Nonequispaced grid sampling in photoacoustics with a nonuniform fast Fourier transform

Abstract. To obtain the initial pressure from the collected data on a planar sensor arrangement in photoacoustic tomography, there exists an exact analytic frequency-domain reconstruction formula. An efficient realization of this formula needs to cope with the evaluation of the data’s Fourier transform on a nonequispaced mesh. We use the nonuniform fast Fourier transform to handle this issue and show its feasibility in three-dimensional experiments with real and synthetic data. This is done in comparison to the standard approach that uses linear, polynomial, or nearest neighbor interpolation. Moreover, we investigate the effect and the utility of flexible sensor location to make optimal use of a limited number of sensor points. The computational realization is accomplished by the use of a multidimensional nonuniform fast Fourier algorithm, where nonuniform data sampling is performed both in frequency and spatial domain. Examples with synthetic and real data show that both approaches improve image quality.

[1]  P.C. Beard.  Two-dimensional ultrasound receive array using an angle-tuned Fabry-Perot polymer film sensor for transducer field characterization and transmission ultrasound imaging , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[2]  Stephen J. Norton,et al.  Ultrasonic Reflectivity Imaging in Three Dimensions: Exact Inverse Scattering Solutions for Plane, Cylindrical, and Spherical Apertures , 1981, IEEE Transactions on Biomedical Engineering.

[3]  Lihong V Wang,et al.  Universal back-projection algorithm for photoacoustic computed tomography , 2005, SPIE BiOS.

[4]  Xiaojun Liu,et al.  Reconstruction of high quality photoacoustic tomography with a limited-view scanning. , 2010, Optics express.

[5]  Martin Frenz,et al.  Fourier reconstruction in optoacoustic imaging using truncated regularized inverse k-space interpolation , 2007 .

[6]  Paul C. Beard,et al.  Photoacoustic tomography with a limited-aperture planar sensor and a reverberant cavity , 2007 .

[7]  P. Kuchment,et al.  Mathematics of thermoacoustic tomography , 2007, European Journal of Applied Mathematics.

[8]  B T Cox,et al.  k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields. , 2010, Journal of biomedical optics.

[9]  Viktor Hamburger,et al.  A series of normal stages in the development of the chick embryo , 1992, Journal of morphology.

[10]  Jan Laufer,et al.  Backward-mode multiwavelength photoacoustic scanner using a planar Fabry-Perot polymer film ultrasound sensor for high-resolution three-dimensional imaging of biological tissues. , 2008, Applied optics.

[11]  L. Hörmander.  The analysis of linear partial differential operators , 1990 .

[12]  A.,et al.  FAST FOURIER TRANSFORMS FOR NONEQUISPACED DATA * , .

[13]  Emil Y. Sidky,et al.  Limited data image reconstruction in optoacoustic tomography by constrained total variation minimization , 2011, BiOS.

[14]  Minghua Xu,et al.  Analytic explanation of spatial resolution related to bandwidth and detector aperture size in thermoacoustic or photoacoustic reconstruction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  G. Beylkin.  On the Fast Fourier Transform of Functions with Singularities , 1995 .

[16]  E. T. Quinto,et al.  Local Tomographic Methods in Sonar , 2000 .

[17]  Eric Todd Quinto,et al.  Artifacts in Incomplete Data Tomography with Applications to Photoacoustic Tomography and Sonar , 2014, SIAM J. Appl. Math..

[18]  O. Scherzer.  Handbook of mathematical methods in imaging , 2011 .

[19]  Jin Zhang,et al.  Improving limited-view reconstruction in photoacoustic tomography by incorporating a priori boundary information , 2008, SPIE BiOS.

[20]  Yuan Xu,et al.  Exact frequency-domain reconstruction for thermoacoustic tomography. I. Planar geometry , 2002, IEEE Transactions on Medical Imaging.

[21]  Minghua Xu,et al.  Time-domain reconstruction for thermoacoustic tomography in a spherical geometry , 2002, IEEE Transactions on Medical Imaging.

[22]  Otmar Scherzer,et al.  On the use of frequency-domain reconstruction algorithms for photoacoustic imaging. , 2011, Journal of biomedical optics.

[23]  Otmar Scherzer,et al.  A Reconstruction Algorithm for Photoacoustic Imaging Based on the Nonuniform FFT , 2009, IEEE Transactions on Medical Imaging.

[24]  Karsten Fourmont.  Non-Equispaced Fast Fourier Transforms with Applications to Tomography , 2003 .

[25]  Edward Z. Zhang,et al.  Dual modality optical coherence and whole-body photoacoustic tomography imaging of chick embryos in multiple development stages. , 2014, Biomedical optics express.

[26]  Lihong V. Wang.  Photoacoustic imaging and spectroscopy , 2009 .

[27]  P. Beard.  Biomedical photoacoustic imaging , 2011, Interface Focus.

[28]  P. Burgholzer,et al.  Thermoacoustic tomography with integrating area and line detectors , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[29]  Lihong V. Wang,et al.  Photoacoustic imaging in biomedicine , 2006 .

[30]  H. Weber,et al.  Temporal backward projection of optoacoustic pressure transients using fourier transform methods. , 2001, Physics in medicine and biology.

[31]  V. Hamburger,et al.  A series of normal stages in the development of the chick embryo. 1951. , 2012, Developmental dynamics : an official publication of the American Association of Anatomists.

[32]  Lihong V. Wang,et al.  Reconstructions in limited-view thermoacoustic tomography. , 2004, Medical physics.

[33]  F. Perennes,et al.  Transduction mechanisms of the Fabry-Perot polymer film sensing concept for wideband ultrasound detection , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[34]  B.T. Cox,et al.  The frequency-dependent directivity of a planar fabry-perot polymer film ultrasound sensor , 2007, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[35]  Chao Tao,et al.  Influence of limited-view scanning on depth imaging of photoacoustic tomography , 2012 .

[36]  Huabei Jiang,et al.  4-D Photoacoustic Tomography , 2013, Scientific Reports.

[37]  I T Young,et al.  A comparison of different focus functions for use in autofocus algorithms. , 1985, Cytometry.

[38]  Gabriele Steidl,et al.  A note on fast Fourier transforms for nonequispaced grids , 1998, Adv. Comput. Math..