<img src="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/tomography_fig4.png" alt="" align="right" />In order to investigate changes of forest biomass, scientists use <a href="http://en.wikipedia.org/wiki/Tomography">microwave tomography</a> to image the vegetation. At the smallest scale, individual plants can be imaged to investigate branching and growth, but even <a href="http://en.wikipedia.org/wiki/Synthetic_aperture_radar">synthetic aperture radar</a> can reveal large-scale changes in regional ecology. To the right, you can see the experimental setup to image an individual plant.

<img src="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/tomography_fig7.png" alt="" align="right" />Filtered back-projection is at the core of all of these techniques: using the inverse <a href="http://en.wikipedia.org/wiki/Radon_transform">Radon transform</a> to reconstruct regular images from Fourier samples. Below you can see the final reconstructed image. Since these samples are often not on a uniform Cartesian grid, the <a href="http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/PIRODDI1/NUFT/NUFT.html">non-uniform</a> version of the FFT comes into play (NUFFT), and all of this requires some serious number crunching: bring in the GPU.

Based on their earlier experience using Jacket to <a href="http://blog.accelereyes.com/blog/2011/07/20/echo-generators/">prototype antenna arrays</a>, Drs. Capozzoli, Curcio, di Vico, and Liseno developed a parallel implementation of NUFFT suited for GPUs. Their work was published in <a href="http://www.jstage.jst.go.jp/article/transcom/E94.B/7/E94.B_2092/_article">IEICE Transactions on Communications</a>. As their paper details, NUFFT sampling and reconstruction rely heavily on <a href="http://wiki.accelereyes.com/wiki/index.php/Category:Interpolation">interpolation</a> and <a href="http://wiki.accelereyes.com/wiki/index.php/Category:Fourier_Transforms">FFT</a> -- two things that NVIDIA GPUs are <a href="http://www.accelereyes.com/products/benchmarks_jacket_fcns">great at</a>. Evaluating the performance of various sampling schemes and parallelization techniques, they report <span style="color: #ff0000;">speedups reaching 10x</span> as compared to an 8-core CPU.

Thanks to Drs. Capozzoli, Curcio, di Vico, and Liseno for once again sharing their work!