Computational tomographic reconstruction for limited Ill-posed interferometric data

The test results of continuous local basis functions, that is, the polynomial, cubic B-spline, and convoluted Hanning functions, are presented for tomographic reconstruction of continuous phase objects from multidirectional projection interfrograms with limited data points. The concept of the approach is based on the use of identical but regularly displaced and overlapping continuous functions that have support only in a local region. They thus produce higher-order approximating power. Their performances are fairly similar; however, the convoluted Hanning function appears to be an excellent candidate. For the conducted tests, in general, the function outperforms the conventional methods including the grid method and convolution back-projection, especially as the noise level or degree of data limitation increases.     

Polynomial approximation method for tomographic reconstruction of three-dimensional refractive index fields with limited data

We propose a polynomial approximation method (PAM) for reconstruction of three-dimensional refractive index fields by interferometric tomography using limited data. Based on the assumption that the fields to be reconstructed are usually smooth and can be decomposed into a finite order of (orthogonal) polynomials, a set of linear equations can be constructed using both the measured projection data and the Radon transform of the basis functions. By solving these equations, the least-squares solutions of expansion coefficients can be obtained and then substituted back to yield the desired fields. Numerical results have demonstrated that the proposed method is fast, robust to noise and can achieve satisfactory results for refractive index fields with limited projection views and large opaque objects.     

复杂刚性运动物体的高精度三维测量算法

基于相移法的三维形貌重建精度高,对环境噪声和阴影等不敏感,但由于多幅条纹解相位,难以应用于动态物体的三维测量中,为此,提出了一种新的算法.基于Harris算法提取刚性运动棋盘格的角点,确定相邻两帧采集条纹图像之间的像素偏差并校正采集条纹图像;根据投影仪和摄像机的标定参数建立投影图像和采集图像之间的空间变换矩阵,并根据变...     

海面弱小目标高光谱融合技术研究

海面目标受海水扰动影响,难以被宽波段光电传感器探测识别。高光谱传感器可以获取海面目标和水体的光谱数据,利用目标和海水的光谱特性差异可以有效抑制海面扰动影响,提高探测识别能力。针对高光谱数据降维融合容易丢失海面弱小目标问题,研究了弱小目标光谱数据融合方法。通过相似性分类产生类矩阵,由类矩阵主成分变换的降维投影矩阵来投影变换原有光谱数据,获得降维数据矩阵。降维矩阵通过空间变换转换到RGB彩色空间,生成伪彩色融合图像。通过远距离弱小目标和水中鱼群高光谱数据,验证了改进方法的融合性能。实验结果表明:相似性分类融合方法不仅能将高维光谱数据融合成一幅伪彩色图像,还能有效避免弱小目标融合丢失问题,提高了目标探测识别能力。     

Acquisition time reduction in magnetic resonance spectroscopic imaging using discrete wavelet encoding

This paper describes a new magnetic resonance spectroscopic imaging (MRSI) technique based upon the discrete wavelet transform to reduce acquisition time and cross voxel contamination. Prototype functions called wavelets are used in wavelet encoding to localize defined regions in localized space by dilations and translations. Wavelet encoding in MRSI is achieved by matching the slice selective RF pulse profiles to a set of dilated and translated wavelets. Single and dual band slice selective excitation and refocusing pulses, with profiles resembling Haar wavelets, are used in a spin-echo sequence to acquire 2D-MRSI wavelet encoding data. The 2D space region is spanned up to the desired resolution by a proportional number of dilations (increases in the localization gradients) and translations (frequency shift) of the Haar wavelets (RF pulses). Acquisition time is reduced by acquiring successive MR signals from regions of space with variable size and different locations with no requirement for a TR waiting time between acquisitions. An inverse wavelet transform is performed on the data to produce the correct spatial MR signal distribution.     

Matrix completion-based reconstruction for undersampled magnetic resonance fingerprinting data

An iterative reconstruction method for undersampled magnetic resonance fingerprinting data is presented. The method performs the reconstruction entirely in k-space and is related to low rank matrix completion methods. A low dimensional data subspace is estimated from a small number of k-space locations fully sampled in the temporal direction and used to reconstruct the missing k-space samples before MRF dictionary matching. Performing the iterations in k-space eliminates the need for applying a forward and an inverse Fourier transform in each iteration required in previously proposed iterative reconstruction methods for undersampled MRF data. A projection onto the low dimensional data subspace is performed as a matrix multiplication instead of a singular value thresholding typically used in low rank matrix completion, further reducing the computational complexity of the reconstruction. The method is theoretically described and validated in phantom and in-vivo experiments. The quality of the parameter maps can be significantly improved compared to direct matching on undersampled data.     

