Cleaning radio interferometric images using a spherical wavelet decomposition

TL;DR

This paper introduces a spherical wavelet-based method for radio interferometric image cleaning that improves accuracy and efficiency by directly generating model visibilities from wavelet coefficients, reducing computation time.

Contribution

The authors develop a prototype imager that uses spherical wavelet decomposition to efficiently generate model visibilities directly from clean components.

Findings

Execution time scales with wavelet resolution as O(1.07^J).

Time scales linearly with the number of clean components, N_C.

Wavelet sparsity reduces processing of zero coefficients.

Abstract

The deconvolution, or cleaning, of radio interferometric images often involves computing model visibilities from a list of clean components, in order that the contribution from the model can be subtracted from the observed visibilities. This step is normally performed using a forward fast Fourier transform (FFT), followed by a 'degridding' step that interpolates over the uv plane to construct the model visibilities. An alternative approach is to calculate the model visibilities directly by summing over all the members of the clean component list, which is a more accurate method that can also be much slower. However, if the clean components are used to construct a model image on the surface of the celestial sphere then the model visibilities can be generated directly from the wavelet coefficients, and the sparsity of the model means that most of these coefficients are zero, and can be ignored. We have constructed a prototype imager that uses a spherical-wavelet representation of the model image to generate model visibilities during each major cycle, and find empirically that the execution time scales with the wavelet resolution level, J, as O(1.07 J), and with the number of distinct clean components, N_C, as O(N_C). The prototype organises the wavelet coefficients into a tree structure, and does not store or process the zero wavelet coefficients.