Optimized phase screen modeling for optical turbulence

An alternative method for statistical interpolation is formalized. A new theorem is proved, providing theoretical basis for optimizing statistical accuracy in successively conditioned rendering applications. The theorem is empirically validated by two simulations, each comparing two different statistical interpolators. The interpolators are used to model high-resolution phase fluctuations over finite apertures. The theorem correctly predicts which interpolator is more optimal, based on empirical trials with greater than 99.9% certainty. The theorem is suitable as a quick alternative to the Monte Carlo optimization techniques used previously.     

Image Interpolation via Gaussian-Sinc Interpolators with Partition of Unity

In this paper, we propose a novel image interpolation method by using Gaussian-Sinc automatic interpolators with partition of unity property. A comprehensive comparison is made with classical image interpolation methods, such as the bicubic interpolation, Lanczos interpolation, cubic Schaum interpolation, cubic B-spline interpolation and cubic Moms interpolation. The experimental results show the effectiveness of the improved image interpolation method via some image quality metrics such as PSNR and SSIM.     

Multiquadric and its shape parameter—A numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation

Hardy’s multiquadric and its related interpolators have been found to be highly efficient for interpolating continuous, multivariate functions, as well as for the solution of partial differential equations. Particularly, the interpolation error can be dramatically reduced by varying the shape parameter to make the interpolator optimally flat. This improvement of accuracy is accomplished without reducing the fill distance of collocation points, that is, without the increase of computational cost. There exist a number of mathematical theories investigating the multiquadric family of radial basis functions. These theories are often not fully tested due to the computation difficulty associated with the ill-conditioning of the interpolation matrix. This paper overcomes this difficulty by utilizing arbitrary precision arithmetic in the computation. The issues investigated include conditional positive definiteness, error estimate, optimal shape parameter, traditional and effective condition numbers, round-off error, derivatives of interpolator, and the edge effect of interpolation.     

基于SVM的ECT图像重建算法

电容层析成像（ECT）技术是基于电容敏感机理的过程层析成像技术。ECT的图像重建是一个典型的有限样本非线性映射问题。支持向量机（SVM）作为一种小样本处理方法,具有较强的泛化能力,被认为是目前针对小样本分类问题的最佳理论。提出了一种基于SVM的四层神经网络的图像重建算法,仿真结果表明,该算法用于三相流图像重建具有较强的空间分辨率和泛化能力。     

Wavelet-based image enhancement in x-ray imaging and tomography

We consider an application of the wavelet transform to image processing in x-ray imaging and three-dimensional (3-D) tomography aimed at industrial inspection. Our experimental setup works in two operational modes-digital radiography and 3-D cone-beam tomographic data acquisition. Although the x-ray images measured have a large dynamic range and good spatial resolution, their noise properties and contrast are often not optimal. To enhance the images, we suggest applying digital image processing by using wavelet-based algorithms and consider the wavelet-based multiscale edge representation in the framework of the Mallat and Zhong approach [IEEE Trans. Pattern Anal. Mach. Intell. 14, 710 (1992)]. A contrast-enhancement method by use of equalization of the multiscale edges is suggested. Several denoising algorithms based on modifying the modulus and the phase of the multiscale gradients and several contrast-enhancement techniques applying linear and nonlinear multiscale edge stretching are described and compared by use of experimental data. We propose the use of a filter bank of wavelet-based reconstruction filters for the filtered-backprojection reconstruction algorithm. Experimental results show a considerable increase in the performance of the whole x-ray imaging system for both radiographic and tomographic modes in the case of the application of the wavelet-based image-processing algorithms.     

Tomographic optical breast imaging guided by three-dimensional mammography

We introduce a modified Tikhonov regularization method to include three-dimensional x-ray mammography as a prior in the diffuse optical tomography reconstruction. With simulations we show that the optical image reconstruction resolution and contrast are improved by implementing this x-ray-guided spatial constraint. We suggest an approach to find the optimal regularization parameters. The presented preliminary clinical result indicates the utility of the method.     

Local cone-beam tomography image reconstruction on chords

We develop reconstruction algorithms for local cone-beam tomography for use with generalized scanning trajectories. The algorithms are grounded theoretically in a recently developed chord-based theory for exact image reconstruction and principles of lambda tomography. Being chord based, they are distinct mathematically and conceptually from conventional local tomography reconstruction algorithms. The salient feature of our algorithms is that they permit reconstruction of discontinuities in the profiles of the object function along chords. By consideration of all possible chords, a 3D image that describes the locations of object discontinuities can be reconstructed. Results from microlocal analysis are applied for understanding the object features that can be reconstructed stably by use of the algorithms. A computer-simulation study is conducted to demonstrate the algorithms and compare their performance with an existing algorithm.     

