Three-dimensional nonlinear image reconstruction for microwave biomedical imaging

Active microwave imaging has attracted significant interests in biomedical applications, in particular for breast imaging. However, the high electrical contrasts in breast tissue also increases the difficulty of forming an accurate image because of the increased multiple scattering. To model such strong three-dimensional (3-D) multiple scattering effects in biomedical imaging applications, we develop a full 3-D inverse scattering algorithm based on the combination of the contrast source inversion and the fast Fourier transform algorithm. Numerical results show that our algorithm can accurately invert for the high-contrast media in breast tissue.     

Fast algorithms for GS-model-based image reconstruction in data-sharing Fourier imaging

Many imaging experiments involve acquiring a time series of images. To improve imaging speed, several "data-sharing" methods have been proposed, which collect one (or a few) high-resolution reference(s) and a sequence of reduced data sets. In image reconstruction, two methods, known as "Keyhole" and reduced-encoding imaging by generalized-series reconstruction (RIGR), have been used. Keyhole fills in the unmeasured high-frequency data simply with those from the reference data set(s), whereas RIGR recovers the unmeasured data using a generalized series (GS) model, of which the basis functions are constructed based on the reference image(s). This correspondence presents a fast algorithm (and two extensions) for GS-based image reconstruction. The proposed algorithms have the same computational complexity as the Keyhole algorithm, but are more capable of capturing high-resolution dynamic signal changes.     

Fast MR image reconstruction for partially parallel imaging with arbitrary k-space trajectories

Both acquisition and reconstruction speed are crucial for magnetic resonance (MR) imaging in clinical applications. In this paper, we present a fast reconstruction algorithm for SENSE in partially parallel MR imaging with arbitrary k-space trajectories. The proposed method is a combination of variable splitting, the classical penalty technique and the optimal gradient method. Variable splitting and the penalty technique reformulate the SENSE model with sparsity regularization as an unconstrained minimization problem, which can be solved by alternating two simple minimizations: One is the total variation and wavelet based denoising that can be quickly solved by several recent numerical methods, whereas the other one involves a linear inversion which is solved by the optimal first order gradient method in our algorithm to significantly improve the performance. Comparisons with several recent parallel imaging algorithms indicate that the proposed method significantly improves the computation efficiency and achieves state-of-the-art reconstruction quality.     

Simple linear models of scanning impedance imaging for fast reconstruction of relative conductivity of biological samples

Scanning impedance imaging (SH) uses a noncontacting electrical probe held at a known voltage and scanned over a thin sample on a ground plane in a conductive medium to obtain images of current. The current image is related in a nonlinear way to the conductivity of the sample. This paper develops the theory behind SII showing how the measured current relates to the desired conductivity. Also included is the development of a simplified, linear model that is effective in explaining many of the experimental results. Good agreement of the linear model with step-response data over an insulator is shown. The linear model shows that the current is a blurred version of the conductivity. Simple deblurring methods can, therefore, be applied to obtain relative conductivity images from the raw current data. Raw SII data from a flower-petal and a leaf sample are shown as well as relative conductivity images deblurred using the linear model.     

Fast spatio-temporal image reconstruction for dynamic PET

In tomographic imaging, dynamic images are typically obtained by reconstructing the frames of a time sequence independently, one by one. A disadvantage of this frame-by-frame reconstruction approach is that it fails to account. For temporal correlations in the signal. Ideally, one should treat the entire image sequence as a single spatio-temporal signal. However, the resulting reconstruction task becomes computationally intensive. Fortunately, as the authors show in this paper, the spatio-temporal reconstruction problem call be greatly simplified by first applying a temporal Karhunen-Loeve (KL) transformation to the imaging equation. The authors show that if the regularization operator is chosen to be separable into space and time components, penalized weighted least squares reconstruction of the entire image sequence is approximately equivalent to frame-by-frame reconstruction in the space-KL domain. By this approach, spatio-temporal reconstruction can be achieved at reasonable computational cost. One can achieve further computational savings by discarding high-order KL components to avoid reconstructing them. Performance of the method is demonstrated through statistical evaluations of the bias-variance tradeoff obtained by computer simulation reconstruction     

Fast image reconstruction network in image stitching

Compared with the traditional feature-based image stitching algorithm, the free-view image stitching algorithm based on deep learning has the advantages of fast stitching speed and good effect. However, these algorithms still cannot achieve real-time splicing speed. For the image reconstruction stage, we redesign a new fast image reconstruction network. This network is designed based on ShuffleNet, and the new network structure and loss function will reduce the time required for image reconstruction. In addition, this network can also reduce the performance loss after the network is lightweight. It is proved by experiments that the fast image reconstruction network can realize real-time high-resolution free-view image reconstruction.     

