The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Athina P Petropulu - One of the best experts on this subject based on the ideXlab platform.
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multidimensional sparse fourier transform based on the fourier projection Slice Theorem
IEEE Transactions on Signal Processing, 2019Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose Multidimensional Random Slice-based Sparse Fourier Transform (MARS-SFT), a sparse Fourier transform for multidimensional, frequency-domain sparse signals, inspired by the idea of the Fourier projection-Slice Theorem. MARS-SFT identifies frequencies by operating on one-dimensional Slices of the discrete-time domain data, taken along specially designed lines; these lines are parametrized by slopes that are randomly generated from a set at runtime. The discrete Fourier transforms (DFTs) of data Slices represent DFT projections onto the lines along which the Slices were taken. On designing the line lengths and slopes so that they allow for orthogonal and uniform projections of the sparse frequencies, frequency collisions are avoided with high probability, and the multidimensional frequencies can be recovered from their projections with low sample and computational complexity. We show analytically that the large number of degrees of freedom of frequency projections allows for the recovery of less sparse signals. Although the theoretical results are obtained for uniformly distributed frequencies, empirical evidence suggests that MARS-SFT is also effective in recovering clustered frequencies. We also propose an extension of MARS-SFT to address noisy signals that contain off-grid frequencies and demonstrate its performance in digital beamforming automotive radar signal processing. In that context, the robust MARS-SFT is used to identify range, velocity, and angular parameters of targets with low sample and computational complexity.
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robust sparse fourier transform based on the fourier projection Slice Theorem
IEEE Radar Conference, 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We have recently proposed a sparse Fourier transform based on the Fourier projection-Slice Theorem (FPS-SFT), which is an efficient implementation of the discrete Fourier transform for multidimensional signals that are sparse in the frequency domain. For a K-sparse signal, FPS-SFT achieves sample complexity of O(K) and computational complexity of O(K log K). While FPS-SFT considers the ideal scenario, i.e., exactly sparse data that contain on-grid frequencies, in this paper, we propose a robust FPS-SFT (RFPS-SFT), which applies to noisy signals that contain off-grid frequencies; such signals arise in radar applications. RFPS-SFT employs a windowing step and a voting-based frequency decoding step; the former reduces the frequency leakage of off-grid frequencies below the noise level, thus preserving the sparsity of the signal, while the latter significantly lowers the frequency localization error stemming from the noise. The performance of the proposed method is demonstrated both theoretically and numerically.
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fps sft a multi dimensional sparse fourier transform based on the fourier projection Slice Theorem
International Conference on Acoustics Speech and Signal Processing, 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose a multidimensional sparse Fourier transform inspired by the idea of the Fourier projection-Slice Theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional Slices from a multidimensional data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of multidimensional DFT of the data onto those lines. The multidimensional frequencies that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving less sparse scenarios containing non-uniformly distributed frequencies.
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ICASSP - Fps-Sft: A Multi-Dimensional Sparse Fourier Transform Based on the Fourier Projection-Slice Theorem
2018 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose a multidimensional sparse Fourier transform inspired by the idea of the Fourier projection-Slice Theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional Slices from a multidimensional data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of multidimensional DFT of the data onto those lines. The multidimensional frequencies that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving less sparse scenarios containing non-uniformly distributed frequencies.
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robust sparse fourier transform based on the fourier projection Slice Theorem
arXiv: Signal Processing, 2017Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational complexity of $O(N)$ and $O(N \log N)$, respectively, where $N$ is the number of samples in the signal space. We have recently proposed a sparse Fourier transform based on the Fourier projection-Slice Theorem (FPS-SFT), which applies to multidimensional signals that are sparse in the frequency domain. FPS-SFT achieves sample complexity of $O(K)$ and computational complexity of $O(K \log K)$ for a multidimensional, $K$-sparse signal. While FPS-SFT considers the ideal scenario, i.e., exactly sparse data that contains on-grid frequencies, in this paper, by extending FPS-SFT into a robust version (RFPS-SFT), we emphasize on addressing noisy signals that contain off-grid frequencies; such signals arise from radar applications. This is achieved by employing a windowing technique and a voting-based frequency decoding procedure; the former reduces the frequency leakage of the off-grid frequencies below the noise level to preserve the sparsity of the signal, while the latter significantly lowers the frequency localization error stemming from the noise. The performance of the proposed method is demonstrated both theoretically and numerically.
Shaogang Wang - One of the best experts on this subject based on the ideXlab platform.
