Filtered maximum likelihood expectation maximization based global reconstruction for bioluminescence tomography

The reconstruction of bioluminescence tomography (BLT) is severely ill-posed due to the insufficient measurements and diffuses nature of the light propagation. Predefined permissible source region (PSR) combined with regularization terms is one common strategy to reduce such ill-posedness. However, the region of PSR is usually hard to determine and can be easily affected by subjective consciousness. Hence, we theoretically developed a filtered maximum likelihood expectation maximization (fMLEM) method for BLT. Our method can avoid predefining the PSR and provide a robust and accurate result for global reconstruction. In the method, the simplified spherical harmonics approximation (SP_N) was applied to characterize diffuse light propagation in medium, and the statistical estimation-based MLEM algorithm combined with a filter function was used to solve the inverse problem. We systematically demonstrated the performance of our method by the regular geometry- and digital mouse-based simulations and a liver cancer-based in vivo experiment.

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Graphical abstract The filtered MLEM-based global reconstruction method for BLT.

     

An improved ordered subsets expectation maximization positron emission computerized tomography reconstruction

Ordered subsets expectation maximization (OS-EM) reconstruction method is usually used in positron emission tomography (PET). But it has some disadvantage such as long computation time and bad reconstruction quality. Filtered back projection (FBP), that has many advantages such as simple structure and short reconstruction time, is firstly introduced into the initialization stage of the OS-EM to fast the reconstruction process. Then, the smoothness method is applied after the OS-EM algorithm to improve the reconstruction speed and quality. The reconstructed images are compared for both the simulated phantom data and the brain magnetic resonance imaging data. The improved OS-EM is shown to be more feasible than the standard OS-EM within the same iteration steps and in higher signal noise ratio (SNR) condition.     

Iterative three-dimensional expectation maximization restoration of single photon emission computed tomography images: application in striatal imaging

Single photon emission computed tomography imaging suffers from poor spatial resolution and high statistical noise. Consequently, the contrast of small structures is reduced, the visual detection of defects is limited and precise quantification is difficult. To improve the contrast, it is possible to include the spatially variant point spread function of the detection system into the iterative reconstruction algorithm. This kind of method is well known to be effective, but time consuming. We have developed a faster method to account for the spatial resolution loss in three dimensions, based on a postreconstruction restoration method. The method uses two steps. First, a noncorrected iterative ordered subsets expectation maximization (OSEM) reconstruction is performed and, in the second step, a three-dimensional (3D) iterative maximum likelihood expectation maximization (ML-EM) a posteriori spatial restoration of the reconstructed volume is done. In this paper, we compare to the standard OSEM-3D method, in three studies (two in simulation and one from experimental data). In the two first studies, contrast, noise, and visual detection of defects are studied. In the third study, a quantitative analysis is performed from data obtained with an anthropomorphic striatal phantom filled with 123-I. From the simulations, we demonstrate that contrast as a function of noise and lesion detectability are very similar for both OSEM-3D and OSEM-R methods. In the experimental study, we obtained very similar values of activity-quantification ratios for different regions in the brain. The advantage of OSEM-R compared to OSEM-3D is a substantial gain of processing time. This gain depends on several factors. In a typical situation, for a 128 x 128 acquisition of 120 projections, OSEM-R is 13 or 25 times faster than OSEM-3D, depending on the calculation method used in the iterative restoration. In this paper, the OSEM-R method is tested with the approximation of depth independent resolution. For the striatum this approximation is appropriate, but for other clinical situations we will need to include a spatially varying response. Such a response is already included in OSEM-3D.     

Iterative concurrent reconstruction algorithms for emission computed tomography

Direct reconstruction techniques, such as those based on filtered backprojection, are typically used for emission computed tomography (ECT), even though it has been argued that iterative reconstruction methods may produce better clinical images. The major disadvantage of iterative reconstruction algorithms, and a significant reason for their lack of clinical acceptance, is their computational burden. We outline a new class of 'concurrent' iterative reconstruction techniques for ECT in which the reconstruction process is reorganized such that a significant fraction of the computational processing occurs concurrently with the acquisition of ECT projection data. These new algorithms use the 10-30 min required for acquisition of a typical SPECT scan to iteratively process the available projection data, significantly reducing the requirements for post-acquisition processing. These algorithms are tested on SPECT projection data from a Hoffman brain phantom acquired with a 2 x 10(5) counts in 64 views each having 64 projections. The SPECT images are reconstructed as 64 x 64 tomograms, starting with six angular views. Other angular views are added to the reconstruction process sequentially, in a manner that reflects their availability for a typical acquisition protocol. The results suggest that if T s of concurrent processing are used, the reconstruction processing time required after completion of the data acquisition can be reduced by at least 1/3T s.     

