If a spatial-domain function has a finite support, its Fourier transform is an entire function. The Taylor series expansion of an entire function converges at every finite point in the complex plane. The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood. Trying to obtain such an exact Taylor expansion is difficult. This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions. Computer simulations show that the proposed algorithm converges very slowly, indicating that the problem is too ill-posed to be practically solvable using available methods.
Keywords: Analytic continuation; Entire function; Image reconstruction; Iterative projections onto convex sets algorithm; Limited angle tomography.
© 2021. The Author(s).