A projection method of blind superresolution
Kazuki Nishi, Shigeru Ando · Optical Society of America Annual Meeting · 1992
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.