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. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

In Vivo Three-Dimensional Raster Scan Optoacoustic Mesoscopy Using Frequency Domain Inversion

“…The algorithm exploits the fast computational speed of FFT to reconstruct B-scans in fractions of a second to afford 3D images immediately after acquisition. Reconstruction speeds have been previously accelerated using standard frequency domain reconstruction with experimental optoacoustic data, with a 53 s-reconstruction time for a data size of 200 x 200 x 100 voxels in Fourier domain, compared to nearly 3 hours in time-domain based reconstruction for the same data set 27 , representing a 200-fold faster reconstruction. Recently, Fourier reconstruction times of 0.25 s were reported for B scans with 600 x 751 pixels 44 and of 0.7 s for multi-layer volumetric reconstruction of a 40 x 40 x 2000 voxel-data set 45 .…”

“…Numerical errors during the interpolation step have been reduced by employing a Sinc interpolation function, yet this remains computationally expensive 53 . Alternatively, non-equispaced grid sampling has been implemented to avoid the interpolation step in Fourier domain 27 ; however, this results in a significant increase in computational complexity. In this work, we used a cubic spline interpolation as a compromise between quality and computational cost.…”

“…However, frequency domain inversions have not been widely considered in optoacoustic imaging, outside of a few demonstrations with simulated and ex vivo data [16][17][18][19] . These ex vivo preliminary studies have been followed by investigations on interpolation schemes for data conversion from a non-uniform to a uniform sampling grids, or on applications of non-uniform Fast Fourier Transform and zero-padding approaches to reduce artefacts in the final reconstructed image [24][25][26][27] . Nevertheless, to the best of our knowledge, thealgorithm has never been applied to reconstruct in vivo optoacoustic data, has not been shown to yield the high image quality reached with time-domain inversions, nor has its performance been quantitatively compared in terms of speed and reconstruction quality with time-domain backprojection.…”

Accelerated high-resolution photoacoustic tomography via compressed sensing

“…The optimal choice for PAT applications is yet to be determined. For instance, [66] has shown that a non-uniform distribution of the sampling locations in single-point sub-sampling can be used to focus into a specific area (at the expense of the resolution elsewhere). A theoretical examination, e.g., through micro-local analysis [67], could help to gain new insights on this.…”

Towards an Improvement of Fourier Transform

“…It used in a wide range of applications, such as image filtering, image analysis, image reconstruction, and image compression. In the literature, several papers have described methods for approximating one-dimensional Non uniform Fast Fourier Transforms by interpolating an oversampled Fast Fourier transforms, start with [17] and including [18], [19], [20], [21], [22], [23], [24], [25], [26], [27]. In [28] the fundamentals of Fourier transform, Fourier series, discrete Fourier transform and fast Fourier transform with simple examples and review of Fourier transform to supply a clear understanding of its applications in power quality issues.…”