Reconstruction of speckled images using bispectra

Estimating alignment errors in sets of 2-D images

“…A special case of the three point function that is defined on a triplet of wavevectors such that the sum of the wavevectors vanishes is called the bispectrum. The latter has been useful in studying the reconstruction of images (Giannakis, 1989;Schulz and Snyder, 1992), especially from image invariants (Sadler and Giannakis, 1992;Wood, 1996), the reconstruction of speckled images in speckle interferometry (Jin et al, 1992), the causes of the 100 kyr glacial cycle (Muller and MacDonald, 1997) and the imaging through atmospheric turbulence (Ayers et al, 1988).…”

Multiframe Astronomical Image Registration Based on Block Homography Estimation

“…By using spot inference, Ozkan et al [2] proposed a method to recover the extended spatial target phase spectra by using crossspectra; combining with the spot inference method, the extended astronomical image is restored. After that, Jin et al [3] proposed a method to restore the extended spatial target phase by using bispectra, and the bispectra method is spatially invariant compared with the crossspectra method. Ayers and Dainty [4] innovatively proposed an image restoration concept by using blind deconvolution algorithm in the spatial target observation field.…”

“…In particular, a boundary piecewise process is used to deal with the pixels on the image boundaries, as shown in Figure 3. Then, the conditional probability distribution model on the neighbor of each pixel is calculated, as Equation (3). Assume that each key point yields to Gaussian distribution on its neighbor.…”

Fractional bispectrum transform: definition and properties

“…The bispectrum is defined as the Fourier transform (FT) of the third order cumulant or moment of a stationary signal and can be used as a noise reduction technique in some circumstances [1,2]. The definition of bispectrum of a 'stationary signal' is given as both the FT of the moment [3] or the cumulant [4].…”