A spatially variant total variational model for chromatic aberration correction

In this paper, we propose a spatially variant total variational model to correct chromatic aberration (CA) that causes false color artifacts near edges in captured images. In general, it may be very difficult to determine suitably CA regions in captured images. Instead of using local image processing methods, our idea is to make use of spatially variant model to control the gradient and intensity matching between the red and blue color channels and the green color channel at the edges. The total variation regularization is also employed to constraint the change of the intensity of red and blue color channels during the gradient and intensity matching. We present both theoretical results and algorithms for the proposed model. Experimental results are given to illustrate the effectiveness of the proposed model and algorithm and show that their corrected images are visually better than those corrected by the other testing methods.     

Conjugate phase MRI reconstruction with spatially variant sample density correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.     

Improved SPECT quantitation using fully three-dimensional iterative spatially variant scatter response compensation

The quality and quantitative accuracy of iteratively reconstructed SPECT images improves when better point spread function (PSF) models of the gamma camera are used during reconstruction. Here, inclusion in the PSF model of photon crosstalk between different slices caused by limited gamma camera resolution and scatter is examined. A three-dimensional (3-D) projector back-projector (proback) has been developed which models both the distance dependent detector point spread function and the object shape-dependent scatter point spread function of single photon emission computed tomography (SPECT). A table occupying only a few megabytes of memory is sufficient to represent this scatter model. The contents of this table are obtained by evaluating an analytical expression for object shape-dependent scatter. The proposed approach avoids the huge memory requirements of storing the full transition matrix needed for 3-D reconstruction including object shape-dependent scatter. In addition, the method avoids the need for lengthy Monte Carlo simulations to generate such a matrix. In order to assess the quantitative accuracy of the method, reconstructions of a water filled cylinder containing regions of different activity levels and of simulated 3-D brain projection data have been evaluated for technetium-99m. It is shown that fully 3-D reconstruction including complete detector response and object shape-dependent scatter modeling clearly outperforms simpler methods that lack a complete detector response and/or a complete scatter response model. Fully 3-D scatter correction yields the best quantitation of volumes of interest and the best contrast-to-noise curves.     

旋转运动空间可变模糊图像的代数复原

提出了一种基于最小二乘和空间相关约束沿模糊路径卷积的代数复原方法。为了有效和快速地恢复角点处的图像信息,采用了最优估值理论。在微机上对算法进行了验证,实验结果表明,算法能有效地去除旋转运动的空间可变模糊。     

Fan-beam reconstruction algorithm for a spatially varying focal length collimator

Fan-beam collimators are used in single-photon-emission computed tomography (SPECT) to improve the sensitivity for imaging of small organs. The disadvantage of fan-beam collimation is the truncation of projection data surrounding the organ of interest or, in those cases of imaging large patients, of the organ itself, producing reconstruction artifacts. A spatially varying focal length fan-beam collimator has been proposed to eliminate the truncation problem and to maintain good sensitivity for the organ of interest. The collimator is constructed so that the shortest focal lengths are located at the center of the collimator and the longest focal length is located at the periphery. The focal length is assumed to increase monotonically toward the edge of the collimator. A reconstruction algorithm for this type of fan-beam collimation, expressed as an infinite series of convolutions followed by one backprojection, is presented. Simulations show that only a small number of N terms in the series is needed to obtain high-quality reconstructions. Computer simulations showed that if the focal length function is smooth, the reconstructions are free of artifacts.     

A backprojection filtering algorithm for a spatially varying focal length collimator

Fan-beam collimators are used in single photon emission computed tomography to improve the sensitivity for imaging of small organs. The disadvantage of fan-beam collimation is the truncation of projection data surrounding the organ of interest or, in those cases of imaging large patients, of the organ itself producing reconstruction artifacts. A spatially varying focal length fan-beam collimator has been proposed to eliminate the truncation problem and to maintain good sensitivity for the organ of interest. The collimator is constricted so that the focal lengths of the holes vary across the face of the collimator with the shortest focal lengths at the center and the longer focal lengths at the periphery of the collimator. The variation of the focal length can have various functional forms but in the authors' work it is assumed to increase monotonically toward the edge of the collimator. A backprojection filtering reconstruction algorithm is derived for this type of collimation. The algorithm first backprojects the projections, then performs a two-dimensional filtering. The algorithm is efficient and has been tested via computer simulations.     