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multidimensional sparse fourier transform based on the fourier projection Slice Theorem
IEEE Transactions on Signal Processing, 2019Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose Multidimensional Random Slice-based Sparse Fourier Transform (MARS-SFT), a sparse Fourier transform for multidimensional, frequency-domain sparse signals, inspired by the idea of the Fourier projection-Slice Theorem. MARS-SFT identifies frequencies by operating on one-dimensional Slices of the discrete-time domain data, taken along specially designed lines; these lines are parametrized by slopes that are randomly generated from a set at runtime. The discrete Fourier transforms (DFTs) of data Slices represent DFT projections onto the lines along which the Slices were taken. On designing the line lengths and slopes so that they allow for orthogonal and uniform projections of the sparse frequencies, frequency collisions are avoided with high probability, and the multidimensional frequencies can be recovered from their projections with low sample and computational complexity. We show analytically that the large number of degrees of freedom of frequency projections allows for the recovery of less sparse signals. Although the theoretical results are obtained for uniformly distributed frequencies, empirical evidence suggests that MARS-SFT is also effective in recovering clustered frequencies. We also propose an extension of MARS-SFT to address noisy signals that contain off-grid frequencies and demonstrate its performance in digital beamforming automotive radar signal processing. In that context, the robust MARS-SFT is used to identify range, velocity, and angular parameters of targets with low sample and computational complexity.
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robust sparse fourier transform based on the fourier projection Slice Theorem
IEEE Radar Conference, 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We have recently proposed a sparse Fourier transform based on the Fourier projection-Slice Theorem (FPS-SFT), which is an efficient implementation of the discrete Fourier transform for multidimensional signals that are sparse in the frequency domain. For a K-sparse signal, FPS-SFT achieves sample complexity of O(K) and computational complexity of O(K log K). While FPS-SFT considers the ideal scenario, i.e., exactly sparse data that contain on-grid frequencies, in this paper, we propose a robust FPS-SFT (RFPS-SFT), which applies to noisy signals that contain off-grid frequencies; such signals arise in radar applications. RFPS-SFT employs a windowing step and a voting-based frequency decoding step; the former reduces the frequency leakage of off-grid frequencies below the noise level, thus preserving the sparsity of the signal, while the latter significantly lowers the frequency localization error stemming from the noise. The performance of the proposed method is demonstrated both theoretically and numerically.
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fps sft a multi dimensional sparse fourier transform based on the fourier projection Slice Theorem
International Conference on Acoustics Speech and Signal Processing, 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose a multidimensional sparse Fourier transform inspired by the idea of the Fourier projection-Slice Theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional Slices from a multidimensional data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of multidimensional DFT of the data onto those lines. The multidimensional frequencies that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving less sparse scenarios containing non-uniformly distributed frequencies.
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ICASSP - Fps-Sft: A Multi-Dimensional Sparse Fourier Transform Based on the Fourier Projection-Slice Theorem
2018 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose a multidimensional sparse Fourier transform inspired by the idea of the Fourier projection-Slice Theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional Slices from a multidimensional data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of multidimensional DFT of the data onto those lines. The multidimensional frequencies that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving less sparse scenarios containing non-uniformly distributed frequencies.
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robust sparse fourier transform based on the fourier projection Slice Theorem
arXiv: Signal Processing, 2017Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational complexity of $O(N)$ and $O(N \log N)$, respectively, where $N$ is the number of samples in the signal space. We have recently proposed a sparse Fourier transform based on the Fourier projection-Slice Theorem (FPS-SFT), which applies to multidimensional signals that are sparse in the frequency domain. FPS-SFT achieves sample complexity of $O(K)$ and computational complexity of $O(K \log K)$ for a multidimensional, $K$-sparse signal. While FPS-SFT considers the ideal scenario, i.e., exactly sparse data that contains on-grid frequencies, in this paper, by extending FPS-SFT into a robust version (RFPS-SFT), we emphasize on addressing noisy signals that contain off-grid frequencies; such signals arise from radar applications. This is achieved by employing a windowing technique and a voting-based frequency decoding procedure; the former reduces the frequency leakage of the off-grid frequencies below the noise level to preserve the sparsity of the signal, while the latter significantly lowers the frequency localization error stemming from the noise. The performance of the proposed method is demonstrated both theoretically and numerically.
Vishal M Patel - One of the best experts on this subject based on the ideXlab platform.
