A bootstrap resampling method for pre-corrected PET data is proposed and applied to measured data in order to simulate repeated experiments. An elliptical phantom with two hot spheres (1.2 cm and 2.2 cm diameter) in a...
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A bootstrap resampling method for pre-corrected PET data is proposed and applied to measured data in order to simulate repeated experiments. An elliptical phantom with two hot spheres (1.2 cm and 2.2 cm diameter) in a warm background was scanned in a GE Advance PET system. The sphere to background ratio was 3.3:1. Randoms, scatter, attenuation and dead time corrections were applied to the sinogram data. The method was validated using the Student's t- and F-statistical tests. Validation tests indicate that applying the bootstrap method to the pre-corrected PET data preserved the statistical characteristics of the images. The quality of image reconstruction of both measured data and resampled data were tested using the Channelized Hotelling Observer (CHO). Two reconstruction methods, filtered backprojection (FBP) and penalized maximum likelihood using space-alternating generalized EM (PML-SAGE), were compared. In the initial study, detectabilities of FBP were higher than the ones of PML-SAGE for the small sphere detection, while detectabilities of PML-SAGE were higher than the ones of FBP for the big sphere detection. Detectabilities for resampled data appears higher than those for experiment data; the number of tested resampled data was 100, and 20 for experiment data.
A bandlimited signal can be reconstructed from its periodic nonuniformly spaced samples provided the average sampling rate is at least the Nyquist rate. Unlike many previously published methods, the algorithm derived ...
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A bandlimited signal can be reconstructed from its periodic nonuniformly spaced samples provided the average sampling rate is at least the Nyquist rate. Unlike many previously published methods, the algorithm derived in this paper is designed that pays special attention to various practical constraints. In particular, we propose a fast and numerically robust reconstruction method which can utilize FIR filters with a small number of taps and requires only a modest amount of oversampling to achieve high accuracy. The efficiency and accuracy of the algorithm is obtained by fully exploiting the sampling structure combined with utilizing localized Fourier analysis. We discuss applications in time-interleaved analog-to-digital converters where nonuniform periodic sampling arises due to timing mismatches. Finally, numerical simulations demonstrate the performance of our algorithm.
Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomial or piecewise sinusoidal signals, an...
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Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomial or piecewise sinusoidal signals, and call the number of degrees of freedom per unit of time the rate of innovation. Classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited. In this paper, we show that many signals with finite rate of innovation can be sampled and perfectly reconstructed using kernels of compact support and a local reconstruction algorithm. The class of kernels that we can use is very rich and includes functions satisfying strang-fix conditions, exponential splines and functions with rational Fourier transforms. Extension of such results to the 2-dimensional case are also discussed and an application to image super-resolution is presented.
The theory of compressive sensing (CS) has been widely used in the field of image signal processing, and CS can improve the reconstruction quality of images. While traditional iterative algorithms lead to resource was...
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ISBN:
(数字)9798350375909
ISBN:
(纸本)9798350375916
The theory of compressive sensing (CS) has been widely used in the field of image signal processing, and CS can improve the reconstruction quality of images. While traditional iterative algorithms lead to resource waste due to too many iterations, a deep reconstruction network CSResNet is proposed to save the amount of computation in the paper. Firstly, network training is used to replace the sampling matrix. Secondly, the structure is optimized by adding a residual network to form a deep network to recover the image. Finally, the experiment results are shown to demonstrate the advantages of the algorithm in the paper.
One of the limitations of using iterative reconstruction methods in tomography is the slow performance compared with the direct reconstruction methods, such as Filtered Backprojection. Here, the authors demonstrate a ...
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One of the limitations of using iterative reconstruction methods in tomography is the slow performance compared with the direct reconstruction methods, such as Filtered Backprojection. Here, the authors demonstrate a very fast implementation of most types of iterative reconstruction methods. The key idea of the authors' method is to generate the huge system matrix only once, and store it using sparse matrix techniques. From the sparse matrix one can perform the matrix vector products very fast, which implies a major acceleration of the reconstruction algorithms. Here, the authors demonstrate that iterative reconstruction algorithms can be implemented and run almost as fast as direct reconstruction algorithms. The method has been implemented in a software package that is available for free, providing reconstruction algorithms using ART, EM, and the Least Squares Conjugate Gradient Method.
We propose a voxel-based multi-variate analysis to evaluate the performance of tomographic image reconstruction. This technique allows simultaneous comparison of the underlying task with resolution and noise behavior ...
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We propose a voxel-based multi-variate analysis to evaluate the performance of tomographic image reconstruction. This technique allows simultaneous comparison of the underlying task with resolution and noise behavior as well as other effects across the entire volume for different reconstructions. We demonstrate the idea with a 2D simulation and apply the method to compare 3D [/sup 15/O]water studies reconstructed by 3D reprojection (3DRP) and Fourier rebinning (FORE) for a motor task. The difference between the two reconstructions was found to be significant relative to the baseline-activation effect (26% vs. 74% for single-session analysis and 32% vs. 68% for 4-session analysis). Although the differences in resolution and noise characteristics are similar to those reported in the literature, the major pattern that separates the two reconstructions is a mean difference in the axial direction. However, both 3DRP and FORE are capable of discriminating the baseline scans from the activation scans.
Viewed abstractly, all the algorithms considered here are designed to provide a nonnegative solution x to the system of linear equations y=Px, where y is a vector with positive entries and P a matrix whose entries are...
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Viewed abstractly, all the algorithms considered here are designed to provide a nonnegative solution x to the system of linear equations y=Px, where y is a vector with positive entries and P a matrix whose entries are nonnegative and with no purely zero columns. The expectation maximization maximum likelihood (EMML) method as it occurs in emission tomography and the simultaneous multiplicative algebraic reconstruction technique (SMART) are slow to converge on large data sets; accelerating convergence through the use of block-iterative or ordered subset versions of these algorithms is a topic of considerable interest. These block-iterative versions involve relaxation and normalization parameters the correct selection of which may not be obvious to all users. The algorithms are not faster merely by virtue of being block-iterative; the correct choice of the parameters is crucial. Through a detailed discussion of the theoretical foundations of these methods we come to a better understanding of the precise roles these parameters play.
A task-based method for evaluating cone-beam CT image reconstruction algorithms is proposed. The task is signal-known-exactly/background-known-exactly detection. The aim is to compute the efficiency of image reconstru...
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A task-based method for evaluating cone-beam CT image reconstruction algorithms is proposed. The task is signal-known-exactly/background-known-exactly detection. The aim is to compute the efficiency of image reconstruction with respect to this task. The efficiency is the ratio of the square of the signal detectability by the ideal observer in the reconstructed image and in the projection data. As reconstruction, here, is a non-invertible linear operator, the efficiency is less than or equal to one. For the model used to describe the projection data the ideal observer is equivalent to the Hotelling observer. To obtain Hotelling observer performance, the Hotelling template is computed in both the projection data and reconstructed image domains. Under the assumption of uncorrelated noise, the data domain Hotelling template computation is straight-forward;however, its computation in the reconstructed image space is complicated by having a very large non-diagonal covariance. In this work, an efficient, accurate method is developed for evaluating the Hotelling template in the reconstructed image space in cone-beam CT. Obtaining this template, enables the accurate computation of the efficiency of the cone-beam CT image reconstruction algorithm.
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