Single and multipinhole collimator design evaluation method for small animal SPECT

High-resolution functional imaging of small animals is often obtained by single pinhole SPECT with circular orbit acquisition. Multipinhole SPECT adds information due to its improved sampling, and can improve the trade-off between resolution and sensitivity. To evaluate different pinhole collimator designs an efficient method is needed that quantifies the reconstruction image quality. In this paper, we propose a fast, approximate method that examines the quality of individual voxels of a postsmoothed maximum likelihood expectation maximization (MLEM) reconstruction by studying their linearized local impulse response (LLIR) and (co)variance for a predefined target resolution. For validation, the contrast-to-noise ratios (CNRs) in some voxels of a homogeneous sphere and of a realistic rat brain software phantom were calculated for many single and multipinhole designs. A good agreement was observed between the CNRs obtained with the approximate method and those obtained with postsmoothed MLEM reconstructions of simulated noisy projections. This good agreement was quantified by a least squares fit through these results, which yielded a line with slope 1.02 (1.00 expected) and a y-intercept close to zero (0 expected). 95.4% of the validation points lie within three standard deviations from that line. Using the approximate method, the influence on the CNR of varying a parameter in realistic single and multipinhole designs was examined. The investigated parameters were the aperture diameter, the distance between the apertures and the axis-of-rotation, the focal distance, the acceptance angle, the position of the apertures, the focusing distance, and the number of pinholes. The results can generally be explained by the change in sensitivity, the amount of postsmoothing, and the amount of overlap in the projections. The method was applied to multipinhole designs with apertures focusing at a single point, but is also applicable to other designs.     

Phase-driven spatially variant regularization for image resolution enhancement

A phase-driven spatially variant regularization approach is proposed in this letter to perform image resolution enhancement. The proposed approach adaptively adjusts the degree of regularization using the phase coherence measure of the local content of the image. This is in contrast to that a spatially invariant regularization parameter is exploited for the whole image in conventional approaches. Experiments are conducted to demonstrate the superior performance of the proposed approach.     

A regularized deconvolution-fitting method for Compton-scatter correction in SPECT

A method is presented for estimating the Compton-scatter component within the photopeak for local energy spectra measured by an Anger camera in SPECT. Assuming that the measured energy spectrum is the source scatter energy distribution convolved with a known camera energy-resolution function plus an unscattered spectral component, a least-square inverse operation is performed to recover the source scatter distribution. Since this inverse operation is ill-posed, the regularization technique is applied for stabilization. With the method, scatter fractions similar to those from polynomial spectral fitting (PSF) have been observed for experimentally measured, high-count data with a hot (Tc(99m) or I(131)) sphere in a cold cylinder, and the inverse (Tc(99m) only). The method is also less sensitive to the width of the fitting window. A regularization parameter from 1 to 10 is recommended for practical cases. The shape of a recovered source scatter distribution matches that determined by a high-resolution semiconductor-detector measurement as well as by Monte Carlo simulation.     

A class-adaptive spatially variant mixture model for image segmentation.

We propose a new approach for image segmentation based on a hierarchical and spatially variant mixture model. According to this model, the pixel labels are random variables and a smoothness prior is imposed on them. The main novelty of this work is a new family of smoothness priors for the label probabilities in spatially variant mixture models. These Gauss-Markov random field-based priors allow all their parameters to be estimated in closed form via the maximum a posteriori (MAP) estimation using the expectation-maximization methodology. Thus, it is possible to introduce priors with multiple parameters that adapt to different aspects of the data. Numerical experiments are presented where the proposed MAP algorithms were tested in various image segmentation scenarios. These experiments demonstrate that the proposed segmentation scheme compares favorably to both standard and previous spatially constrained mixture model-based segmentation.     