On few-view tomographic reconstruction with megavoltage photon beams

Currently portal imaging devices are used to obtain information on patient localization during radiation therapy treatments. Such obtained information is two dimensional in nature, limited to the plane of the captured image. It has been proposed that megavoltage computed tomography images be reconstructed to overcome this limitation. This study explores the feasibility of reconstructing tomographic images from fan-beam projection data acquired with a commercial portal imaging device on a standard radiotherapy linear accelerator. Several CT reconstruction algorithms are examined as to their performance and suitability for applications in radiation therapy verification. The results show that it is possible, using some of the iterative reconstruction techniques, to obtain an image useful for patient localization from only several (< or =10) projection views.     

磁感应成像重构算法的研究进展

磁感应成像（MIT）是一种无创和非接触的针对生物组织电导率分布的功能性电阻抗成像技术。MIT有以下优点:穿透性好、快速、便捷、低成本和无创,故其在医学成像上有很好的应用前景。MIT的研究包括系统结构、传感器、正问题和重构算法几个方面。本文阐述在MIT成像原理的基础上,对其重构算法的研究现状进行综述,对主要的重构算法进行归纳总结,分析几种算法的特点和应用领域,最后指出未来的研究趋势。     

Improvement of fluorescence-enhanced optical tomography with improved optical filtering and accurate model-based reconstruction algorithms

The goal of preclinical fluorescence-enhanced optical tomography (FEOT) is to provide three-dimensional fluorophore distribution for a myriad of drug and disease discovery studies in small animals. Effective measurements, as well as fast and robust image reconstruction, are necessary for extensive applications. Compared to bioluminescence tomography (BLT), FEOT may result in improved image quality through higher detected photon count rates. However, background signals that arise from excitation illumination affect the reconstruction quality, especially when tissue fluorophore concentration is low and/or fluorescent target is located deeply in tissues. We show that near-infrared fluorescence (NIRF) imaging with an optimized filter configuration significantly reduces the background noise. Model-based reconstruction with a high-order approximation to the radiative transfer equation further improves the reconstruction quality compared to the diffusion approximation. Improvements in FEOT are demonstrated experimentally using a mouse-shaped phantom with targets of pico- and subpico-mole NIR fluorescent dye.     

Statistical image reconstruction for transmission tomography using relaxed ordered subset algorithms

Statistical reconstruction methods offer possibilities for improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications in x-ray computed tomography (CT). To reduce reconstruction times, we have applied (under) relaxation to ordered subset algorithms. This enables us to use subsets consisting of only single projection angle, effectively increasing the number of image updates within an entire iteration. A second advantage of applying relaxation is that it can help improve convergence by removing the limit cycle behaviour of ordered subset algorithms, which normally do not converge to an optimal solution but rather a suboptimal limit cycle consisting of as many points as there are subsets. Relaxation suppresses the limit cycle behaviour by decreasing the stepsize for approaching the solution. A simulation study for a 2D mathematical phantom and three different ordered subset algorithms shows that all three algorithms benefit from relaxation: equal noise-to-resolution trade-off can be achieved using fewer iterations than the conventional algorithms, while a lower minimal normalized mean square error (NMSE) clearly indicates a better convergence. Two different schemes for setting the relaxation parameter are studied, and both schemes yield approximately the same minimal NMSE.     

