Abstract
The blind deconvolution is a method for estimating original signals from observed ones without any knowledge about the degradation process. But the conventional methods never extrapolate the spectra of the observed signals beyond a passband of the process. A blind superresolution method proposed by this paper can perform superresolution by assuming only a finite spatial extent of the input signals without knowing the frequency response, including an exact cutoff frequency, of a degradation process. The algorithm is as follows: Estimating roughly a cutoff frequency Ω, we obtain spectral relations X(ω) = H−1(ω)Y(ω)(Y(ω): known output spectra, H(ω): unknown frequency transmittance, X(ω): unknown input spectra) which can be rewritten as a single simultaneous equation with unknown variables H−1(ω)(− Ω < ω < Ω and X(ω) (−∞ < ω < ∞). Since this equation determines a convex subspace, we can solve the variables by introducing other convex conditions such as positivity of the input and / or a limited range [0,1] of the frequency transmittance. The roughly estimated Ω can be updated if necessary such that a proper amount of extraporation is achieved. We confirm the validity of this method through several computer simulations.
© 1992 Optical Society of America
PDF ArticleMore Like This
Ferréol Soulez and Michael Unser
JT3A.38 3D Image Acquisition and Display: Technology, Perception and Applications (3D) 2016
Miles N. Wernick, Caesar E. Ordonez, and Chin-Tu Chen
MF4 OSA Annual Meeting (FIO) 1992
Cameron J. Dasch
TuXX1 OSA Annual Meeting (FIO) 1992