Fourier rebinning applied to multiplanar circular-orbit cone-beam SPECT

We study the application of Fourier rebinning methods to dual-planar cone-beam SPECT. Dual-planar cone-beam SPECT involves the use of a pair of dissimilar cone-beam collimators on a dual-camera SPECT system. Each collimator has its focus in a different axial plane. While dual-planar data is best reconstructed with fully three-dimensional (3-D) iterative methods, these methods are slow and have prompted a search for faster reconstruction techniques. Fourier rebinning was developed to estimate equivalent parallel projections from 3-D PET data, but it simply expresses a relationship between oblique projections taken in planes not perpendicular to the axis of rotation and direct projections taken in those that are. We find that it is possible to put cone-beam data in this context as well. The rebinned data can then be reconstructed using either filtered backprojection (FBP) or parallel iterative algorithms such as OS-EM. We compare the Feldkamp algorithm and fully 3-D OSEM reconstruction with Fourier-rebinned reconstructions on realistically-simulated Tc-99m HMPAO brain SPECT data. We find that the Fourier-rebinned reconstructions exhibit much less image noise and lower variance in region-of-interest (ROI) estimates than Feldkamp. Also, Fourier-rebinning followed by OSEM with nonuniform attenuation correction exhibits less bias in ROI estimates than Feldkamp with Chang attenuation correction. The Fourier-rebinned ROI estimates exhibit bias and variance comparable to those from fully 3-D OSEM and require considerably less processing time. However, in areas off the axis of rotation, the axial-direction resolution of FORE-reconstructed images is poorer than that of images reconstructed with 3-D OSEM. We conclude that Fourier rebinning is a practical and potentially useful approach to reconstructing data from dual-planar circular-orbit cone-beam systems.     

Generalization of spatially variant apodization to nonintegerNyquist sampling rates

Spatially variant apodization (SVA) is reformulated for use on synthetic aperture radar imagery with an arbitrary sampling rate. The algorithm is implemented as a spatially varying three-point finite impulse response filter, and constraints on the filter parameters are developed from physically motivated concepts. By varying the parameters of the filter, the sidelobe energy is reduced with no effective loss of resolution. The procedure produces an output comparable to that of the integer Nyquist version of SVA, and effectively eliminates sidelobe artifacts with no loss of mainlobe resolution.     

Stereoscopic image interpolation using a spatially variant regularisation approach

This paper studies the problem of stereoscopic image interpolation, where a pair of images with mixed-resolution is given. Specifically, one image yields a low resolution, while the other one yields a higher resolution. The aim of the proposed approach is to reconstruct another pair of images with same high resolutions. To achieve this objective, the proposed approach imposes a regularisation on the reconstructed high-resolution image to perform image interpolation. Furthermore, the degree of regularisation is adaptively adjusted according to the local gradient of the reconstructed high-resolution image. Experiments are conducted to demonstrate that the proposed approach outperforms several conventional image interpolation approaches.     

Practical aspects of a data-driven motion correction approach for brain SPECT

Patient motion can cause image artifacts in single photon emission computed tomography despite restraining measures. Data-driven detection and correction of motion can be achieved by comparison of acquired data with the forward projections. This enables the brain locations to be estimated and data to be correctly incorporated in a three-dimensional (3-D) reconstruction algorithm. Digital and physical phantom experiments were performed to explore practical aspects of this approach. METHODS: Noisy simulation data modeling multiple 3-D patient head movements were constructed by projecting the digital Hoffman brain phantom at various orientations. Hoffman physical phantom data incorporating deliberate movements were also gathered. Motion correction was applied to these data using various regimes to determine the importance of attenuation and successive iterations. Studies were assessed visually for artifact reduction, and analyzed quantitatively via a mean registration error (MRE) and mean square difference measure (MSD). RESULTS: Artifacts and distortion in the motion corrupted data were reduced to a large extent by application of this algorithm. MRE values were mostly well within 1 pixel (4.4 mm) for the simulated data. Significant MSD improvements (>2) were common. Inclusion of attenuation was unnecessary to accurately estimate motion, doubling the efficiency and simplifying implementation. Moreover, most motion-related errors were removed using a single iteration. The improvement for the physical phantom data was smaller, though this may be due to object symmetry. CONCLUSION: These results provide the basis of an implementation protocol for clinical validation of the technique.     

