Object Function

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Mark A. Anastasio - One of the best experts on this subject based on the ideXlab platform.

  • A simple Fourier transform-based reconstruction formula for photoacoustic computed tomography with a circular or spherical measurement geometry
    Photons Plus Ultrasound: Imaging and Sensing 2013, 2013
    Co-Authors: Kun Wang, Mark A. Anastasio
    Abstract:

    Photoacoustic computed tomography (PACT), also known as optoacoustic tomography or thermoacoustic tomography, is an emerging biomedical imaging technique that combines optical absorption contrast with ultrasound detection principles. Recently, a novel analytic image reconstruction formula has been proposed that operates on a data Function expressed in the temporal frequency and spatial domains. The validity the formula has been demonstrated for a two-dimensional (2D) circular measurement geometry. In this study, computer simulation studies are conducted to validate the reconstruction formula for a three-dimensional (3D) spherical measurement geometry. This formula provides new insights into how the spatial frequency components of the sought-after Object Function can be explicitly determined by the temporal frequency components of the data Function measured with a 2D circular or 3D spherical measurement geometry in PACT. Comparing with existing Fourier transform-based reconstruction formulas, the reconstruction formula possesses a simple structure that requires no computation of series expansions or multi-dimensional interpolation in Fourier space.

  • A simple Fourier transform-based reconstruction formula for photoacoustic computed tomography with a circular or spherical measurement geometry
    Physics in medicine and biology, 2012
    Co-Authors: Kun Wang, Mark A. Anastasio
    Abstract:

    Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging modality that has great potential for a wide range of biomedical imaging applications. In this note, we derive a hybrid reconstruction formula that is mathematically exact and operates on a data Function that is expressed in the temporal frequency and spatial domains. This formula explicitly reveals new insights into how the spatial frequency components of the sought-after Object Function are determined by the temporal frequency components of the data Function measured with a circular or spherical measurement geometry in two- and three-dimensional implementations of PACT, respectively. The structure of the reconstruction formula is surprisingly simple compared with existing Fourier-domain reconstruction formulae. It also yields a straightforward numerical implementation that is robust and two orders of magnitude more computationally efficient than filtered backprojection algorithms.

Kun Wang - One of the best experts on this subject based on the ideXlab platform.

  • A simple Fourier transform-based reconstruction formula for photoacoustic computed tomography with a circular or spherical measurement geometry
    Photons Plus Ultrasound: Imaging and Sensing 2013, 2013
    Co-Authors: Kun Wang, Mark A. Anastasio
    Abstract:

    Photoacoustic computed tomography (PACT), also known as optoacoustic tomography or thermoacoustic tomography, is an emerging biomedical imaging technique that combines optical absorption contrast with ultrasound detection principles. Recently, a novel analytic image reconstruction formula has been proposed that operates on a data Function expressed in the temporal frequency and spatial domains. The validity the formula has been demonstrated for a two-dimensional (2D) circular measurement geometry. In this study, computer simulation studies are conducted to validate the reconstruction formula for a three-dimensional (3D) spherical measurement geometry. This formula provides new insights into how the spatial frequency components of the sought-after Object Function can be explicitly determined by the temporal frequency components of the data Function measured with a 2D circular or 3D spherical measurement geometry in PACT. Comparing with existing Fourier transform-based reconstruction formulas, the reconstruction formula possesses a simple structure that requires no computation of series expansions or multi-dimensional interpolation in Fourier space.

  • A simple Fourier transform-based reconstruction formula for photoacoustic computed tomography with a circular or spherical measurement geometry
    Physics in medicine and biology, 2012
    Co-Authors: Kun Wang, Mark A. Anastasio
    Abstract:

    Photoacoustic computed tomography (PACT), also known as optoacoustic tomography, is an emerging imaging modality that has great potential for a wide range of biomedical imaging applications. In this note, we derive a hybrid reconstruction formula that is mathematically exact and operates on a data Function that is expressed in the temporal frequency and spatial domains. This formula explicitly reveals new insights into how the spatial frequency components of the sought-after Object Function are determined by the temporal frequency components of the data Function measured with a circular or spherical measurement geometry in two- and three-dimensional implementations of PACT, respectively. The structure of the reconstruction formula is surprisingly simple compared with existing Fourier-domain reconstruction formulae. It also yields a straightforward numerical implementation that is robust and two orders of magnitude more computationally efficient than filtered backprojection algorithms.

Kanae Nishizawa - One of the best experts on this subject based on the ideXlab platform.

  • imaging of small spherical structures in ct simulation study using measured point spread Function
    Medical & Biological Engineering & Computing, 2008
    Co-Authors: Masaki Ohkubo, Shinichi Wada, Masayuki Kunii, Toru Matsumoto, Kanae Nishizawa
    Abstract:

    Size and density measurements of Objects undertaken using computed tomography (CT) are clinically significant for diagnosis. To evaluate the accuracy of these quantifications, we simulated three-dimensional (3D) CT image blurring; this involved the calculation of the convolution of the 3D Object Function with the measured 3D point spread Function (PSF). We initially validated the simulation technique by performing a phantom experiment. Blurred computed images showed good 3D agreement with measured images of the phantom. We used this technique to compute the 3D blurred images from the Object Functions, in which Functions are determined to have the shape of an ideal sphere of varying diameter and assume solitary pulmonary nodules with a uniform density. The accuracy of diameter and density measurements was determined. We conclude that the proposed simulation technique enables us to estimate the image blurring precisely of any 3D structure and to analyze clinical images quantitatively.