Phase relaxation in disordered nuclear paramagnets

A new method for the construction of main correlation functions of nuclear paramagnets has been developed on the basis of the combination of the projection technique and cumulant expansions. It gives satisfactory results for the free induction decay and resonance line shape function in magnetically concentrated crystals. Polarization transfer in magnetically dilute crystals has been taken into account. It significantly retards a decrease in the FID at times longer than the phase relaxation time T ₂. The FID remains mainly monotonic in contrast to magnetically concentrated crystals, where the FID oscillates. The results have been compared to the existing experimental data.     

Tailored utilization of acquired k-space points for GRAPPA reconstruction

The generalized auto-calibrating partially parallel acquisition (GRAPPA) is an auto-calibrating parallel imaging technique which incorporates multiple blocks of data to derive the missing signals. In the original GRAPPA reconstruction algorithm only the data points in phase encoding direction are incorporated to reconstruct missing points in k-space. It has been recognized that this scheme can be extended so that data points in readout direction are also utilized and the points are selected based on a k-space locality criterion. In this study, an automatic subset selection strategy is proposed which can provide a tailored selection of source points for reconstruction. This novel approach extracts a subset of signal points corresponding to the most linearly independent base vectors in the coefficient matrix of fit, effectively preventing incorporating redundant signals which only bring noise into reconstruction with little contribution to the exactness of fit. Also, subset selection in this way has a regularization effect since the vectors corresponding to the smallest singular values are eliminated and consequently the condition of the reconstruction is improved. Phantom and in vivo MRI experiments demonstrate that this subset selection strategy can effectively improve SNR and reduce residual artifacts for GRAPPA reconstruction.     

A comparison of models used as alternative magnetic resonance image reconstruction methods

In magnetic resonance (MR) imaging, excellent reconstructions are obtained on large data sets using the inverse discrete Fourier transform (IDFT). Modeling procedures have been proposed to overcome the image artifacts from the truncation of small data sets. In this paper, a relationship between image reconstruction using modeling and the standard IDFT is presented. A comparison of the assumptions behind the Smith and Haacke models is given and an experimental evaluation of the validity of the models provided. Various methods of evaluating model coefficients are discussed. Images are reconstructed from both models using the Transient Error reconstruction approach (TERA) algorithm. TERA is an algorithm that reintroduces data information components that cannot be modeled: useful when the assumed model characteristics do not completely match all portions of the image. Although very different in their basic assumptions, both the Smith and Haacke models were found to reduce truncation artifacts and improve resolution when used with the TERA algorithm.     

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.     

Hybrid Lifting Wavelet-Like Transform for Solution of Electromagnetic Integral Equation

A hybrid lifting wavelet-like transform scheme is successfully applied to the solution of electric field integral equation using Rao-Wilton-Glisson basis functions. To speed up the matrix transform process, the lifting scheme is adopted. Numerical examples of different three-dimensional perfectly electric conducting objects are considered. Compared with the method of moments, the proposed matrix transform scheme can save considerable CPU time and memory.     

Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.     

A novel algorithm for the reduction of undersampling artefacts in magnetic resonance images

An innovative algorithm is presented which is effective in reducing the truncation artefacts occurring in magnetic resonance images due to missing k-space samples. The algorithm works first by filling the incomplete matrix of coefficients with zeroes and then adjusting, by an iterative process, the missing coefficients by performing a reduction of the undersampling artefacts. Then, this set of coefficients is used as a basis for a superresolution algorithm that estimates the missing coefficients by modeling the data as a linear combination of increasing and decreasing exponential functions using Prony's method. In fact, the Prony's method consists of the interpolation of a given data set with a sum of exponential functions: the MRI signals can be well represented as a sum of exponential functions and the missing data can be extrapolated by this representation. The algorithm has been proven to perform better than either a simple algorithm, which detects and then reduces the undersampling artefacts, or an algorithm that models the measured data with approximation functions. The presented algorithm is quite simple and is applicable both to missing rows (phase-frequency acquisitions) and to radial-missing angle (acquisition from projections) undersampling. Experimental results are reported; comparisons, made between the results obtained using the presented algorithm and the alternative methods described above, clearly demonstrate the superiority of the algorithm.     

协方差矩阵重构的稳健自适应波束形成算法

针对协方差矩阵含有期望信号成分以及波束指向角失配时,传统自适应波束形成器性能严重下降的问题,提出了协方差矩阵重构的稳健自适应波束形成算法。该算法将全空域划分成若干互不重叠的区域,分别对应干扰区域与信号区域,先利用Capon波束形成器对干扰区域积分,由此构造出干扰协方差矩阵。然后,利用标准Capon波束形成器的波束域MUSIC谱估计法对信号区域积分,重构出信号协方差矩阵,以其主特征向量作为期望信号导引向量估计。由于算法重构了干扰加噪声协方差矩阵并对导引向量进行了修正,保证了自适应波束形成器的性能。理论分析和仿真实验结果表明,算法在训练数据含有期望信号成分和波束指向角度失配情况下具有良好的性能。      

