Miscellaneous



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Research

Compressive Sensing (CS) has shown us that it is very much possible to accurately reconstruct certain compressible signals from relatively few linear measurements, for example by solving nonsmooth convex optimization problems.

In fact our research group has done quite a bit of investigation in this area. My focus for the time being is based on the paper by J. Yang, Y. Zhang, and W. Yin., which proposes a simple and fast algorithm for signal reconstruction from partial Fourier data. Their algorithm minimizes the sum of three terms corresponding to total variation, L1-norm regularization and least squares data fitting.

In particular, I am working on the design and implementation of the advanced algorithms specifically for computation on NVIDIA GPUs. Thanks to the generosity and support of NVIDIA through their Professor Partnership Program we have been able to build our own workstation. Our machine is a Lenovo Thinkstation D20 with 2 Quad-Core Xeon processors and 10GB of memory, housing one of NVIDIA's workhorses the Telsa C1060 GPU.

Since building our machine in early December we have started rolling out with new projects and experiments that look very promising. As a quick example, below we see a set of images that have been reconstructed using only 22% of the full measurements. From simple inspection, we see that our reconstruction (using RecPF/gRecPF) is better than that of state-of-the-art methods used today, such as back projection.



In the figure above we have (a) original image and two recontstructions: (b) our reconstructed image using 22% of the full measurements and (c) using back projection.

Numerical simulations on recovering magnetic resonance images (MRI) have indicated that our proposed algorithm is highly efficient, stable and robust. Below I have some results which demonstrate the speed up that is gained from a very naive implementation using Matlab/ Jacket we see about 5x speed up compared to that of the CPU algorighthm running on the D20 machine. Further speedup is expected for a C-based implementation of our algorithm on the Tesla card.

In this first figure we see the comparison of RecPF vs. gRecPF, this plot shows 50 separate runs and their respective times in seconds we can observe that gRecPF is faster on every run.



In fact we see that on average gRecPF keeps modestly faster times that RecPF. In the figure below, we have 25 separte trials each of which consist of the average time for 50 runs.




A remark should be made about the computer system that is being used in these experiments. Our CPU algorithm is taking advantage of all 8 cores, so we would get more speed up when compared to a traditional workstations.




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