A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT.

Department of Mathematics, University Innsbruck, 6020 Innsbruck, Austria.
IEEE transactions on medical imaging (Impact Factor: 3.54). 11/2009; 28(11):1727-35. DOI: 10.1109/TMI.2009.2022623
Source: PubMed

ABSTRACT Fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in reconstructed images. We propose a novel reconstruction algorithm that applies the one-dimensional nonuniform fast Fourier transform to photoacoustic imaging. It is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of Fourier reconstruction.

1 Bookmark
  • [Show abstract] [Hide abstract]
    ABSTRACT: Recovery of image data from photoacoustic measurements asks for the inversion of the spherical mean value operator. In contrast to direct inversion methods for specific geometries, we consider a semismooth Newton scheme to solve a total variation regularized least squares problem. During the iteration, each matrix vector multiplication is realized in an efficient way using a recently proposed spectral discretization of the spherical mean value operator. All theoretical results are illustrated by numerical experiments.
    Advances in Computational Mathematics 01/2014; DOI:10.1007/s10444-014-9364-1 · 1.56 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The spherical mean Radon transform maps a function in an $n$-dimensional space to its integrals (or averages) over spherical surfaces. Recovering a function from its spherical mean Radon transform with centers of spheres of integration restricted to some hypersurface is at the heart of several modern imaging technologies, including SONAR, ultrasound imaging, and photo- and thermoacoustic tomography. In this paper we study the inversion of the spherical mean Radon transform with centers restricted to a cylindrical domain of the form $B \times \mathbb{R}^{n_2}$, where $B$ is any bounded domain in $\mathbb{R}^{n_1}$. As our main results we derive explicit inversion formulas of the backprojection type for that transform. For that purpose we show that the spherical mean Radon transform with centers on a cylindrical surface can be decomposed into two lower dimensional spherical mean Radon transforms. For a cylindrical center set in $\mathbb{R}^3$, we demonstrate that the derived inversion formulas can be implemented by filtered-backprojection type algorithms only requiring $\mathcal O(N^{4/3})$ floating point operations, where $N$ is the total number of unknowns to be recovered. We finally present some results of our numerical simulations performed in Matlab, showing that our implementations accurately recover a 3D image of millions of unknowns in a few minutes on an ordinary notebook.
  • Source
    [Show abstract] [Hide abstract]
    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 datas Fourier transform on a non-equispaced mesh. In this paper, we use the non-uniform fast Fourier transform to handle this issue and show its feasibility in 3D experiments. This is done in comparison to the standard approach that uses polynomial interpolation. Moreover, we investigate the effect and the utility of flexible sensor location on the quality of photoacoustic image reconstruction. The computational realization is accomplished by the use of a multi-dimensional non-uniform fast Fourier algorithm, where non-uniform data sampling is performed both in frequency and spatial domain. We show that with appropriate sampling the imaging quality can be significantly improved. Reconstructions with synthetic and real data show the superiority of this method.

Full-text (2 Sources)

Available from
May 22, 2014