DEIReconstructor： a software for diffraction enhanced imaging processing and tomography reconstruction

Diffraction enhanced imaging （DEI） has been widely applied in many fields, especially when imaging low-Z samples or when the difference in the attenuation coefficient between different regions in the sample is too small to be detected. Recent developments of this technique have presented a need for a new software package for data analysis. Here, the Diffraction Enhanced Image Reconstructor （DEIReconstructor）, developed in Matlab, is presented. DEIReconstructor has a user-friendly graphical user interface and runs under any of the 32~bit or 64- bit Microsoft Windows operating systems including XP and WinT. Many of its features are integrated to support imaging preprocessing, extract absorption, refractive and scattering information of diffraction enhanced imaging and allow for parallel-beam tomography reconstruction for DEI-CT. Furthermore, many other useful functions are also implemented in order to simplify the data analysis and the presentation of results. The compiled software package is freely available.     

Preliminary attempt on maximum likelihood tomosynthesis reconstruction of DEI data

Tomosynthesis is a three-dimension reconstruction method that can remove the effect of superim- position with limited angle projections. It is especially promising in mammography where radiation dose is concerned. In this paper, we propose a maximum likelihood tomosynthesis reconstruction algorithm （ML-TS） on the apparent absorption data of diffraction enhanced imaging （DEI）. The motivation of this contribution is to develop a tomosynthesis algorithm in low-dose or noisy circumstances and make DEI get closer to clinic application. The theoretical statistical models of DEI data in physics are analyzed and the proposed algorithm is validated with the experimental data at the Beijing Synchrotron Radiation Facility （BSRF）. The results of ML-TS have better contrast compared with the well known ＇shift-and-add＇ algorithm and FBP algorithm.     

A Combined Reconstruction Algorithm for Limited-View Multi-Element Photoacoustic Imaging

We present a photoacoustic imaging system with a linear transducer array scanning in limited-view felds and develop a combined reconstruction algorithm, which is a combination of the limited-field filtered back projection （LFBP） algorithm and the simultaneous iterative reconstruction technique （SIRT） algorithm, to reconstruct the optical absorption distribution. In this algorithm, the LFBP algorithm is exploited to reconstruct the original photoacoustic image, and then the SIRT algorithm is used to improve the quality of the final reconstructed photoacoustic image. Numerical simulations with calculated incomplete data validate the reliability of this algorithm and the reconstructed experimental results further demonstrate that the combined reconstruction algorithm effectively reduces the artifacts and blurs and yields better quality of reconstruction image than that with the LFBP algorithm.     

Algorithm Study on Reconstruction of Refractive Angles in Fan Beam Diffraction Enhanced Computed Tomography

Based on the 360° computing method of refractive angle for parallel beam diffraction enhanced imaging computed tomography （DE-CT） technique, a new algorithm used to calculate the refractive angle for fan-beam DE-CT technique is developed. The refractive index gradient can be obtained by using the new algorithm with projection data of an object in the range of 0 - 360°, and the new algorithm only needs to set the analyser at half slope position of the rocking curve.     

DEIReconstructor:a software for diffraction enhanced imaging processing and tomography reconstruction

Diffraction enhanced imaging (DEI) has been widely applied in many fields, especially when imaging low-Z samples or when the difference in the attenuation coefficient between different regions in the sample is too small to be detected. Recent developments of this technique have presented a need for a new software package for data analysis. Here, the Diffraction Enhanced Image Reconstructor (DEIReconstructor), developed in Matlab, is presented. DEIReconstructor has a user-friendly graphical user interface and runs under any of the 32-bit or 64-bit Microsoft Windows operating systems including XP and Win7. Many of its features are integrated to support imaging preprocessing, extract absorption, refractive and scattering information of diffraction enhanced imaging and allow for parallel-beam tomography reconstruction for DEI-CT. Furthermore, many other useful functions are also implemented in order to simplify the data analysis and the presentation of results. The compiled software package is freely available.     

Modified adaptive algebraic tomographic reconstruction of gas distribution from incomplete projection by a two-wavelength absorption scheme

A modified adaptive algebraic reconstruction technique (MAART) with an auto-adjustment relaxation parameter and smoothness regularization is developed to reveal the tomographic reconstruction of H 2 O distribution in combustion from incomplete projections. Determinations of relaxation parameter and regularization factor are discussed with regard to the consideration of improvement in reconstruction and reduction of computational burden. A two-wavelength scheme from tunable diode laser absorption measurement, 7444.36 and 7185.59 cm 1 , is used to simplify the nonlinear solution problem for obtaining the tomographic distributions of concentration and temperature simultaneously. Results of calculations demonstrate that MAART can perform the reconstruction results more efficiently with little complex modification and much lower iterations as compared with the traditional algebraic reconstruction technique (ART) or simultaneous iterative reconstruction technique (SIRT) methods. The stability of the algorithm is studied by reconstruction from projections with random noise at different levels to demonstrate the dependence of reconstruction results on precise line-of-sight measurements.     

Study of a millimeter-wave squint indirect holographic algorithm suitable for imaging with large field-of-view

In this paper a millimeter-wave （MMW） squint indirect holographic method is presented, which is suitable for imaging with a large field-of-view. The proposed system employs the squint operation mode to remove the background and twin- image interferences, which achieves a similar effect to off-axis holography but leaves out the large-aperture quasi-optical component. The translational scanning manner enables a large field of view and ensures the image uniformity, which is difficult to realize in off-axis holography. In addition, a corresponding imaging algorithm for the presented scheme is developed to reconstruct the image from the recorded hologram. Some imaging results on typical objects, obtained with electromagnetic simulation, demonstrate good performance of the imaging scheme and validate the effectiveness of the image reconstruction algorithm.     