Correction of spatially dependent phase shifts for partial Fourier imaging

Partial Fourier MR images (PFI) are constructed from data that have fewer phase encoding views than are conventionally acquired using direct Fourier transform spin echo acquisition. The PFI data acquisition is structured to obtain the same spatial resolution as conventional acquisition, trading off signal-to-noise reduction for acquisition time improvement. The "missing" views can be zero filled or, if the data are Hermitian, supplied by symmetry (basic algorithm). The effect of spatially dependent phase shifts (SDPS) on PFI constructed with zero-fill or the basic algorithm is illustrated. The causes and typical magnitudes of such SDPS are discussed. In spin echo data only the low order, slowly varying SDPS, is shown to be significant. Through use of simulated and actual data sets these typical SDPS are shown to produce significant artifacts in PFI, when the amount of missing data is close to one-half. The artifacts are reduced when less data are missing. Good images can be generated with the zero-fill algorithm if less than 25% of the data is missing. Several methods of correcting phase shifts in PFI are developed: the basic Hermitian algorithm with frequency (x) direction correction (BAX), basic Fourier correction algorithm (BFC) and an improved iterative Fourier correction algorithm (IFC). The BFC and IFC can produce good images when as much as 46% of the data is missing. Data with rapidly varying SDPS, for example, gradient refocused data, make the phase correction task more difficult. With less than 25% of the data missing, however, acceptable gradient refocused PFI images can be created.     

Fast imaging algorithm for DMD-based photolithography with partially coherent illumination

In the paper, the characteristic of imaging with digital micro-mirror device (DMD) illuminated by a partially coherent light is discussed using Abbe's method. When a mask is sampled by DMD, the intensity in the substrate is modulated by sinc function and cut off by pupil function, according to oblique illumination theory and Fourier transform property of exponential function, a fast partially coherent imaging algorithm for DMD-based dynamic projection photolithography is proposed to combine Hopkins's method with Abbe's method. In the algorithm, the transmission cross coefficient (TCC) matrix of DMD projection photolithography is constructed as two-matrix multiplication according to illuminate source points. The new development presented in this paper utilizes matrix multiplication technique to speed up the computation of TCC matrix by tenfold on an average, which is beneficial to real time mask shift and mask optimization in DMD-based gray-tone photolithography.     

Preservation of long range temporal correlations under extreme random dilution

Many natural time series exhibit long range temporal correlations that may be characterized by power-law scaling exponents. However, in many cases, the time series have uneven time intervals due to, for example, missing data points, noisy data, and outliers. Here we study the effect of randomly missing data points on the power-law scaling exponents of time series that are long range temporally correlated. The Fourier transform and detrended fluctuation analysis (DFA) techniques are used for scaling exponent estimation. We find that even under extreme dilution of more than 50%, the value of the scaling exponent remains almost unaffected. Random dilution is also applied on heart interbeat interval time series. It is found that dilution of 70%-80% of the data points leads to a reduction of only 8% in the scaling exponent; it is also found that it is possible to discriminate between healthy and heart failure subjects even under extreme dilution of more than 90%.     

A fourier transform solution for radiative transfer in a slab with isotropic scattering and boundary reflection

The Fourier transform method is used to formulate an exact solution for radiative heat transfer in an isotropically scattering, absorbing and emitting plane-parallel slab with specularly reflecting boundaries. The analysis leads to a solution involving expansion coefficients which can be determined from a matrix equation to the desired degree of accuracy. The numerical results obtained for the hemispherical reflectivity and transmissivity show that even the lowest order solution gives good accuracy.     

取样布拉格光纤光栅的传输矩阵

根据在一般坐标系下均匀布拉格光纤光栅的传输矩阵,得到了取样布拉格光纤光栅的传输矩阵。利用傅里叶变换得到了取样布拉格光纤光栅的谐振方程。结果表明,在不考虑平均折射率变化的情况下,谐振峰的位置是由光栅的周期和取样周期共同确定的,与取样时的占空比、光栅长度和耦合系数没有关系。类似于物理光栅,取样布拉格光纤光栅也存在缺级现象,给出了出现缺级的条件。     

螺旋MRI的网格化数据重建算法比较

螺旋MRI的原始数据是在不均匀的 k- 空间螺旋轨迹上采样得到的,需要通过网格化算法等手段将数据变成等间距的网格数据后,才能采用FFT进行重建,最后得到供临床使用的图像. 本文对Jackson网格化算法和Claudia大矩阵算法的重建速度和图像结果进行了比较, 并得出以下结论：1）在获得相近图像质量的情况下,Claudia大矩阵重采样算法比Jackson算法要快且更方便在仪器上实现. 2）在Jackson双倍细网格算法的实现方式中,数据驱动插值比网格驱动插值更有效率. 3）在Claudia大矩阵重采样算法中,对冗余比大于310∶1的数据进行图像重建的时候,网格点的幅值不平均化比平均化后的效果还要好. 这几个结论都将有利于MRI图像重建技术的进一步提高. 