions. These solutions correspond to different regularization parameters with neighbor orders of magnitude. The main advantages lie in three aspects. First, it can produce comparable or better results in comparison with the conventional Tikhonov regularization with L-curve routine. Second, it replaces the time-consuming SVD computation with a trace-based pseudoinverse strategy, thus greatly reducing the computational cost. Third, it is robust and practical even when the L-curve technique fails. Results from numerical and phantom experiments demonstrate that the proposed method is easy to implement and effective in improving the quality of reconstruction.     

Reconstruction of nonuniform transmission lines from time-domainreflectometry

A novel technique is developed to reconstruct the physical structures of a nonuniform transmission line from its time-domain or frequency-domain reflection (scattering) coefficient. This technique takes the past history of reflection processes of nonuniform line into considerations, and its accuracy exceeds that of a conventional time-domain reflectometry (TDR) technique. Experimental results are presented to illustrate the validity of this reconstruction technique     

An improved reconstruction algorithm for 3-D diffraction tomography using spherical-wave sources

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a weakly scattering object. In this paper, a novel reconstruction algorithm for three-dimensional diffraction tomography employing spherical-wave sources is mathematically developed and numerically implemented. Our algorithm is numerically robust and is much more computationally efficient than the conventional filtered backpropagation algorithm. Our previously developed algorithm for DT using plane-wave sources is contained as a special case.     

Computerized tomography with ultrasound

The mathematical basis for transmission computed tomographic imaging using straight-line reconstruction equations is discussed. Both narrow-band and broad-band solutions are described. The Born and Rytov methods are discussed and the Rytov inversion equation presented with some results. Problems with implementation of the method are mentioned. Backscatter reconstruction methods of seismology are discussed as to their strengths and weaknesses for use in tissue imaging.     

Fast interpolation algorithm using FFT

An interpolation algorithm for finite-duration real sequences using the discrete Fourier transform is presented. The proposed method is shown to result in a significant saving of computational labour over the discrete version of the time-domain classical interpolation formula. Estimation of inbetween samples for large sequences is possible within a mean square error of 0.00114 with this method. Some considerations with regard to the computation of FFTs are also discussed.     

On a limited-view reconstruction problem in diffraction tomography

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a scattering object. We previously demonstrated that by exploiting the redundant information in the DT data, the scattering object could be exactly reconstructed using measurements taken over the angular range [0, phimin], where pi < phimin < or = 3pi/2. In this paper, we reveal a relationship between the maximum scanning angle and image resolution when a filtered backpropagation (FBPP) reconstruction algorithm is employed for image reconstruction. Based on this observation, we develop short-scan FBPP algorithms that reconstruct a low-pass filtered scattering object from measurements acquired over the angular range [0, phi(c)], where phi(c) < phimin.     

Distortion in diffraction tomography caused by multiple scattering

In this paper, we have first presented a new computational procedure for the calculation of the "true" forward scattered fields of a multicomponent object. By "true" we mean fields that are not limited by the first-order approximations, such as those used in the first-order Born and Rytov calculations. Although the results shown will only include the second-order fields for a multicomponent object, the computational procedure can easily be generalized for higher order scattering effects. Using this procedure we have shown by computer simulation that even when each component of a two-component object is weakly scattering, the multiple scattering effects become important when the components are blocking each other. We have further shown that when strongly scattering components that are large compared to a wavelength are not blocking each other, the scattering effects can be ignored. Both these conclusions agree with intuitive reasoning. Since all the currently available diffraction tomography algorithms are based on the assumption that the object satisfies the first-order scattering assumption, it is interesting to test them under conditions when this assumption is violated. We have used the scattered fields obtained with the new computational procedure to test these algorithms, and shown the resulting artifacts. Our main conclusion drawn from this computer simulation study is that even when object inhomogeneities are as small as 5 percent of the background, multiple scattering can introduce severe distortions in multicomponent objects.     

Reconstruction of multidimensional bandlimited signals from nonuniform and generalized samples

This paper addresses the problem of multidimensional signal reconstruction from nonuniform or generalized samples. Typical solutions in the literature for this problem utilize continuous filtering. The key result of the current paper is a multidimensional "interpolation" identity, which establishes the equivalence of two multidimensional processing operations. One of these uses continuous domain filters, whereas the other uses discrete processing. This result has obvious benefits in the context of the afore mentioned problem. The results here expand and generalize earlier work by other authors on the one-dimensional (1-D) case. Potential applications include two-dimensional (2-D) images and video signals.     

Advantages of nonuniform arrays using root-MUSIC

In this paper, we consider the Direction-Of-Arrival (DOA) estimation problem in the Nonuniform Linear Arrays (NLA) case, particularly the arrays with missing sensors. We show that the root-MUSIC algorithm can be directly applied to this case and that it can fully exploit the advantages of using an NLA instead of a Uniform Linear Array (ULA). Using theoretical analysis and simulations, we demonstrate that employing an NLA with the same number of sensors as the ULA, yields better performance. Moreover, reducing the number of sensors while keeping the same array aperture as the ULA slightly modifies the Mean Square Error (MSE). Therefore, thanks to the NLA, it is possible to maintain a good resolution while decreasing the number of sensors. We also show that root-MUSIC presents good performance and is one of the simplest high resolution methods for this type of arrays. Closed-form expressions of the estimator variance and the Cramer–Rao Bound (CRB) are derived in order to support our simulation results. In addition, the analytical expression of the CRB of the NLA to the CRB of the ULA ratio is calculated in order to show the advantages of the NLA.     