Subset-dependent relaxation in block-iterative algorithms for image reconstruction in emission tomography

This paper presents a row-action maximum likelihood algorithm (RAMLA), in which the relaxation parameter is controlled in such a way that the noise propagation from projection data to the reconstructed image is substantially independent of the access order of the input data (subsets) in each cycle of the sub-iterations. The 'subset-dependent' relaxation parameter lambda(k) (q) is expressed as lambda(k)(q) = beta0/(beta0 + q + gamma k M), where M is the number of angular views, q (0 < or = q < or = M - 1) is the access order of the angular view, k is the iteration number and beta0 and gamma are constants. The constant beta0 deals with the balance of the noise propagation and the constant gamma controls the convergence of iterations. The value of beta0 is determined from the geometrical correlation coefficients among lines of coincidence response. The proposed RAMLA using the subset-dependent (dynamic) relaxation 'dynamic RAMLA (DRAMA)' provides a reasonable signal-to-noise ratio with a satisfactory spatial resolution by a few iterations in the two-dimensional image reconstruction for PET. Dynamic OS-EM (DOSEM) has also been developed, which allows the use of a larger number of subsets (OS level) Msub without loss of signal-to-noise ratio as compared to the conventional OS-EM. DRAMA is a special case of DOSEM, where Msub = M, and it is no more profitable to use DOSEM with a smaller Msub (< M), because DRAMA provides similar performance with the fastest convergence and smallest computer burden. This paper describes the theory, algorithm and the results of the simulation studies on the performance of DRAMA and DOSEM.     

Comparison of analyzer-based imaging computed tomography extraction algorithms and application to bone-cartilage imaging

In x-ray phase-contrast analyzer-based imaging, the contrast is provided by a combination of absorption, refraction and scattering effects. Several extraction algorithms, which attempt to separate and quantify these different physical contributions, have been proposed and applied. In a previous work, we presented a quantitative comparison of five among the most well-known extraction algorithms based on the geometrical optics approximation applied to planar images: diffraction-enhanced imaging (DEI), extended diffraction-enhanced imaging (E-DEI), generalized diffraction-enhanced imaging (G-DEI), multiple-image radiography (MIR) and Gaussian curve fitting (GCF). In this paper, we compare these algorithms in the case of the computed tomography (CT) modality. The extraction algorithms are applied to analyzer-based CT images of both plastic phantoms and biological samples (cartilage-on-bone cylinders). Absorption, refraction and scattering signals are derived. Results obtained with the different algorithms may vary greatly, especially in the case of large refraction angles. We show that ABI-CT extraction algorithms can provide an excellent tool to enhance the visualization of cartilage internal structures, which may find applications in a clinical context. Besides, by using the refraction images, the refractive index decrements for both the cartilage matrix and the cartilage cells have been estimated.     

A performance study of 3D reconstruction algorithms for positron emission tomography

This paper investigates the statistical and systematic accuracy of five three-dimensional reconstruction algorithms for multi-ring PET scanners operated without septa: the reprojection method, the direct Fourier reconstruction, the FAVOR algorithm, and the single-slice and multi-slice rebinning algorithms. Simulated data of a uniform cylinder, of Gaussian sources, and of spherical sources are used to compare respectively the noise properties, the modulation transfer function, and the recovery coefficients of the algorithms. Brain scans reconstructed with the different algorithms are compared by calculating the linear regression of the mean values within regions of interest. The most significant observations are a slight loss of transaxial resolution with the reprojection algorithm in the external slices of the scanner, and increased noise in the images reconstructed using multi-slice rebinning.     

Isotope computed tomography using cone-beam geometry: a comparison of two reconstruction algorithms

A CT scanner has been constructed specifically to determine the three-dimensional distribution of bone mineral in the medullary cavities of the radius, ulna and femur. A source of x-rays (153Gd) and a multiwire proportional counter (MWPC) are mounted at opposite ends of a diameter of an annular mounting. The limb is placed on the axis of rotation of the annulus and a series of two-dimensional transmission projections are obtained at equal angular spacings over 360 degrees. The distribution of bone mineral is reconstructed from the projections either by the method of maximum entropy (ME) or by convolution and back projection (CBP). These two methods have been evaluated by reconstructing a single slice of a phantom, representing the forearm, from projections simulated by computer. With a clinically acceptable exposure time, the mean medullary densities of the ulna and radius were determined with systematic errors of less than 3.5% (ME) and 11% (CBP), although for the latter method of reconstruction the systematic error was reduced to less than 2% by increasing the number of views. The mean medullary densities of the ulna and radius were determined with precisions better than 2.5% (ME) and 3.5% (CBP).     

