Investigation of the noise properties of a new class of reconstruction methods in diffraction tomography

In diffraction tomography (DT), the measured scattered data are unavoidably contaminated by noise. Because the detectability of an object in a noisy image relies strongly on the signal-to-noise ratio, it is important in certain applications to reduce the statistical variation in the reconstructed image. Recently, we revealed the existence of statistically complementary information inherent in the scattered data and proposed a linear strategy that makes use of this information to achieve a bias-free reduction of the image variance in two-dimensional (2D) DT. This strategy leads to the development of an infinite class of estimation methods, that from the measured scattered data, can estimate the Radon transform of the scattering object function. From the estimated Radon transforms, one can readily reconstruct the object function by using a variety of existing reconstruction algorithms. The estimation methods in the class are mathematically equivalent, but they respond to noise differently. We investigated the noise properties of these estimation methods by use of computer simulation studies. The results of our simulation studies demonstrate quantitatively that it is possible to achieve a bias-free variance reduction in the reconstructed scattering object by utilizing complementary statistical information that is inherent in the scattered data. © 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 437–446, 1999     

Theory and algorithms for image reconstruction on chords and within regions of interest

We introduce a formula for image reconstruction on a chord of a general source trajectory. We subsequently develop three algorithms for exact image reconstruction on a chord from data acquired with the general trajectory. Interestingly, two of the developed algorithms can accommodate data containing transverse truncations. The widely used helical trajectory and other trajectories discussed in literature can be interpreted as special cases of the general trajectory, and the developed theory and algorithms are thus directly applicable to reconstructing images exactly from data acquired with these trajectories. For instance, chords on a helical trajectory are equivalent to the n-PI-line segments. In this situation, the proposed algorithms become the algorithms that we proposed previously for image reconstruction on PI-line segments. We have performed preliminary numerical studies, which include the study on image reconstruction on chords of two-circle trajectory, which is nonsmooth, and on n-PI lines of a helical trajectory, which is smooth. Quantitative results of these studies verify and demonstrate the proposed theory and algorithms.     

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.     

基于梯度投影稀疏重建算法的电容层析成像图像重建

为解决两相流中存在中心物体、物体比较小或存在多个物体且相距较近时电容层析成像(ECT)重建图像精度较差的问题,基于稀疏分布的流型其介电常数分布满足稀疏性的先验条件,采用梯度投影稀疏重建(GPSR-BB)算法进行ECT图像重建。仿真及实验测试结果表明:GPSR-BB算法对于流体中小目标以及复杂流型的图像重建质量较好,重建图像的形状保真度高。     

Median-prior tomography reconstruction combined with nonlinear anisotropic diffusion filtering

Positron emission tomography (PET) is becoming increasingly important in the fields of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation for image reconstruction in emission tomography place conditions on which types of images are accepted as solutions. The recently introduced median root prior (MRP) favors locally monotonic images. MRP can preserve sharp edges, but a steplike streaking effect and much noise are still observed in the reconstructed image, both of which are undesirable. An MRP tomography reconstruction combined with nonlinear anisotropic diffusion interfiltering is proposed for removing noise and preserving edges. Analysis shows that the proposed algorithm is capable of producing better reconstructed images compared with those reconstructed by conventional maximum-likelihood expectation maximization (MLEM), MAP, and MRP-based algorithms in PET image reconstruction.     

Full- and minimal-scan reconstruction algorithms for fan-beam diffraction tomography

Diffraction tomography (DT) is a tomographic inversion technique that reconstructs the spatially variant refractive-index distribution of a scattering object. In fan-beam DT, the interrogating radiation is not a plane wave but rather a cylindrical wave front emanating from a line source located a finite distance from the scattering object. We reveal and examine the redundant information that is inherent in the fan-beam DT data function. Such redundant information can be exploited to reduce the reconstructed image variance or, alternatively, to reduce the angular scanning requirements of the fan-beam DT experiment. We develop novel filtered backpropagation and estimate-combination reconstruction algorithms for full-scan and minimal-scan fan-beam DT. The full-scan algorithms utilize measurements taken over the angular range 0 相似文献   

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.     