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multidimensional sparse fourier transform based on the fourier projection Slice Theorem
IEEE Transactions on Signal Processing, 2019Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose Multidimensional Random Slice-based Sparse Fourier Transform (MARS-SFT), a sparse Fourier transform for multidimensional, frequency-domain sparse signals, inspired by the idea of the Fourier projection-Slice Theorem. MARS-SFT identifies frequencies by operating on one-dimensional Slices of the discrete-time domain data, taken along specially designed lines; these lines are parametrized by slopes that are randomly generated from a set at runtime. The discrete Fourier transforms (DFTs) of data Slices represent DFT projections onto the lines along which the Slices were taken. On designing the line lengths and slopes so that they allow for orthogonal and uniform projections of the sparse frequencies, frequency collisions are avoided with high probability, and the multidimensional frequencies can be recovered from their projections with low sample and computational complexity. We show analytically that the large number of degrees of freedom of frequency projections allows for the recovery of less sparse signals. Although the theoretical results are obtained for uniformly distributed frequencies, empirical evidence suggests that MARS-SFT is also effective in recovering clustered frequencies. We also propose an extension of MARS-SFT to address noisy signals that contain off-grid frequencies and demonstrate its performance in digital beamforming automotive radar signal processing. In that context, the robust MARS-SFT is used to identify range, velocity, and angular parameters of targets with low sample and computational complexity.
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robust sparse fourier transform based on the fourier projection Slice Theorem
IEEE Radar Conference, 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We have recently proposed a sparse Fourier transform based on the Fourier projection-Slice Theorem (FPS-SFT), which is an efficient implementation of the discrete Fourier transform for multidimensional signals that are sparse in the frequency domain. For a K-sparse signal, FPS-SFT achieves sample complexity of O(K) and computational complexity of O(K log K). While FPS-SFT considers the ideal scenario, i.e., exactly sparse data that contain on-grid frequencies, in this paper, we propose a robust FPS-SFT (RFPS-SFT), which applies to noisy signals that contain off-grid frequencies; such signals arise in radar applications. RFPS-SFT employs a windowing step and a voting-based frequency decoding step; the former reduces the frequency leakage of off-grid frequencies below the noise level, thus preserving the sparsity of the signal, while the latter significantly lowers the frequency localization error stemming from the noise. The performance of the proposed method is demonstrated both theoretically and numerically.
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fps sft a multi dimensional sparse fourier transform based on the fourier projection Slice Theorem
International Conference on Acoustics Speech and Signal Processing, 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose a multidimensional sparse Fourier transform inspired by the idea of the Fourier projection-Slice Theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional Slices from a multidimensional data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of multidimensional DFT of the data onto those lines. The multidimensional frequencies that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving less sparse scenarios containing non-uniformly distributed frequencies.
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ICASSP - Fps-Sft: A Multi-Dimensional Sparse Fourier Transform Based on the Fourier Projection-Slice Theorem
2018 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2018Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:We propose a multidimensional sparse Fourier transform inspired by the idea of the Fourier projection-Slice Theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional Slices from a multidimensional data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of multidimensional DFT of the data onto those lines. The multidimensional frequencies that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving less sparse scenarios containing non-uniformly distributed frequencies.
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robust sparse fourier transform based on the fourier projection Slice Theorem
arXiv: Signal Processing, 2017Co-Authors: Shaogang Wang, Vishal M Patel, Athina P PetropuluAbstract:The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational complexity of $O(N)$ and $O(N \log N)$, respectively, where $N$ is the number of samples in the signal space. We have recently proposed a sparse Fourier transform based on the Fourier projection-Slice Theorem (FPS-SFT), which applies to multidimensional signals that are sparse in the frequency domain. FPS-SFT achieves sample complexity of $O(K)$ and computational complexity of $O(K \log K)$ for a multidimensional, $K$-sparse signal. While FPS-SFT considers the ideal scenario, i.e., exactly sparse data that contains on-grid frequencies, in this paper, by extending FPS-SFT into a robust version (RFPS-SFT), we emphasize on addressing noisy signals that contain off-grid frequencies; such signals arise from radar applications. This is achieved by employing a windowing technique and a voting-based frequency decoding procedure; the former reduces the frequency leakage of the off-grid frequencies below the noise level to preserve the sparsity of the signal, while the latter significantly lowers the frequency localization error stemming from the noise. The performance of the proposed method is demonstrated both theoretically and numerically.
Josien P. W. Pluim - One of the best experts on this subject based on the ideXlab platform.
