Frequency extrapolation by nonconvex compressive sensing
- Los Alamos National Laboratory
- UNIV OF CHICAGO
Tomographic imaging modalities sample subjects with a discrete, finite set of measurements, while the underlying object function is continuous. Because of this, inversion of the imaging model, even under ideal conditions, necessarily entails approximation. The error incurred by this approximation can be important when there is rapid variation in the object function or when the objects of interest are small. In this work, we investigate this issue with the Fourier transform (FT), which can be taken as the imaging model for magnetic resonance imaging (MRl) or some forms of wave imaging. Compressive sensing has been successful for inverting this data model when only a sparse set of samples are available. We apply the compressive sensing principle to a somewhat related problem of frequency extrapolation, where the object function is represented by a super-resolution grid with many more pixels than FT measurements. The image on the super-resolution grid is obtained through nonconvex minimization. The method fully utilizes the available FT samples, while controlling aliasing and ringing. The algorithm is demonstrated with continuous FT samples of the Shepp-Logan phantom with additional small, high-contrast objects.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1043540
- Report Number(s):
- LA-UR-10-08028; LA-UR-10-8028; TRN: US1203259
- Country of Publication:
- United States
- Language:
- English
Similar Records
SU-C-207-05: A Comparative Study of Noise-Reduction Algorithms for Low-Dose Cone-Beam Computed Tomography
SU-E-I-45: Reconstruction of CT Images From Sparsely-Sampled Data Using the Logarithmic Barrier Method