Simultaneous tomographic reconstruction and segmentation with class priors

We consider tomographic imaging problems where the goal is to obtain both a reconstructed image and a corresponding segmentation. A classical approach is to first reconstruct and then segment the image; more recent approaches use a discrete tomography approach where reconstruction and segmentation are combined to produce a reconstruction that is identical to the segmentation. We consider instead a hybrid approach that simultaneously produces both a reconstructed image and segmentation. We incorporate priors about the desired classes of the segmentation through a Hidden Markov Measure Field Model, and we impose a regularization term for the spatial variation of the classes across neighbouring pixels. We also present an efficient implementation of our algorithm based on state-of-the-art numerical optimization algorithms. Simulation experiments with artificial and real data demonstrate that our combined approach can produce better results than the classical two-step approach.     

Neural network-based image reconstruction for positron emission tomography

Positron emission tomography (PET) is one of the key molecular imaging modalities in medicine and biology. Penalized iterative image reconstruction algorithms frequently used in PET are based on maximum-likelihood (ML) and maximum a posterior (MAP) estimation techniques. The ML algorithm produces noisy artifacts whereas the MAP algorithm eliminates noisy artifacts by utilizing availableprior information in the reconstruction process. The MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class and irrespective of the strength of interaction between the nearest neighbors. A Hebbian neural learning scheme is proposed to model the nature of interpixel interaction to reconstruct artifact-free edge preserving reconstruction. A key motivation of the proposed approach is to avoid oversmoothing across edges that is often the case with MAP algorithms. It is assumed that local correlation plays a significant role in PET image reconstruction, and proper modeling of correlation weight (which defines the strength of interpixel interaction) is essential to generate artifact-free reconstruction. The Hebbian learning-based approach modifies the interaction weight by adding a small correction that is proportional to the product of the input signal (neighborhood pixels) and output signal. Quantitative analysis shows that the Hebbian learning-based adaptive weight adjustment approach is capable of producing better reconstructed images compared with those reconstructed by conventional ML and MAP-based algorithms in PET image reconstruction.     

Optical Imaging with Partially Coherent Non-thermal Light

The reconstruction of an object from its image is studied from the point of view of the coherence theory including detection in the process of imaging. Finite-size objects permit the use of the theory of entire functions to prove that if the transformation from object to image is linear (detection is not included in imaging) the object can be reconstructed uniquely. Non-linear transformations from object to image (detection is included in imaging) for weak visibility objects and for a particular choice of the diffraction function are also studied. In the first case a finite-size object is determined uniquely, in the second case the reconstructed object is determined apart from the phase, which can sometimes be determined from the dispersion relations. Further, the similarity between an object and its image is investigated. It is shown that partial coherence creates typical non-linearity in imaging which results in an interval of eigenvalues (similarity coefficients) and that there may arise the branching of a structure imaged similarly into several structures imaged similarly.     

Prediction of human observer performance by numerical observers: an experimental study

Numerical observers are investigated for predicting the outcome of a free-response human observer study involving the detection of simulated pulmonary nodules in images reconstructed from low-dose computed tomography projection data by use of several reconstruction algorithms. A new way of calculating the figure of merit of a numerical observer is proposed wherein the detectability of signals in a particular image depends on the noise properties associated with that image and not the other images in the data set. The resulting variants of numerical observers are found to perform better than their traditional counterparts. In particular, the imagewise variant of the region-of-interest observer is found to predict best the rank ordering of algorithms by human observers for the free-response task.     

Image reconstruction in photoacoustic tomography involving layered acoustic media

Photoacoustic tomography (PAT), also known as thermoacoustic or optoacoustic tomography, is a rapidly emerging biomedical imaging technique that combines optical image contrast with ultrasound detection principles. Most existing reconstruction algorithms for PAT assume the object of interest possesses homogeneous acoustic properties. The images produced by such algorithms can contain significant distortions and artifacts when the object's acoustic properties are spatially variant. In this work, we establish an image reconstruction formula for PAT applications in which a planar detection surface is employed and the to-be-imaged optical absorber is embedded in a known planar layered acoustic medium. The reconstruction formula is exact in a mathematical sense and accounts for multiple acoustic reflections between the layers of the medium. Computer-simulation studies are conducted to demonstrate and investigate the proposed method.     