  • an effective method to verify line and point spread Functions measured in computed tomography
    Medical Physics, 2006
    Co-Authors: Masaki Ohkubo, Toru Matsumoto, Sinichi Wada, Kanae Nishizawa
    Abstract:

    This study describes an effective method for verifying line spread Function (LSF) and point spread Function (PSF) measured in computed tomography (CT). The CT image of an assumed Object Function is known to be calculable using LSF or PSF based on a model for the spatial resolution in a linear imaging system. Therefore, the validities of LSF and PSF would be confirmed by comparing the computed images with the images obtained by scanning phantoms corresponding to the Object Function. Differences between computed and measured images will depend on the accuracy of the LSF and PSF used in the calculations. First, we measured LSF in our scanner, and derived the two-dimensional PSF in the scan plane from the LSE Second, we scanned the phantom including uniform cylindrical Objects parallel to the long axis of a patient's body (z direction). Measured images of such a phantom were characterized according to the spatial resolution in the scan plane, and did not depend on the spatial resolution in the z direction. Third, images were calculated by two-dimensionally convolving the true Object as a Function of space with the PSF. As a result of comparing computed images with measured ones, good agreement was found and was demonstrated by image subtraction. As a criterion for evaluating quantitatively the overall differences of images, we defined the normalized standard deviation (SD) in the differences between computed and measured images. These normalized SDs were less than 5.0% (ranging from 1.3% to 4.8%) for three types of image reconstruction kernels and for various diameters of cylindrical Objects, indicating the high accuracy of PSF and LSF that resulted in successful measurements. Further, we also obtained another LSF utilizing an inappropriate manner, and calculated the images as above. This time, the computed images did not agree with the measured ones. The normalized SDs were 6.0% or more (ranging from 6.0% to 13.8%), indicating the inaccuracy of the PSF and LSE We could verify LSFs and PSFs for three types of reconstruction kernels, and demonstrated differences between modulation transfer Functions (MTFs) derived from validated LSFs and inaccurate LSFs. Our technique requires a simple phantom that is suitable for clinical scanning, and does not require a particular phantom containing some metals or specific fine structures, as required in methods previously used for measurements of spatial resolution. Therefore, the scanned image of the phantom will be reliable and of good quality, and this is used directly as a confident reference image for the verification. When one obtains LSF, PSF or MTF values, verification using our method is recommended. Further, when another method for the measurement of LSF and PSF is developed, it could be validated using our technique, as illustrated in the method proposed by Boone [Med. Phys. 28, 356-360 (2001)] and used in this paper.

M Tanaka - One of the best experts on this subject based on the ideXlab platform.

  • conjugate gradient method applied to inverse scattering problem
    IEEE Transactions on Antennas and Propagation, 1995
    Co-Authors: H Harada, David Wall, Takashi Takenaka, M Tanaka
    Abstract:

    A new reconstruction algorithm for diffraction tomography is presented. The algorithm is based on the minimization of a Functional which is defined as the norm of the discrepancy between the measured scattering amplitude and the calculated one for an estimated Object Function. By using the conjugate gradient method to minimize the Functional, one can derive an iterative formula for getting the Object Function. Numerical results for some two-dimensional scatterers show that the algorithm is very effective in reconstructing refractive index distributions to which the first-order Born approximation can not be applied. In addition, the number of iterations is reduced by using a priori information about the outer boundary of the Objects. Furthermore, the method is not so sensitive to the presence of noise in the scattered field data. >

Franz Pfeiffer - One of the best experts on this subject based on the ideXlab platform.

  • 3D algebraic iterative reconstruction for cone-beam x-ray differential phase-contrast computed tomography.
    PloS one, 2015
    Co-Authors: Astrid Velroyen, Martin Bech, Ming Jiang, Franz Pfeiffer
    Abstract:

    Due to the potential of compact imaging systems with magnified spatial resolution and contrast, cone-beam x-ray differential phase-contrast computed tomography (DPC-CT) has attracted significant interest. The current proposed FDK reconstruction algorithm with the Hilbert imaginary filter will induce severe cone-beam artifacts when the cone-beam angle becomes large. In this paper, we propose an algebraic iterative reconstruction (AIR) method for cone-beam DPC-CT and report its experiment results. This approach considers the reconstruction process as the optimization of a discrete representation of the Object Function to satisfy a system of equations that describes the cone-beam DPC-CT imaging modality. Unlike the conventional iterative algorithms for absorption-based CT, it involves the derivative operation to the forward projections of the reconstructed intermediate image to take into account the differential nature of the DPC projections. This method is based on the algebraic reconstruction technique, reconstructs the image ray by ray, and is expected to provide better derivative estimates in iterations. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a mini-focus x-ray tube source. It is shown that the proposed method can reduce the cone-beam artifacts and performs better than FDK under large cone-beam angles. This algorithm is of interest for future cone-beam DPC-CT applications.