Accurate image reconstruction from few-view and limited-angle data in diffraction tomography

We present a method for obtaining accurate image reconstruction from highly sparse data in diffraction tomography (DT). A practical need exists for reconstruction from few-view and limited-angle data, as this can greatly reduce required scan times in DT. Our method does this by minimizing the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the estimated image matches the measured Fourier data samples. Using simulation studies, we show that the TV-minimization algorithm allows accurate reconstruction in a variety of few-view and limited-angle situations in DT. Accurate image reconstruction is obtained from far fewer data samples than are required by common algorithms such as the filtered-backpropagation algorithm. Overall our results indicate that the TV-minimization algorithm can be successfully applied to DT image reconstruction under a variety of scan configurations and data conditions of practical significance.     

Experimental Analysis of the Errors due to Polynomial Interpolation in Digital Image Correlation

Digital image correlation attempts to estimate displacement fields by digitally correlating two images acquired before and after motion. To do so, pixel intensity has to be interpolated at non‐integer locations. The ideal interpolator is the sinc, but as it requires infinite support, it is not normally used and is replaced by polynomials. Polynomial interpolation produces visually appealing results but introduces positional errors in the signal, thus causing the digital image correlation algorithms to converge to incorrect results. In this work, an experimental campaign is described, that aims to characterise the errors introduced by interpolation, focusing in particular on the systematic error and the standard deviation of displacements.     

Multicriteria maximum likelihood neural network approach to positron emission tomography

The emerging technology of positron emission image reconstruction is introduced in this paper as a multicriteria optimization problem. We show how selected families of objective functions may be used to reconstruct positron emission images. We develop a novel neural network approach to positron emission imaging problems. We also studied the most frequently used image reconstruction methods, namely, maximum likelihood under the framework of single performance criterion optimization. Finally, we introduced some of the results obtained by various reconstruction algorithms using computer‐generated noisy projection data from a chest phantom and real positron emission tomography (PET) scanner data. Comparison of the reconstructed images indicated that the multicriteria optimization method gave the best in error, smoothness (suppression of noise), gray value resolution, and ghost‐free images. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 361–364, 2000     

3-D ultrasound volume reconstruction using the direct frame interpolation method

A new method for 3-D ultrasound volume reconstruction using tracked freehand 3-D ultrasound is proposed. The method is based on solving the forward volume reconstruction problem using direct interpolation of high-resolution ultrasound B-mode image frames. A series of ultrasound B-mode image frames (an image series) is acquired using the freehand scanning technique and position sensing via optical tracking equipment. The proposed algorithm creates additional intermediate image frames by directly interpolating between two or more adjacent image frames of the original image series. The target volume is filled using the original frames in combination with the additionally constructed frames. Compared with conventional volume reconstruction methods, no additional filling of empty voxels or holes within the volume is required, because the whole extent of the volume is defined by the arrangement of the original and the additionally constructed B-mode image frames. The proposed direct frame interpolation (DFI) method was tested on two different data sets acquired while scanning the head and neck region of different patients. The first data set consisted of eight B-mode 2-D frame sets acquired under optimal laboratory conditions. The second data set consisted of 73 image series acquired during a clinical study. Sample volumes were reconstructed for all 81 image series using the proposed DFI method with four different interpolation orders, as well as with the pixel nearest-neighbor method using three different interpolation neighborhoods. In addition, volumes based on a reduced number of image frames were reconstructed for comparison of the different methods' accuracy and robustness in reconstructing image data that lies between the original image frames. The DFI method is based on a forward approach making use of a priori information about the position and shape of the B-mode image frames (e.g., masking information) to optimize the reconstruction procedure and to reduce computation times and memory requirements. The method is straightforward, independent of additional input or parameters, and uses the high-resolution B-mode image frames instead of usually lower-resolution voxel information for interpolation. The DFI method can be considered as a valuable alternative to conventional 3-D ultrasound reconstruction methods based on pixel or voxel nearest-neighbor approaches, offering better quality and competitive reconstruction time.     

Time-varying reconstruction of the ionosphere. 1. The algorithm

Total electron content data can be used to reconstruct images of ionospheric electron density using computed ionospheric tomography (CIT). All existing CIT algorithms are formulated with the assumption that the ionosphere does not move during data collection. Since existing algorithms are static reconstruction algorithms, the motion of the ionosphere becomes a source of image degradation. This article presents a time-varying CIT algorithm that reconstructs several time slices of the ionosphere instead of a single static image. Thus, the new algorithm is not adversely affected by the motion of the ionosphere. The new algorithm uses a priori information on the vertical distribution of ionospheric electron density, but no a priori information on ionospheric motion, so the motion is reconstructed solely on the basis of information contained in the data. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol 9: 484–490, 1998     

Efficient frequency-domain sample selection for recovering limited-support images

An image whose region of support is smaller than its bounding rectangle can, in principle, be reconstructed from a subset of the Nyquist samples. However, determining such a sampling set that gives a stable reconstruction is a difficult and computationally intensive problem. An algorithm is developed for determining periodic nonuniform sampling patterns that is orders of magnitude faster than existing algorithms. The speedup is achieved by using a sequential selection algorithm and heuristic metrics for the quality of sampling sets that are fast to compute, as opposed to the more rigorous linear algebraic metrics that have been used previously. Simulations show that the sampling sets determined using the new algorithm give image reconstructions that are of accuracy comparable with those determined by other slower algorithms.     

