A sensitivity measure for image reconstruction from irregular 2-D DTFT samples

The problem of reconstructing an image from irregular samples of its 2-D DTFT 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, sufficient conditions for the uniqueness and conditioning of the reconstruction problem are both not apparent. The Good-Thomas FFT is used to unwrap the 2-D problem into a 1-D problem, from which uniqueness results and, more importantly, insights into the problem conditioning are available. We propose the variance of distances between adjacent frequency locations as a sensitivity measure, which aids in determining a well-conditioned configuration of frequency values. The sensitivity measure is analyzed on its accuracy of estimating the conditioning and on its computational speed. The image is then reconstructed by solving the problem using the conjugate gradient method.