Iterative image reconstruction from the bispectrum

Abstract

We present iterative least-squares methods for reconstructing diffraction-limited images from the object bispectrum obtained by speckle masking (bispectral analysis) and from other Fourier data. The theory and first astronomical speckle masking applications are described. An approximation of the least-squares integral is derived which makes it possible to calculate easily thousands of iterations with images of 512x512 pixels. Various extensions of the basic method to the simultaneous treatment of many object pixels are dicussed. Finally, applications of modified versions of the method to the Knox-Thompson method, shearing interferometry, deconvolution of aberrated images, optical long-baseline interferometry, radio interferometry (especially, mm- and submm-interferometry) and other methods are discussed