An image reconstruction algorithm for three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) has been studied by many authors and in most of this work it has been considered to be a two-dimensional problem. Many groups are now turning their attention to the full three-dimensional case in which the computational demands become much greater. It is interesting to look for ways to reduce this demand and in this paper we describe an implementation of an algorithm that is able to achieve this by precomputing many of the quantities needed in the image reconstruction. The algorithm is based on a method called NOSER introduced some years ago by Cheney et al. [3]. In this paper we have significantly extended the method by introducing a more realistic electrode model into the analysis. We have given explicit formulae for the quantities involved so that the reader can reproduce our results.     

A neural network image reconstruction technique for electrical impedance tomography

Reconstruction of images in electrical impedance tomography requires the solution of a nonlinear inverse problem on noisy data. This problem is typically ill-conditioned and requires either simplifying assumptions or regularization based on a priori knowledge. The authors present a reconstruction algorithm using neural network techniques which calculates a linear approximation of the inverse problem directly from finite element simulations of the forward problem. This inverse is adapted to the geometry of the medium and the signal-to-noise ratio (SNR) used during network training. Results show good conductivity reconstruction where measurement SNR is similar to the training conditions. The advantages of this method are its conceptual simplicity and ease of implementation, and the ability to control the compromise between the noise performance and resolution of the image reconstruction.     

扫描隧道显微镜图像重建的研究

在扫描隧道显微镜轮廓测量过程中,探针自身的几何形状会混入测量结果中,从而造成相应的测量误差。本文提出了根据对标准样品的测量结果,反算出探针的几何形状的算法,并应用于实没图像示解出探针的几何形状。在求得探针的几何形状后,文中推导了去除探针几何形状造成的误差,对扫描隧道显微镜图像进行重建的算法,并对实测样品进行了处理。结果表明上术坷有效地减少小探针自形状造成的测量误差。     

Fast minimization methods for solving constrained total-variation superresolution image reconstruction

In this paper, we study the problem of reconstructing a high-resolution image from several decimated, blurred and noisy low-resolution versions of the high-resolution image. The problem can be formulated as a combination of the total variation (TV) inpainting model and the superresolution image reconstruction model. The main purpose of this paper is to develop an inexact alternating direction method for solving such constrained TV image reconstruction problem. Experimental results are given to show that the proposed algorithm is effective and efficient.     

Ramp-preserving denoising for conductivity image reconstruction in magnetic resonance electrical impedance tomography

In magnetic resonance electrical impedance tomography, among several conductivity image reconstruction algorithms, the harmonic B(z) algorithm has been successfully applied to B(z) data from phantoms and animals. The algorithm is, however, sensitive to measurement noise in B(z) data. Especially, in in vivo animal and human experiments where injection current amplitudes are limited within a few milliampere at most, measured B(z) data tend to have a low SNR. In addition, magnetic resonance (MR) signal void in outer layers of bones and gas-filled organs, for example, produces salt-pepper noise in the MR phase and, consequently, B(z) images. The B(z) images typically present areas of sloped transitions, which can be assimilated to ramps. Conductivity contrasts change ramp slopes in B(z) images and it is critical to preserve positions of those ramps to correctly recover edges in conductivity images. In this paper, we propose a ramp-preserving denoising method utilizing a structure tensor. Using an eigenvalue analysis, we identified local regions of salt-pepper noise. Outside the identified local regions, we applied an anisotropic smoothing to reduce noise while preserving their ramp structures. Inside the local regions of salt-pepper noise, we used an isotropic smoothing. After validating the proposed denoising method through numerical simulations, we applied it to in vivo animal imaging experiments. Both numerical simulation and experimental results show significant improvements in the quality of reconstructed conductivity images.     

基于各向异性的快速超分辨率图像重建

针对传统超分辨率图像重建算法速度慢的缺点,提 出了一种基于自适应各向异性正则化的快速超分辨率图像重建算法。本文 算法兼顾重建图像质量的同时,提升了图形的重建速度。基于传统迭代算法,本文算法通过 优化约束条件,大量剔除了冗余过程, 弥补了传统算法的不足;同时引入一种具有自适应能力的各向异性平滑项,可以适应各种 复杂的运动模型。另外,提出 以图像的峰值信噪比(PSNR)为标准,作为重建迭代的截止 条件。运 用本文算法对序列低分辨率图像进行重建,证明了本文算法可以更快实现超分辨率图像重 建。     

Fast higher-order MR image reconstruction using singular-vector separation

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.     

圆锥扫描机制下的红外图像帧重建仿真研究

重点研究了圆锥扫描机制下,红外图像帧重建的仿真实现.在简要介绍圆锥扫描机制下基于变行频采样机理和红外图像完整重建技术的基础上,进行了大量的重建图像仿真研究.作为示例,文中列出第1、3、5、7、9场的扫描数据图像及其相应的场重建图像.从图像仿真结果可以看出这种技术能够完成红外图像的重建,重建的红外图像具有较高的分辨率,能够充分利用红外器件获得的扫描数据和相应的空间信息.     

Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography

Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms of the Maxwell equations expressed in scalar and vector potentials. The approach leads to boundary conditions that naturally align with the quantities measured by EIT instrumentation. A two-dimensional implementation for image reconstruction from EIT data is realized. The effect of frequency on the field distribution is illustrated using the high-frequency model and is compared with Laplace solutions. Numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation. The results show that scalar/vector potential reconstruction produces images which are essentially indistinguishable from a Laplace algorithm for frequencies below 1 MHz but superior at frequencies reaching 10 MHz.     

Fast fully 3-D image reconstruction in PET using planograms

We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space. Thus, backprojection of all the LORs passing through a point in the FOV corresponds to integration of a 2-D plane through the 4-D "planogram." The key step is that the integration along a set of parallel 2-D planes through the planogram, that is, backprojection of a plane of points, can be replaced by a 2-D section through the origin of the 4-D Fourier transform of the data. Backprojection can be performed as a sequence of Fourier transform operations, for faster implementation. In addition, we derive the central-section theorem for planogram format data, and also derive a reconstruction filter for both backprojection-filtering and filtered-backprojection reconstruction algorithms. With software-based Fourier transform calculations we provide preliminary comparisons of planogram backprojection to standard 3-D backprojection and demonstrate a reduction in computation time by a factor of approximately 15.     

Fast,iterative image reconstruction for MRI in the presence of field inhomogeneities

In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast Fourier trasform (FFT) methods. Several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities, but these methods assume that the field map that characterizes the off-resonance frequencies is spatially smooth. Recently, iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off-resonance effects. However, straightforward implementations of such iterative methods suffer from inconveniently long computation times. This paper describes a tool for accelerating iterative reconstruction of field-corrected MR images: a novel time-segmented approximation to the MR signal equation. We use a min-max formulation to derive the temporal interpolator. Speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast Fourier transform with normalized root mean squared approximation errors of 0.07%. The proposed method provides fast, accurate, field-corrected image reconstruction even when the field map is not smooth.     

Fast progressive reconstruction of a transformed image (Corresp.)

Fast methods for performing progressive reconstruction of Fourier and Hadamard transformed images have been developed. Reconstruction of anN times Npoint transformed image can be evaluated in orderN^{2} log_{2} Ninstructions. Accumulation of round-off errors due to iteration is reduced by the factor(log_{2} N + 1) / N^{2}, compared with direct evaluation of the inverse transform.     

A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry

The conductivity and permittivity of breast tumors are known to differ significantly from those of normal breast tissues, and electrical impedance tomography (EIT) is being studied as a modality for breast cancer imaging to exploit these differences. At present, X-ray mammography is the primary standard imaging modality used for breast cancer screening in clinical practice, so it is desirable to study EIT in the geometry of mammography. This paper presents a forward model of a simplified mammography geometry and a reconstruction algorithm for breast tumor imaging using EIT techniques. The mammography geometry is modeled as a rectangular box with electrode arrays on the top and bottom planes. A forward model for the electrical impedance imaging problem is derived for a homogeneous conductivity distribution and is validated by experiment using a phantom tank. A reconstruction algorithm for breast tumor imaging based on a linearization approach and the proposed forward model is presented. It is found that the proposed reconstruction algorithm performs well in the phantom experiment, and that the locations of a 5-mm-cube metal target and a 6-mm-cube agar target could be recovered at a target depth of 15 mm using a 32 electrode system.     

基于压缩感知和红外玫瑰线扫描的红外图像重构

红外亚成像制导技术是由点源探测技术到成像制导技术的一种过渡, 由单元探测器和光机扫描装置组成.红外玫瑰线扫描亚成像系统是亚成像制导中的一种, 红外玫瑰线扫描亚成像系统按照特定的图案采集视场中的部分数据并得到一幅含有目标位置信息的亚图像.受单像素相机的启发, 主要研究红外玫瑰线扫描亚成像系统中的压缩成像.压缩感知可以在更少的采样数据条件下重构红外图像, 其应用到红外亚成像制导系统中一个关键的问题就是观测矩阵的构造.关于随机观测矩阵的研究已经比较广泛, 但随机矩阵很难实现.本文提出了一种简单的适用于红外玫瑰线扫描亚成像系统的确定性观测矩阵.此外还提出了一种快速有效的恢复算法, 称为优化子空间追踪算法.仿真结果显示构造的观测矩阵能够压缩和重构红外图像, 且重构效果优于随机高斯观测矩阵和随机伯努利观测矩阵, 提出的恢复算法也具有较好的表现.