Multiscale and multidirectional very long baseline interferometry imaging with CLEAN

Open Access

Algorithm 1

Wavelet CLEAN algorithm.

Require: Dirty Image: I^D

Require: Dirty Beam: B^D

Require: gain: g

Require: scale-widths for Wavelet-decomposition (DoB):

fitted to uυ-coverage

Define “clean” DWT by difference of Bessel functions with scales

Fit Gaussian functions to the central peaks of the Bessel functions, define a difference of Gaussians (DoG) dictionary by these fits:

. We note that this dictionary approximates the Bessel dictionary, but without the sidelobes.

Define “dirty” DWT by DoB with “dirty” scales

,^Where

Decompose dirty image by

Decompose dirty beam by

Decompose the scales of the dirty beam by

Find normalization constants:

Normalize beam and psf by

… for all i and j.

Find weights:

(these weights were proven to be optimal).

Initialize restoring image: M = 0,

while residual not noise-like do,

while number of maximal iterations not reached do,

Find Maximum of [w_j ·· abs(I_j)] searching over scales j and pixels k,

Store maximum

in list of components,

For every scale

Update dirty image/residual: I^D = I^D − B^D * M,

Reinitialize the decomposition:

optional: self-calibration,

optional: project solution to positive values.

Add residual image:

Ensure: M is approximation to true sky image.

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