Natural pixel decomposition for interferometric tomographic reconstruction from ill-posed data

Reconstruction of three-dimensional refractive-index fields from multidirectional holographic interferograms can be a powerful flow diagnostic tool in many engineering applications. It is noninvasive and can capture gross fields instantaneously. Interferometric tomography for reconstructing flow fields, however, confronts ill-posed problems, that is, last of sufficient data. As the flow fields are sampled in the presence of opaque models and enclosures, the data are sparse, nonuniform, and sometimes incomplete in projection and scanning. Here, a new method, termed the variable grid method, to incorporate the distinct features of interferometric data for flow field reconstruction is developed and tested. The method is based on natural pixel decomposition. It utilizes variable rectangular grid elements in representing a field with a finite series. The variable grid method allows better reconstruction resolution with greater accuracy in the region where sampled rays are more closely crossed. This region is usually of interest in engineering.     

An iterative method based on 1D subspace for projective reconstruction

Heyden et al. introduced an iterative factorization method for projective reconstruction from image sequences. In their formulation, the projective structure and motion are computed by using an iterative factorization based on 4D subspace. In this paper, the problem is reformulated based on fact that the x, y, and z coordinates of each feature in projective space are known from their projection. The projective reconstruction, i.e., the relative depths w and the 3D motion, is obtained by a simple iterative factorization based on 1D subspace. This allows the use of very fast algorithms even when using a large number of features and large number of frames. The experiments with both simulate and real data show that the method presented in the paper is efficient and has good convergency.     

An iterative method for improving the quality of reconstruction of a three-dimensional surface

A complex image with constraints imposed on the amplitude and phase image components is processed using the Gerchberg iterative algorithm for the first time. The use of the Gerchberg iterative algorithm makes it possible to improve the quality of a three-dimensional surface profile reconstructed by the previously proposed method that is based on the multiangle projection of fringes and the joint processing of the obtained images by Fourier synthesis.     

一种提高激光告警器性能的自适应方法

激光告警是激光对抗的重要前提和基本手段，如何在复杂背景噪声下识别来袭激光信号，进而准确报警是激光告警面临的首要问题。该文分析了激光告警设备检测概率与信噪比的关系，从关系式可以看出，为了提高激光告警设备的检测概率，需要增加激光信号的信噪比。提出了一种最大信噪比的自适应算法，进行了算法分析，并利用矩阵变换作出了算法简化，从而保证了系统信噪比的最佳化。最后对最佳权向量的求解这个问题，给出了适用于工程化的最佳权向量求解的简单迭代算法。     

Residue-squaring iterative diagonalization method for perturbation problems

We present a new method for the evaluation of the change in eigenvalues due to a perturbation of strength λ. It is a fast converging iterative method which, at thenth step, gives results accurate to order (2 ⁿ⁺¹?1) in λ. Unlike the Rayleigh-Schrödinger perturbation theory in quantum mechanics, which becomes prohibitively cumbersome when carried to higher orders, the present method involves a routine which remains stralghtforward at all stages.     

An iterative method to solve acoustic scattering problems using a boundary integral equation

In this work, a simple iterative method to solve the acoustic scattering/radiation problems using the boundary integral equation (BIE) formulation is presented. The operator equation obtained in the BIE formulation is converted into a matrix equation using the well-known method of moments solution procedure. The present method requires much fewer mathematical operations per iteration when compared to other available iterative methods. Further, the present iterative method can easily handle multiple incident fields, a highly desirable feature not available in any other iterative method, much the same way as direct solution techniques. Several numerical examples are presented to illustrate the efficiency and accuracy of the method.     

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

Sparse-view x-ray computed tomography(CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform(NUFFT) is presented in this work along with advanced total variation(TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.     

An iterative approach to curved ray reconstruction of birefringent fields

The transmission of polarized light through non-homogeneous birefringent fields is examined, and an iterative approach for incorporating ray curvature into the analysis of tomographic data is proposed. The method extends strain-gradient theory and applies iterative algorithms which have been used by other researchers to reconstruct fields which are non-homogeneous but optically Isotropic. Optical anisotropy is incorporated by using a light propagation model which includes both bending and separation of initially coincident light ray pairs. To illustrate the method, data are generated computationally and are analysed to determine the bending moment in a prismatic beam and the forces acting on a diametrically loaded disc.     

