A few weeks ago, we published a <a title="blog entry" href="http://blog.accelereyes.com/blog/2011/05/05/speeding-up-compressed-sensing-algorithms/">blog entry</a> that demonstrated the ability of Jacket to speed up "compressive sensing", a technology that has wide applications in areas such as Image processing, reconstruction and spectroscopy. Here, we discuss the work of Nabor Reyna Jr. and Wotao Yin from Rice University using Jacket to speed up "compressive sensing" algorithms in reconstruction.

This work deals with reconstruction of signals using partial Fourier matrices (RecPF).  The major computational components of the algorithm involve shrinkage and FFTs.  Jacket is employed to accelerate this compute-heavy code, and the resultant version (gRecPF) was about <span style="color: #ff0000;">5x faster!</span>
<p style="padding-left: 30px;"><a href="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/gRecPF.jpg"><img class="size-medium wp-image-1468 aligncenter" title="gRecPF" src="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/gRecPF-300x242.jpg" alt="" width="300" height="242" /></a></p>
To reduce the cost involved in generating the random matrices involved in the above method, a second method (RecPC) that employed Circulant matrices in place of the Fourier matrices was developed. A Jacket version of the same was also implemented (gRecPC) and this led to a <span style="color: #ff0000;">3X speedup!</span>

<a href="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/gRecPC.png"><img class="size-medium wp-image-1472 aligncenter" title="gRecPC" src="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/gRecPC-300x213.png" alt="" width="300" height="213" /></a>

Here are some sample reconstructed images using  gRecPC

[caption id="attachment_1473" align="aligncenter" width="300" caption="MRI Image Reconstruction using 20% sample mask"]<a href="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/gRecPC_sample.png"><img class="size-medium wp-image-1473" title="gRecPC: MRI example" src="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/gRecPC_sample-300x144.png" alt="" width="300" height="144" /></a>[/caption]

[caption id="attachment_1474" align="aligncenter" width="300" caption="Reconstructed Image of Great Wall of China using 30% partial circulant samples"]<a href="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/thegreatwall_rcv.png"><img class="size-medium wp-image-1474" title="thegreatwall_rcv" src="http://blog.accelereyes.com/blog/wp-content/uploads/2011/07/thegreatwall_rcv-300x225.png" alt="" width="300" height="225" /></a>[/caption]

A more detailed summary of the work may be found <a title="here" href="http://www.caam.rice.edu/~optimization/L1/RecPF/">here</a> and <a title="here" href="http://www.caam.rice.edu/~optimization/L1/RecPC/">here</a>.  We thank Nabor Reyna and Wotao Yin from Rice University for exploring Jacket as a solution to important computational problems of today, and look forward to hearing more from them as they continue this line of research!

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