雷达成像和衍射层析的内在联系梳理

从方程描述、方程求解和方程解析解三个层面,对雷达成像和衍射层析的内在联系进行了系统性梳理.首先,介绍了描述成像问题的电磁散射方程,发现描述雷达的方程是二维的面积分方程,而描述衍射层析的方程是三维的体积分方程.指出成像对象不同是导致方程不同的根源,并利用等效原理建立了两种成像间的联系.其次,指出两种成像的相同点是,对非线性的电磁散射方程的线性化近似求解.最后,指出两种成像的回波信号(在空间谱域)和成像目标(在空间域)均构成一组傅里叶变换对.给出了两种成像的解析解的统一数学模型,即成像结果可表示为观测点(散射系数或散射势)卷积点扩展函数(PSF)的形式.通过PSF对两者的成像性能进行了比较.     

Wide-band microwave diffraction tomography under Born approximation

Studies of the diffraction tomography of dielectric objects in forward and backward scattering using a frequency diversity technique in the microwave region are presented. Numerical results show that the image reconstructed in the backward scattering case is better than that obtained in the forward scattering case. This shows that this cost-effective technique has potential in medical and nondestructive testing applications     

Improving microwave imaging by enhancing diffraction tomography

In this paper, a technique for enhancing the reconstruction quality of diffraction tomography for microwave imaging is presented. The technique invokes the WKB approximation in conjunction with utilizing measurement data at more than one frequency to overcome some of the limitations of diffraction tomography. The resulting formulation has a mathematical interpretation which leads to some interesting insights into the limitations of diffraction tomography. Numerical implementation of the technique is also described and actual simulation results using this implementation for a variety of two-dimensional (2-D) objects are provided. These show that indeed significant improvements over conventional diffraction tomography are possible with our enhanced technique     

Maximum entropy image reconstruction in X-ray and diffraction tomography

The authors propose a Bayesian approach with maximum-entropy (ME) priors to reconstruct an object from either the Fourier domain data (the Fourier transform of diffracted field measurements) in the case of diffraction tomography, or directly from the original projection data in the case of X-ray tomography. The objective function obtained is composed of a quadratic term resulting from chi(2) statistics and an entropy term that is minimized using variational techniques and a conjugate-gradient iterative method. The computational cost and practical implementation of the algorithm are discussed. Some simulated results in X-ray and diffraction tomography are given to compare this method to the classical ones.     

Consistency conditions and linear reconstruction methods in diffraction tomography

Because an image can be reconstructed from knowledge of its Radon transform (RT), the task of reconstructing an image is tantamount to that of estimating its RT. Based upon the Fourier diffraction projection (FDP) theorem, from the statistical perspective of unbiased reduction of image variance, we previously proposed an infinite family of estimation methods for obtaining the RT from the scattered data in diffraction tomography (DT). In this work, using the FDP theorem, we define the diffraction Radon transform (DRT), which can be treated as the data function in DT. Subsequently, using strategies similar to those that analyze the consistency conditions on the exponential Radon transform in two-dimensional (2-D) single-photon emission computed tomography with uniform attenuation, we studied the consistency condition on the DRT and we show that there is a hierarchy of estimation methods that actually project the noisy data function onto its consistency space in different ways. In terms of a weighted inner product of the consistency and inconsistency parts of a noisy data function, we further demonstrate that a subset of the family of estimation methods can be interpreted as orthogonal projections onto the consistency space of the DRT. In particular, the statistically suboptimal estimation method in the family corresponds to an orthogonal projection associated with an ordinary inner product of the consistency and inconsistency parts of a noisy data function.     

基于非均匀FFT的压缩感知雷达信号快速重构方法

雷达处理是压缩感知理论重要的应用方向之一,基于压缩感知的雷达处理可以降低对回波信号的采样速率要求,并且在部分应用中也可改善处理性能。然而,压缩感知重构算法的计算复杂性限制了压缩感知理论在实际雷达信号处理中的应用,尤其是大尺度雷达数据的处理。本文提出了一种基于压缩感知的雷达信号快速重构方法,利用均匀和非均匀快速傅里叶变换运算实现了常规压缩感知重构算法中的矩阵-向量乘法运算,有效降低了重构算法的计算复杂度,加快了压缩感知雷达信号的重构速度。同时,由于引入了快速傅里叶变换运算,该方法消除了大多数常规重构算法对感知矩阵的存储需求。仿真实验验证了该方法的可行性和高效性。      

迂回相位编码的傅里叶变换计算全息图及其再现

光学全息图直接利用光学干涉法在记录介质上记录物光波和参考光波叠加后形成的干涉图样,而采用计算全息(CGH)的方法可不借助参考光直接记录物光波的复振幅信息.如果对迂回相位编码的全息图再进行一次逆的快速傅里叶变换,则可由计算机模拟完成物光波的全息图再现.试验结果也验证了该方法的可行性.     

A Reconstruction Algorithm for Photoacoustic Imaging Based on the Nonuniform FFT

Fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in reconstructed images. We propose a novel reconstruction algorithm that applies the one-dimensional nonuniform fast Fourier transform to photoacoustic imaging. It is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of Fourier reconstruction.      

Comparison of zero crossing counter to FFT spectrum of ultrasound Doppler

Doppler data were obtained from a normal carotid, popliteal, and radial artery. It was found that the results of a digital zero-crossing counter-mean frequency estimate and the first moment of the FFT (fast-Fourier-transform)-generated spectra were comparable for high signal-to-noise ratio (SNR), as in the case of the carotid arterial waveform. However, the digital zero-crossing with thresholding was a more accurate representation of the expected velocity-vs.-time waveforms in the case of low-SNR Doppler obtained from the popliteal and radial arteries.<>