An iterative implementation of rotated coordinates for inverse problems

A generalized inversion method is presented that uses a rotated coordinates technique [Collins and Fishman, J. Acoust. Soc. Am. 98, 1637-1644 (1995)] in simulated annealing to invert for both the location of an acoustic source and parameters that describe the ocean seabed. The rotated coordinates technique not only aids in the inversion process but also indicates the coupling of the source and environmental parameters and the relative sensitivities of the cost function to changes in the various parameters. The information obtained from the rotated coordinates provides insights into how the inversion problem can be effectively decoupled. An iterative process consisting of multiple simulated annealing runs that each use a different set of rotated coordinates is demonstrated. This multistep algorithm is called systematic decoupling using rotated coordinates and is especially helpful when inverting for a large number of unknown parameters. The cost function minimized in the inversion algorithm is model-data cross-hydrophone spectra summed coherently over frequency and receiver pairs. The results of applying this inversion method to simulated data are presented in this paper.     

An iterative reconstruction technique for geometric distortion-corrected segmented echo-planar imaging

In this article, we present a modified interleaved segmented echo-planar imaging (SEPI) sequence with a center-out k-space trajectory that is especially designed for susceptibility-weighted imaging applications. We introduce a simple and efficient technique to phase correct the acquired SEPI data in the presence of moderate field inhomogeneities. This phase correction reduces the distortion in the phase-encoding direction without requiring an extra reference scan. With the use of a center-out k-space trajectory and a low-spatial-frequency phase map, phase discontinuities between segments can be eliminated, in principle, iteratively using a fast Fourier transform from the center segment to the outermost segment in k-space. With an extra echo added in front of the echo train, neither phase unwrapping nor an extra reference scan is required to obtain a low-spatial-frequency phase map. The method is shown to remove blurring and reduce geometric distortion caused by phase changes from echo to echo in both phantom and human data. The method is most useful for high-resolution imaging applications and moderate factors of speed improvement.     

2-d ESR diffusion coefficient imaging with the projection reconstruction method

The static gradient spin echo (SGSE) of the conduction electron spins in a quasi-one dimensional organic conductor is analyzed by simulation and for a microstructured (fluoranthene)(2)PF(6) single crystal. It is shown that useful two-dimensional magnetic resonance images of the diffusion coefficient (mobility) D can be obtained from pixel-by-pixel analysis of the signal decay with pulse separation tau, adopting the projection reconstruction (PR) method for signal generation.     

An ART iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging

X-ray diffraction enhanced imaging （DEI） has extremely high sensitivity for weakly absorbing low- Z samples in medical and biological fields. In this paper, we propose an Algebra Reconstruction Technique （ART） iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging （DEI-CT）. An Ordered Subsets （OS） technique is used to accelerate the ART reconstruction. Few-view reconstruction is also studied, and a partial differential equation （PDE） type filter which has the ability of edge-preserving and denoising is used to improve the image quality and eliminate the artifacts. The proposed algorithm is validated with both the numerical simulations and the experiment at the Beijing synchrotron radiation facility （BSRF）.     

An ART iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging

X-ray diffraction enhanced imaging (DEI) has extremely high sensitivity for weakly absorbing low-Z samples in medical and biological fields. In this paper, we propose an Algebra Reconstruction Technique (ART) iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging (DEI-CT). An Ordered Subsets (OS) technique is used to accelerate the ART reconstruction. Few-view reconstruction is also studied, and a partial differential equation (PDE) type filter which has the ability of edge-preserving and denoising is used to improve the image quality and eliminate the artifacts. The proposed algorithm is validated with both the numerical simulations and the experiment at the Beijing synchrotron radiation facility (BSRF).     

