Location of Repository

Abstract — The problem of reconstructing an image from irregular frequency samples arises in synthetic aperture radar (SAR), magnetic resonance imaging (MRI), limited angle tomography, and 2-D filter design. Since there is no 2-D Lagrange interpolation formula, this problem is usually solved using an iterative algorithm, such as POCS (Projection Onto Convex Sets), or CG (Conjugate Gradient) applied to a linear system of equations with the image pixels as unknowns. However, these require many iterations, and each iteration requires a non-uniform forward 2-D Discrete Fourier Transform (DFT). We present a non-iterative algorithm for the reconstruction of an (M × M) image from a sufficient number of arbitrary samples of its (N × N) 2-D DFT, where N>> M. The algorithm requires only a single sparse (N × N) 2-D DFT, followed by two roughly (M × M) 2-D DFTs. Precomputation for a given configuration of irregular (N × N) 2-D DFT samples is also required. Small and large examples illustrate the algorithm

Topics:
2-rest

Year: 2009

OAI identifier:
oai:CiteSeerX.psu:10.1.1.135.6488

Provided by:
CiteSeerX

Download PDF:To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.