Abstract #2609

Empirical Investigation of the Gardner Transform as a Sparsifying Transform for the Analysis of a New Class of Signals Using Compressed Sensing

Jordan Woehr¹, Michael Smith¹,²

¹Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada; ²Radiology, University of Calgary, Calgary, Alberta, Canada

Compressed sensing (CS) applied to under-sampled <i>k</i>-space is used in magnetic resonance to decrease 2D and 3D imaging times while maintaining image resolution. We present the Gardner transform (GT) as a potential sparsifying transform for use with CS with under-sampled or truncated signals in a non-<i>k</i>-space 4^th dimension, e.g. time or frequency. New classes of signals can be sparsified with the GT such as sums of exponentials, Lorentzians, etc. We discuss the practical issues associated with GT-CS reconstruction of a simulated signal assumed to have two exponential components, MTT_GM and MTT_WM, and an ideal GT of two Dirac delta functions.