Edward Walsh

• 
  Incorporation of Prior Fourier Domain Edge Information in the L1 Minimization Problem for Compressed Sensing
  Edward Walsh

  In applications such as functional Magnetic Resonance Imaging (fMRI), full, uniformly-sampled Cartesian Fourier (frequency space) measurements are acquired. In order to reduce scan time and increase temporal resolution for fMRI studies, one would like to accurately reconstruct these images from a highly reduced set of Fourier measurements. Compressed Sensing (CS) has given rise to techniques that can provide exact and stable recovery of sparse images from a relatively small set of Fourier measurements. For example, if the images are sparse with respect to their gradient, total-variation minimization techniques can be used to recover those images from a highly incomplete set of Fourier measurements. In this discussion, we propose a new algorithm to further reduce the number of Fourier measurements required for exact or stable recovery by utilizing prior edge information from a high resolution reference image. This reference image (routinely acquired during fMRI studies for anatomic landmarking of activations), or more precisely, the fully sampled Fourier measurements of this reference image, can also be used to provide approximate edge information. By combining this edge information with CS techniques for sparse gradient images, numerical experiments show that we can further reduce the number of Fourier measurements required for exact or stable recovery by a factor of 1.6 3, compared with CS techniques alone, without edge information.