Blur identification using a spectral inertia tensor and spectral zeros

Restoration of global motion blur requires the blur parameters (direction and extent) to be known. To this end, spectral approaches based on finding zeros in power spectrum or bispectrum estimates are widely reported. In noisy conditions, however, finding spectral zeros is hardly possible as they are covered by the noise power spectrum. In this paper, we separate the determination of blur direction and blur extent. The advantage is that, once the blur direction is known, it suffices to estimate a slice of the power spectrum or bispectrum in this direction. These one-dimensional estimates are considerably less sensitive to noise than higher-dimensional ones. The blur direction is determined by an inertia-like tensor, which assesses spectral anisotropy caused by the motion blur. This approach is applied to noisy low-dose X-ray images, which are particularly hard to process since the blur degrades the signal but not the relatively strong noise.