Transverse tomography with incoherent optical reconstruction

A thin layer of an object can be imaged by reconstruction from a so-called sinogram. It is produced by an x-ray fan beam rotating around the object while a recording film is moved in a direction perpendicular to the plane of the fan beam. Before reconstruction the sinogram image is convoluted according to a special function to remove artifacts consisting of spurious shadows between different object elements. The reconstruction is done from the convoluted sinogram by means of a back projector, which operates according to a prinicple that is the reverse of the recording of the original sinogram. Tomograms of phantoms, pork chops and the head of a dog show that the process is capable of high spatial resolution but is limited by low contrast.     

Strategy of extraction methods and reconstruction algorithms in computed tomography of diffraction enhanced imaging

Computed tomography of diffraction enhanced imaging (DEI-CT) is a novel x-ray phase-contrast computed tomography which is applied to inspect weakly absorbing low-Z samples. Refraction-angle images which are extracted from a series of raw DEI images measured in different positions of the rocking curve of the analyser can be regarded as projections of DEI-CT. Based on them, the distribution of refractive index decrement in the sample can be reconstructed according to the principles of CT. How to combine extraction methods and reconstruction algorithms to obtain the most accurate reconstructed results is investigated in detail in this paper. Two kinds of comparison, the comparison of different extraction methods and the comparison between "two-step" algorithms and the Hilbert filtered backprojection (HFBP) algorithm, draw the conclusion that the HFBP algorithm based on the maximum refraction-angle (MRA) method may be the best combination at present. Though all current extraction methods including the MRA method are approximate methods and cannot calculate very large refraction-angle values, the HFBP algorithm based on the MRA method is able to provide quite acceptable estimations of the distribution of refractive index decrement of the sample. The conclusion is proved by the experimental results at the Beijing Synchrotron Radiation Facility.     

Vector entropy imaging theory with application to computerized tomography

Medical imaging theory for x-ray CT and PET is based on image reconstruction from projections. In this paper a novel vector entropy imaging theory under the framework of multiple criteria decision making is presented. We also study the most frequently used image reconstruction methods, namely, least square, maximum entropy, and filtered back-projection methods under the framework, of the single performance criterion optimization. Finally, we introduce some of the results obtained by various reconstruction algorithms using computer-generated noisy projection data from the Hoffman phantom and real CT scanner data. Comparison of the reconstructed images indicates that the vector entropy method gives the best in error (difference between the original phantom data and reconstruction), smoothness (suppression of noise), grey value resolution and is free of ghost images.     

Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography

Hemodynamics is thought to play a major role in heart development, yet tools to quantitatively assess hemodynamics in the embryo are sorely lacking. The especially challenging analysis of hemodynamics in the early embryo requires new technology. Small changes in blood flow could indicate when anomalies are initiated even before structural changes can be detected. Furthermore, small changes in the early embryo that affect blood flow could lead to profound abnormalities at later stages. We present a demonstration of 4-D Doppler optical coherence tomography (OCT) imaging of structure and flow, and present several new hemodynamic measurements on embryonic avian hearts at early stages prior to the formation of the four chambers. Using 4-D data, pulsed Doppler measurements could accurately be attained in the inflow and outflow of the heart tube. Also, by employing an en-face slice from the 4-D Doppler image set, measurements of stroke volume and cardiac output are obtained without the need to determine absolute velocity. Finally, an image plane orthogonal to the blood flow is used to determine shear stress by calculating the velocity gradient normal to the endocardium. Hemodynamic measurements will be crucial to identifying genetic and environmental factors that lead to congenital heart defects.     

Alternatives to voxels for image representation in iterative reconstruction algorithms.

Spherically symmetric volume elements are alternatives to the more conventional voxels for the construction of volume images in the computer. The image representation, and the calculation of projections of it, are essential components of iterative algorithms for image reconstruction from projection data. A two-parameter family of spherical volume elements is described that allows control of the smoothness properties of the represented image, whereas conventional voxels are discontinuous. The rotational symmetry of the spherical elements leads to efficient calculation of projections of the represented image, as required in iterative reconstruction algorithms. For volume elements whose shape is ellipsoidal (rather than spherical) it is shown that efficient calculation of the projections is also possible by means of an image space transformation.