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robust initialization of 2d 3d image registration using the projection Slice Theorem and phase correlation
Medical Physics, 2010Co-Authors: M J Van Der Bom, Jelte Timmer, Reyn Homan, Matthew J Gounis, Lambertus W. Bartels, Max A. Viergever, Josien P. W. PluimAbstract:Purpose: The image registration literature comprises many methods for 2D-3D registration for which accuracy has been established in a variety of applications. However, clinical application is limited by a small capture range. Initial offsets outside the capture range of a registration method will not converge to a successful registration. Previously reported capture ranges, defined as the 95% success range, are in the order of 4-11 mm mean target registration error. In this article, a relatively computationally inexpensive and robust estimation method is proposed with the objective to enlarge the capture range. Methods: The method uses the projection-Slice Theorem in combination with phase correlation in order to estimate the transform parameters, which provides an initialization of the subsequent registration procedure. Results: The feasibility of the method was evaluated by experiments using digitally reconstructed radiographs generated from in vivo 3D-RX data. With these experiments it was shown that the projection-Slice Theorem provides successful estimates of the rotational transform parameters for perspective projections and in case of translational offsets. The method was further tested on ex vivo ovine x-ray data. In 95% of the cases, the method yielded successful estimates for initial mean target registration errors up to 19.5 mm. Finally, the methodmore » was evaluated as an initialization method for an intensity-based 2D-3D registration method. The uninitialized and initialized registration experiments had success rates of 28.8% and 68.6%, respectively. Conclusions: The authors have shown that the initialization method based on the projection-Slice Theorem and phase correlation yields adequate initializations for existing registration methods, thereby substantially enlarging the capture range of these methods.« less
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Robust initialization of 2D‐3D image registration using the projection‐Slice Theorem and phase correlation
Medical physics, 2010Co-Authors: M J Van Der Bom, Reyn Homan, Matthew J Gounis, Lambertus W. Bartels, Max A. Viergever, J. Timmer, Josien P. W. PluimAbstract:Purpose: The image registration literature comprises many methods for 2D-3D registration for which accuracy has been established in a variety of applications. However, clinical application is limited by a small capture range. Initial offsets outside the capture range of a registration method will not converge to a successful registration. Previously reported capture ranges, defined as the 95% success range, are in the order of 4-11 mm mean target registration error. In this article, a relatively computationally inexpensive and robust estimation method is proposed with the objective to enlarge the capture range. Methods: The method uses the projection-Slice Theorem in combination with phase correlation in order to estimate the transform parameters, which provides an initialization of the subsequent registration procedure. Results: The feasibility of the method was evaluated by experiments using digitally reconstructed radiographs generated from in vivo 3D-RX data. With these experiments it was shown that the projection-Slice Theorem provides successful estimates of the rotational transform parameters for perspective projections and in case of translational offsets. The method was further tested on ex vivo ovine x-ray data. In 95% of the cases, the method yielded successful estimates for initial mean target registration errors up to 19.5 mm. Finally, the methodmore » was evaluated as an initialization method for an intensity-based 2D-3D registration method. The uninitialized and initialized registration experiments had success rates of 28.8% and 68.6%, respectively. Conclusions: The authors have shown that the initialization method based on the projection-Slice Theorem and phase correlation yields adequate initializations for existing registration methods, thereby substantially enlarging the capture range of these methods.« less
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projection Slice Theorem based 2d 3d registration
Progress in biomedical optics and imaging, 2007Co-Authors: I M J Van Der Bom, Jelte Timmer, Josien P. W. Pluim, Robert Johannes Frederik Homan, Lambertus W. BartelsAbstract:In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This Theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.
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Medical Imaging: Image Processing - Projection-Slice Theorem based 2D-3D registration
Medical Imaging 2007: Image Processing, 2007Co-Authors: I M J Van Der Bom, Josien P. W. Pluim, Robert Johannes Frederik Homan, J. Timmer, Lambertus W. BartelsAbstract:In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This Theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.
Lambertus W. Bartels - One of the best experts on this subject based on the ideXlab platform.