Image reconstruction in intravascular photoacoustic imaging

Intravascular photoacoustic (IVPA) imaging is a technique for visualizing atherosclerotic plaques with differential composition. Unlike conventional photoacoustic tomography scanning, where the scanning device rotates around the subject, the scanning aperture in IVPA imaging is enclosed within the imaged object. The display of the intravascular structure is typically obtained by converting detected photoacoustic waves into Cartesian coordinates, which can produce images with severe artifacts. Because the acquired data are highly limited, there does not exist a stable reconstruction algorithm for such imaging geometry. The purpose of this work was to apply image reconstruction concepts to explore the feasibility and efficacy of image reconstruction algorithms in IVPA imaging using traditional analytical formulas, such as a filtered back-projection (FBP) and the lambda-tomography method. Although the closed-form formulas are not exact for the IVPA system, a general picture of and interface information about objects are provided. To improve the quality of the reconstructed image, the iterative expectation maximization and penalized least-squares methods were adopted to minimize the difference between the measured signals and those generated by a reconstructed image. In this work, we considered both the ideal point detector and the acoustic transducers with finite- size aperture. The transducer effects including the spatial response of aperture and acoustoelectrical impulse responses were incorporated in the system matrix to reduce the aroused distortion in the IVPA reconstruction. Computer simulations and experiments were carried out to validate the methods. The applicability and the limitation of the reconstruction method were also discussed.     

Deterministic versus stochastic level-set regularization in nonlinear phase contrast tomography

A new nonlinear level-set regularization method to reconstruct the complex refractive index distribution with in-line phase contrast tomography measurements is presented under the assumption that the index is piecewise constant. The nonlinear iterative approach is based on the Fréchet derivative of the intensity recorded at a single propagation distance and for several projection angles. The algorithm is successfully applied to a multi-material object for several noise levels. Better reconstruction results are achieved with a stochastic perturbation of the level-set function. This evolution corresponds to a stochastic evolution of the shape of the reconstructed regions. The reconstruction errors can be further decreased with topological derivatives. The different algorithms are tested on various multi-material objects.     

Fuzzy-rule-based image reconstruction for positron emission tomography

Positron emission tomography (PET) and single-photon emission computed tomography have revolutionized the field of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation eliminate noisy artifacts by utilizing available prior information in the reconstruction process but often result in a blurring effect. MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class. Reconstruction with better edge information is often difficult because prior knowledge is not taken into account. The recently introduced median-root-prior (MRP)-based algorithm preserves the edges, but a steplike streaking effect is observed in the reconstructed image, which is undesirable. A fuzzy approach is proposed for modeling the nature of interpixel interaction in order to build an artifact-free edge-preserving reconstruction. The proposed algorithm consists of two elementary steps: (1) edge detection, in which fuzzy-rule-based derivatives are used for the detection of edges in the nearest neighborhood window (which is equivalent to recognizing nearby density classes), and (2) fuzzy smoothing, in which penalization is performed only for those pixels for which no edge is detected in the nearest neighborhood. Both of these operations are carried out iteratively until the image converges. Analysis shows that the proposed fuzzy-rule-based reconstruction algorithm is capable of producing qualitatively better reconstructed images than those reconstructed by MAP and MR P algorithms. The reconstructed images a resharper, with small features being better resolved owing to the nature of the fuzzy potential function.     

Digital holographic reconstruction of a local object field using an adjustable magnification

In the research of digital holography, this paper presents a numerical method using an adjustable magnification for local object field reconstruction together with experiment verification. The method first designs a spherical wave according to the given magnification to illuminate the digital hologram, then through a Fourier transform of diffraction, it calculates the reconstructed image plane. Afterward, a filtering window is set in the image plane to extract the image of the local object field, and then the object field reached hologram plane is formed using diffraction's inverse operation. Finally, the object field is reconstructed through diffraction's angular spectrum theory.     

