Constrained image restoration for use in passive millimeter-wave imaging

Passive millimeter-wave imaging has excellent all weather capability but requires large apertures to give adequate spatial resolution. Linear restoration can enhance the resolution by a factor of two, while under favorable conditions non-linear restoration can enhance it by a factor of four. The amount of enhancement possible is generally limited by the amount of noise present in the original observed image. Preprocessing can reduce the effect of this noise and the image may be selectively restored. The high spatial frequency content of an image exists largely at edges and sharp features and these may be restored using non-linear restoration techniques. The smoother background between these features contains fewer high frequencies and needs less restoration. Adaptive non-linear restoration techniques have been investigated whereby the amount of restoration applied to an image is a function of the first and second derivative of the image intensity. In many non-linear restoration techniques the amount of high spatial frequency content introduced into the restored image is uncontrolled. This problem has been overcome through the use of the Lorentzian algorithm, which imposes a statistical constraint on the distribution of gradients within the restored image. Recently attempts have been made to explain why the distribution of gradients within an image is Lorentzian in terms of randomly distributed gradients of random size. Images are presented to demonstrate the effectiveness of these methods.