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robust initialization of 2d 3d image registration using the projection Slice Theorem and phase correlation
Medical Physics, 2010Co-Authors: M J Van Der Bom, Jelte Timmer, Reyn Homan, Matthew J Gounis, Lambertus W. Bartels, Max A. Viergever, Josien P. W. PluimAbstract:Purpose: The image registration literature comprises many methods for 2D-3D registration for which accuracy has been established in a variety of applications. However, clinical application is limited by a small capture range. Initial offsets outside the capture range of a registration method will not converge to a successful registration. Previously reported capture ranges, defined as the 95% success range, are in the order of 4-11 mm mean target registration error. In this article, a relatively computationally inexpensive and robust estimation method is proposed with the objective to enlarge the capture range. Methods: The method uses the projection-Slice Theorem in combination with phase correlation in order to estimate the transform parameters, which provides an initialization of the subsequent registration procedure. Results: The feasibility of the method was evaluated by experiments using digitally reconstructed radiographs generated from in vivo 3D-RX data. With these experiments it was shown that the projection-Slice Theorem provides successful estimates of the rotational transform parameters for perspective projections and in case of translational offsets. The method was further tested on ex vivo ovine x-ray data. In 95% of the cases, the method yielded successful estimates for initial mean target registration errors up to 19.5 mm. Finally, the methodmore » was evaluated as an initialization method for an intensity-based 2D-3D registration method. The uninitialized and initialized registration experiments had success rates of 28.8% and 68.6%, respectively. Conclusions: The authors have shown that the initialization method based on the projection-Slice Theorem and phase correlation yields adequate initializations for existing registration methods, thereby substantially enlarging the capture range of these methods.« less
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Robust initialization of 2D‐3D image registration using the projection‐Slice Theorem and phase correlation
Medical physics, 2010Co-Authors: M J Van Der Bom, Reyn Homan, Matthew J Gounis, Lambertus W. Bartels, Max A. Viergever, J. Timmer, Josien P. W. PluimAbstract:Purpose: The image registration literature comprises many methods for 2D-3D registration for which accuracy has been established in a variety of applications. However, clinical application is limited by a small capture range. Initial offsets outside the capture range of a registration method will not converge to a successful registration. Previously reported capture ranges, defined as the 95% success range, are in the order of 4-11 mm mean target registration error. In this article, a relatively computationally inexpensive and robust estimation method is proposed with the objective to enlarge the capture range. Methods: The method uses the projection-Slice Theorem in combination with phase correlation in order to estimate the transform parameters, which provides an initialization of the subsequent registration procedure. Results: The feasibility of the method was evaluated by experiments using digitally reconstructed radiographs generated from in vivo 3D-RX data. With these experiments it was shown that the projection-Slice Theorem provides successful estimates of the rotational transform parameters for perspective projections and in case of translational offsets. The method was further tested on ex vivo ovine x-ray data. In 95% of the cases, the method yielded successful estimates for initial mean target registration errors up to 19.5 mm. Finally, the methodmore » was evaluated as an initialization method for an intensity-based 2D-3D registration method. The uninitialized and initialized registration experiments had success rates of 28.8% and 68.6%, respectively. Conclusions: The authors have shown that the initialization method based on the projection-Slice Theorem and phase correlation yields adequate initializations for existing registration methods, thereby substantially enlarging the capture range of these methods.« less
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projection Slice Theorem based 2d 3d registration
Progress in biomedical optics and imaging, 2007Co-Authors: I M J Van Der Bom, Jelte Timmer, Josien P. W. Pluim, Robert Johannes Frederik Homan, Lambertus W. BartelsAbstract:In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This Theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.
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Medical Imaging: Image Processing - Projection-Slice Theorem based 2D-3D registration
Medical Imaging 2007: Image Processing, 2007Co-Authors: I M J Van Der Bom, Josien P. W. Pluim, Robert Johannes Frederik Homan, J. Timmer, Lambertus W. BartelsAbstract:In X-ray guided procedures, the surgeon or interventionalist is dependent on his or her knowledge of the patient's specific anatomy and the projection images acquired during the procedure by a rotational X-ray source. Unfortunately, these X-ray projections fail to give information on the patient's anatomy in the dimension along the projection axis. It would be very profitable to provide the surgeon or interventionalist with a 3D insight of the patient's anatomy that is directly linked to the X-ray images acquired during the procedure. In this paper we present a new robust 2D-3D registration method based on the Projection-Slice Theorem. This Theorem gives us a relation between the pre-operative 3D data set and the interventional projection images. Registration is performed by minimizing a translation invariant similarity measure that is applied to the Fourier transforms of the images. The method was tested by performing multiple exhaustive searches on phantom data of the Circle of Willis and on a post-mortem human skull. Validation was performed visually by comparing the test projections to the ones that corresponded to the minimal value of the similarity measure. The Projection-Slice Theorem Based method was shown to be very effective and robust, and provides capture ranges up to 62 degrees. Experiments have shown that the method is capable of retrieving similar results when translations are applied to the projection images.