Shape connection by pattern recognition and laser metrology

Shape connection based on the pattern recognition of three-dimensional shapes is presented. In this technique, the object shape is reconstructed by laser scanning and image processing. The object is reconstructed from multiple views when an object occlusion appears. From this process, multiple parts of the object are reconstructed. Then, these parts are assembled to obtain the complete object shape. To perform the assembling, a matching procedure is applied to a transverse section of the multiple views by Hu moments. The depth of the transverse section is computed by an approximation network based on the behavior of the laser line and the camera position. Also, vision parameters are deduced by the network and image processing. In this manner, the shape connection is achieved automatically by computational algorithms. Therefore, errors of physical measurement are not passed to the reconstruction system. Thus, the performance and the accuracy of the reconstruction system are improved. This is elucidated by the comparison between the obtained results by the proposed technique and the obtained results by a contact method. Thus, a contribution in laser metrology for shape connection is achieved.     

An optimization method for quantitative impedance tomography

A near-field ultrasonic tomography method providing high resolution imaging for soft tissue in the reflection mode is reported. When the Born approximation is valid, the main limitation of this method is that it requires an incident pulse with infinite bandwidth, whereas the incident pulses used in practice have a limited bandwidth, which makes quantitative reconstruction impossible. The reconstructed image is qualitative in the sense that it is a band-pass filtered reconstruction of the impedance distribution. An optimization method based on the use of the geometrical information provided by the tomographic reconstruction is developed to obtain the quantitative information required. The object was approximated locally by an equivalent canonical body, on the basis of the previous global estimation. The inversion procedure is then carried out using the minimization of a cost function, which is the average over frequency of the difference between the measured field scattered by the object and the estimated field scattered by the equivalent canonical body. Assuming the object to be homogeneous by regions, the last step consists of assigning the estimated local impedance value to the region of interest. When the geometry of the real body is almost canonical, the optimization method yields accurate impedance assessments.     

基于鲁棒正则化极限学习机的电容层析成像图像重建

电容层析成像图像重建是一个非线性及病态性逆问题。基于此,提出了基于迭代重加权最小二乘法的鲁棒正则化极限学习机(RELM-IRLS)算法的电容层析成像图像重建方法,以油/气两相流为研究对象,通过有限元仿真构建随机分布流型,对RELM-IRLS算法完成训练,并与Landweber迭代算法及极限学习机算法进行对比,RELM-IRLS算法的测试集平均误差相比极限学习机算法减小4.6%。仿真及静态实验结果均表明, RELM-IRLS算法所得重建图像质量得到明显提升,且算法具有良好的泛化性能。     

Three-dimensional optical tomography: resolution in small-object imaging

Near-infrared (NIR) optical tomography provide estimates of the internal distribution of optical absorption and transport scattering from boundary measurement of light propagation within biological tissue. Although this is a truly three-dimensional (3D) imaging problem, most research to date has concentrated on two-dimensional modeling and image reconstruction. More recently, 3D imaging algorithms are demonstrating better estimation of the light propagation within the imaging region and are providing the basis of more accurate image construction algorithms. As 3D methods emerge, it will become increasingly important to evaluate their resolution, contrast, and localization of optical property heterogeneity. We present a concise study of 3D reconstructed resolution of a small, low-contrast, absorbing and scattering anomaly as it is placed in different locations within a cylindrical phantom. The object is an 8-mm-diameter cylinder, which represents a typical small target that needs to be resolved in NIR mammographic imaging. The best resolution and contrast is observed when the object is located near the periphery of the imaging region (12-22 mm from the edge) and is also positioned within the multiple measurement planes, with the most accurate results seen for the scatter image when the anomaly is at 17 mm from the edge. Furthermore, the accuracy of quantitative imaging is increased to almost 100% of the target values when a priori information regarding the internal structure of imaging domain is utilized.