Improvement of the recursive projection method for linear iterative scheme stabilization based on an approximate eigenvalue problem

An algorithm for stabilizing linear iterative schemes is developed in this study. The recursive projection method is applied in order to stabilize divergent numerical algorithms. A criterion for selecting the divergent subspace of the iteration matrix with an approximate eigenvalue problem is introduced. The performance of the present algorithm is investigated in terms of storage requirements and CPU costs and is compared to the original Krylov criterion. Theoretical results on the divergent subspace selection accuracy are established. The method is then applied to the resolution of the linear advection–diffusion equation and to a sensitivity analysis for a turbulent transonic flow in the context of aerodynamic shape optimization. Numerical experiments demonstrate better robustness and faster convergence properties of the stabilization algorithm with the new criterion based on the approximate eigenvalue problem. This criterion requires only slight additional operations and memory which vanish in the limit of large linear systems.     

A parallel spatial and Bloch manifold regularized iterative reconstruction method for MR Fingerprinting

Magnetic Resonance Fingerprinting (MRF) reconstructs tissue maps based on a sequence of very highly undersampled images. In order to be able to perform MRF reconstruction, state-of-the-art MRF methods rely on priors such as the MR physics (Bloch equations) and might also use some additional low-rank or spatial regularization. However to our knowledge these three regularizations are not applied together in a joint reconstruction. The reason is that it is indeed challenging to incorporate effectively multiple regularizations in a single MRF optimization algorithm. As a result most of these methods are not robust to noise especially when the sequence length is short. In this paper, we propose a family of new methods where spatial and low-rank regularizations, in addition to the Bloch manifold regularization, are applied on the images. We show on digital phantom and NIST phantom scans, as well as volunteer scans that the proposed methods bring significant improvement in the quality of the estimated tissue maps.     

调制法提高体表内部虚拟超谱图信号检测信噪比

体表内部虚拟超谱图将皮肤组织中的成分和结构信息有机融合表达,具有"图谱合一"的特点,有望应用于临床体表组织疾病的快速检查,但由于检测中信号微弱,极易受到环境光的影响和仪器本身暗电流的限制。为解决这一问题提出斩光盘对光源进行方波调制的方法,搭建实验平台,选择大功率的超连续谱激光和应用广泛的溴钨灯两种光源,在人为添加红色激光、紫色激光干扰和自然环境光干扰三种环境中,采用非调制和调制光源对人体手臂进行VIHBS对比实验,并对调制后的信号实现FFT解调处理。实验结果表明,调制法能够有效的消除环境光和暗电流的影响,提高信号检测的信噪比,为人体组织微弱光学信号的检测开辟了新的思路。     

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.     

A method of tomographic reconstruction of the three-dimensional velocity distribution function of electrons

An experimental method is proposed for the determination of an arbitrary three-dimensional distribution function for initial energies of electrons emitted by a point source with resolution for two exit direction angles. In a computer experiment, two model distribution functions have been reconstructed using the proposed method.     

An iterative method to solve a regularized model for strongly nonlinear long internal waves

We present a simple iterative scheme to solve numerically a regularized internal wave model describing the large amplitude motion of the interface between two layers of different densities. Compared with the original strongly nonlinear internal wave model of Miyata [10] and Choi and Camassa [2], the regularized model adopted here suppresses shear instability associated with a velocity jump across the interface, but the coupling between the upper and lower layers is more complicated so that an additional system of coupled linear equations must be solved at every time step after a set of nonlinear evolution equations are integrated in time. Therefore, an efficient numerical scheme is desirable. In our iterative scheme, the linear system is decoupled and simple linear operators with constant coefficients are required to be inverted. Through linear analysis, it is shown that the scheme converges fast with an optimum choice of iteration parameters. After demonstrating its effectiveness for a model problem, the iterative scheme is applied to solve the regularized internal wave model using a pseudo-spectral method for the propagation of a single internal solitary wave and the head-on collision between two solitary waves of different wave amplitudes.     

An advanced fully 3D OSEM reconstruction for positron emission tomography

A fully 3D OSEM reconstruction method for positron emission tomography （PET） based on symmetries and sparse matrix technique is described. Great savings in both storage space and computation time were achieved by exploiting the symmetries of scanner and sparseness of the system matrix. More reduction of storage requirement was obtained by introducing the approximation of system matrix. Iteration-filter was performed to restrict image noise in reconstruction. Performances of simulation data and phantom data got from Micro-PET （Type： Epuls-166） demonstrated that similar image quality was achieved using the approximation of the system matrix.