Finite-element-based photoacoustic tomography: phantom and chicken bone experiments

We describe a photoacoustic image reconstruction algorithm that is based on the finite-element solution to the photoacoustic wave equation in the frequency domain. Our reconstruction approach is an iterative Newton method coupled with combined Marquardt and Tikhonov regularizations that can extract the spatial distribution of optical-absorption property in heterogeneous media. We demonstrate this algorithm by using phantom and chicken bone measurements from a circular scanning photoacoustic tomography system. The results obtained show that millimeter-sized phantom objects and chicken bones and/or joints can be clearly detected using our finite-element-based photoacoustic tomography method.     

基于啁啾脉冲的反射层析激光雷达成像

反射层析激光雷达成像具有系统简单及对湍流不敏感的优势,但普通脉冲发射信号难以兼顾远距离和高精度探测的要求.基于上述情况,本文提出了一种基于啁啾脉冲信号的反射层析激光雷达成像处理方法.该方法首先对啁啾脉冲回波进行相干压缩处理,通过对处理后信号的包络提取得到目标在各方向的反射层析投影数据,最后利用卷积反投影算法实现高分辨力的图像重构.仿真结果表明,在同一投影角度,利用该方法得到的包络与目标反射率投影相一致;在投影角度范围大于60°时能够得到目标的轮廓信息,角度范围越大,成像越精确.研究结果验证了该方法的有效性.     

Investigating the enhancement of three-dimensional diffraction tomography by using multiple illumination planes

The three dimensional (3-D) extension of the two well-known diffraction tomography algorithms, namely, direct Fourier interpolation (DFI) and filtered backpropagation (FBP), are presented and the problem of the data needed for a full 3-D reconstruction is investigated. These algorithms can be used efficiently to solve the inverse scattering problem for weak scatterers in the frequency domain under the first-order Born and Rytov approximations. Previous attempts of 3-D reconstruction with plane-wave illumination have used data obtained with the incident direction restricted at the xy plane. However, we show that this restriction results in the omission of the contribution of certain spatial frequencies near the omegaz axis for the final reconstruction. The effect of this omission is studied by comparing the results of reconstruction with and without data obtained from other incident directions that fill the spatial frequency domain. We conclude that the use of data obtained for incident direction in only the xy plane is sufficient to achieve a satisfactory quality of reconstruction for a class of objects presenting smooth variation along the z axis, while abrupt variations along the z axis cannot be imaged. This result should be taken into account in the process of designing the acquisition geometry of a tomography scanner.     

基于近场声全息的重建算法分析与研究

针对声全息算法种类繁多及应用场合不同需求,通过有限元仿真和数值仿真相结合,对基于傅里叶变换、统计最优和等效源3种算法进行分析,寻找声源频率、重建距离、采样间距及正则化方法对重建精度的影响,并对其计算效率进行对比。在开阔水域进行实验验证。结果表明:随着声源频率增大,重建距离增加,采样点数减少,声全息算法的重建精度逐渐降低。在低频区域,结合L-曲线正则化法的统计最优近场声全息具有最佳的声场重建效果;基于等效源法的声全息重建精度最高,但容易产生虚像;基于傅里叶变换的声全息算法受重建距离影响严重,但重建速度优异,且声源定位准确。     

Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography

Diffraction tomography (DT) is an inversion scheme used to reconstruct the spatially variant refractive-index distribution of a scattering object. We developed computationally efficient algorithms for image reconstruction in three-dimensional (3D) DT. A unique and important aspect of these algorithms is that they involve only a series of two-dimensional reconstructions and thus greatly reduce the prohibitively large computational load required by conventional 3D reconstruction algorithms. We also investigated the noise characteristics of these algorithms and developed strategies that exploit the statistically complementary information inherent in the measured data to achieve a bias-free reduction of the reconstructed image variance. We performed numerical studies that corroborate our theoretical assertions.     

Thin infrared imaging systems through multichannel sampling

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide-aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3 mm and achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.     

Mart Algorithms for Circular and Helical Cone-Beam Tomography

The present work is concerned with the evaluation of the performance and the efficient implementation of multiplicative algebraic reconstruction technique (MART) to reconstruct three-dimensional (3D) objects for two different source/detector trajectories. Three types of MART algorithms are tested on a numerical phantom (Defrise), and they are implemented on a 3D X-ray system of Vikram Sarabhai Space Centre (VSSC). Circular and helical cone-beam trajectories are used. The results are compared with convolution backprojection (CBP) algorithm for each trajectory. It is found that iterative algorithms perform better than their counterpart, the transform-based CBP algorithm, whenever tomography systems are ill-conditioned due to limited views and/or noisy projection data.