Nonlinear motion correction of respiratory-gated lung SPECT images

We propose a method for correcting the motion of the lungs between different phase images obtained by respiratory-gated single photon emission computed tomography (SPECT). This method is applied to SPECT images that show a preserved activity distribution in the lungs such as 99m-Tc macro aggregated albumin (99m-Tc-MAA) perfusion images and 99m-Tc-Technegas ventilation images. In the proposed method, an objective function, which consists of both the degree of similarity between a reference image and a deformed image, and the smoothness of deformation is defined and optimized using a simulated annealing algorithm. For the degree of similarity term in the objective function, an expansion ratio, defined as the ratio of change in local volume due to deformation, is introduced to preserve the total activity during the motion correction process. This method was applied to data simulated from computer phantoms, data acquired from a physical phantom, and 17 sets of clinical data. In all cases, the motion correction between inspiration and expiration phase images was successfully achieved.     

Identification and restoration of spatially variant motion blurs insequential images

Sequential imaging cameras are designed to record objects in motion. When the speed of the objects exceeds the temporal resolution of the shutter, the image is blurred. Because objects in a scene are often moving in different directions at different speeds, the degradation of a recorded image may be characterized by a space-variant point spread function (PSF). The sequential nature of such images can be used to determine the relative motion of various parts of the image. This information can be used to estimate the space-variant PSF. A modification of the Landweber iteration is developed to utilize the space-variant PSF to produce an estimate of the original image.     

基于响应率修正的傅里叶变换光谱仪非线性校正算法研究

傅里叶变换高光谱仪器在定量化遥感领域展现出极大的优势,非线性校正是保证在轨辐射定标精度不可缺少的过程。针对搭载于风云四号静止轨道干涉式红外探测仪（FY-4/GIIRS）运行轨道受日晒分布不均匀、仪器环境温度日变化剧烈的特点,推导出一种基于仪器光谱响应率修正的非线性校正算法,通过测量一组标准参考辐射源光谱量化值和光谱响应率,拟合得到光谱响应率一次项修正系数。在仪器环境温度变化后,利用一次项修正系数、黑体观测光谱值和黑体观测光谱响应率重新计算光谱响应率常数项修正系数,就可以得到任意仪器环境温度下的仪器非线性校正系数。经仪器发射前地面热真空（TVAC）定标试验数据验证,该算法简单有效,在各试验环境温度工况下,对180～320 K观测范围内的辐射定标精度均有明显的提高。     

模糊图像的自适应滤波及恢复

文章讨论如何根据最小二乘原理和回归模型设计出自适应滤波器，以用于消除图像噪声。提出了一种基于模糊图像的梯度图像计算模糊宽度的方法。根据基本原理，讨论分析了实现该方法的算法。最后给出了对带噪声的散焦模糊图像处理的实验结果。     

运动模糊图像点扩展函数的自动识别方法

在获取图像的过程中,传感器和场景的相对运动所造成的图像模糊是一类常见的图像退化模式。为对模糊图像进行恢复,首先要给出精确的点扩展函数估计。针对匀速运动降晰的情况,提出了一种新的误差-参数曲线法,并依据这种曲线提出了一种点扩展函数的自动估计算法。通过引入奇异因子、光滑因子以及平坦因子来实现点扩展函数的估计。实验结果表明,该方法可以取得较为精确的估计效果。