Evaluation of imaging protocol for ECT based on CS image reconstruction algorithm

Single-photon emission computerized tomography and positron emission tomography are essential med- ical imaging tools, for which the sampling angle number and scan time should be carefully chosen to give a good compromise between image quality and radiopharmaceutical dose. In this study, the image quality of different ac- quisition protocols was evaluated via varied angle number and count number per angle with Monte Carlo simulation data. It was shown that, when similar imaging counts were used, the factor of acquisition counts was more important than that of the sampling number in emission computerized tomography. To further reduce the activity requirement and the scan duration, an iterative image reconstruction algorithm for limited-view and low-dose tomography based on compressed sensing theory has been developed. The total variation regulation was added to the reconstruction process to improve the signal to noise Ratio and reduce artifacts caused by the limited angle sampling. Maximization of the maximum likelihood of the estimated image and the measured data and minimization of the total variation of the image are alternatively implemented. By using this advanced algorithm, the reconstruction process is able to achieve image quality matching or exceed that of normal scans with only half of the injection radiopharmaceutical dose.     

A double constrained robust capon beamforming based imaging method for early breast cancer detection

Ultra-wideband （UWB） microwave images are proposed for detecting small malignant breast tumors based on the large contrast of electric parameters between a malignant tumor and normal breast tissue. In this study, an antenna array composed of 9 antennas is applied to the detection. The double constrained robust capon beamforming （DCRCB） algorithm is used for reconstructing the breast image due to its better stability and high signal-to-interference-plus-noise ratio （SINR）. The successful detection of a tumor of 2 mm in diameter shown in the reconstruction demonstrates the robustness of the DCRCB beamforming algorithm. This study verifies the feasibility of detecting small breast tumors by using the DCRCB imaging algorithm.     

Global vector-field reconstruction of nonlinear dynamical systems from a time series with SVD method and validation with Lyapunov exponents

A method for the global vector-field reconstruction of nonlinear dynamical systems from a time series is studied in this paper. It employs a complete set of polynomials and singular value decomposition (SVD) to estimate a standard function which is certtral to the algorithm. Lyapunov exponents and dimension, calculated from the differential equations of a standard system, are used for the validation of the reconstruction. The algorithm is proven to be practical by applying it to a Roessler system.     

Medical application of diffraction enhanced imaging in mouse liver blood vessels

Neovascularization is correlative with many processes of diseases, especially for tumor growth, invasion, and metastasis. What is more, these tumor microvessels are totally different from normal vessels in morphology. Therefore, observation of the morphologic distribution of microvessels is one of the key points for many researchers in the field. Using diffraction enhanced imaging （DEI）, we observed the mirocvessles with diameter of about 40 μm in mouse liver. Moreover, the refraction image obtained from DEI shows higher image contrast and exhibits potential use for medical applications.     

A Complex Higher-Dimensional Lie Algebra with Real and Imaginary Structure Constants as Well as Its Decomposition

A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.     

Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging

X-ray diffraction sorbing low-Z sample. How enhanced imaging （DEI） is applied to extract phase information from to inspect internal structures of weakly abraw images measured in different positions of rocking curve is the key problem of DEI. In this paper, we present an effective extraction method called polynomial curve fitting method, in order to extract accurate information angular in a fast speed. It is compared with the existing methods such as multiple-images statistical method and Gaussian curve fitting method. The experiments results on a plastic cylinder and a black ant at the Beijing Synchrotron Radiation Facility prove that the polynomial curve fitting method can obtain most approximate refraction-angle values and its computation speed is 10 times faster than the Gaussian curve fitting method.     

A Type of New Loop Algebra and a Generalized Tu Formula

A new Lie algebra, which is far different form the known An-1, is established, for which the corresponding loop algebra is given. From this, two isospectral problems are revealed, whose compatibility condition reads a kind of zero curvature equation, which permits Lax integrable hierarchies of soliton equations. To aim at generating Hamiltonian structures of such soliton-equation hierarchies, a beautiful Killing-Cartan form, a generalized trace functional of matrices, is given, for which a generalized Tu formula （GTF） is obtained, while the trace identity proposed by Tu Guizhang [J. Math. Phys. 30 （1989） 330] is a special case of the GTF. The computing formula on the constant γ to be determined appearing in the GTF is worked out, which ensures the exact and simple computation on it. Finally, we take two examples to reveal the applications of the theory presented in the article. In details, the first example reveals a new Liouville-integrable hierarchy of soliton equations along with two potential functions and Hamiltonian structure. To obtain the second integrable hierarchy of soliton equations, a higher-dimensional loop algebra is first constructed. Thus, the second example shows another new Liouville integrable hierarchy with 5-potential component functions and bi- Hamiltonian structure. The approach presented in the paper may be extensively used to generate other new integrable soliton-equation hierarchies with multi-Hamiltonian structures.     

Two New Expanding Lie Algebras and Their Integrable Models

A new Lax integrable hierarchy is obtained by constructing an isospectraJ problem with constrained conditions. Two kinds of integrable couplings are obtained by constructing two new expanding Lie algebras of the Lie algebra Be, respectively.     

Entropy of Partitions on Sequential Effect Algebras

By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.     

Applications of Polynomial Algebras to 2-Dimensional Deformed Oscillators

The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial algebra with different highest orders.     

Characteristic Numbers of Matrix Lie Algebras

A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.