CLEAN (algorithm)

CLEAN is a deconvolution algorithm widely used in radio astronomy and image processing to mitigate the effects of a "dirty beam" or point spread function (PSF). The dirty beam arises from incomplete sampling of the Fourier transform of the sky brightness, resulting in sidelobes and artifacts in the reconstructed image. CLEAN aims to identify and remove the contributions of these point sources, effectively cleaning the image.

The algorithm operates iteratively, typically in the image domain. It begins by identifying the brightest pixel in the "dirty image," which is the image obtained directly from the Fourier transform of the observed visibilities. This brightest pixel is assumed to represent the location of a true point source in the sky.

A fraction of the flux density of this brightest pixel, known as the "loop gain" or "gain factor," is then subtracted from the dirty image. Simultaneously, a scaled and shifted version of the dirty beam is subtracted from the dirty image, centered on the location of the identified point source. The scaling factor is determined by the loop gain multiplied by the flux density of the identified point source.

This process of identifying the brightest pixel, subtracting a fraction of its flux, and subtracting a scaled dirty beam is repeated iteratively. The algorithm continues until a stopping criterion is met, such as reaching a specified residual flux level or a maximum number of iterations.

The locations and flux densities of the identified point sources are stored in a "CLEAN component" model, often referred to as the "CLEAN model." This model represents the reconstructed image as a collection of point sources.

To obtain the final CLEANed image, the CLEAN model is typically convolved with a "clean beam," which is a smoother, Gaussian-like function that replaces the dirty beam. The residual image (the dirty image after all subtractions) is often added back to the convolved CLEAN model to account for any extended emission that may not have been adequately represented by the point source model.

Variants of the CLEAN algorithm exist, including Hogbom CLEAN, Clark CLEAN, and multi-scale CLEAN, each with its own approach to identifying and subtracting components. These variations often address limitations of the original algorithm, such as its performance in the presence of extended emission or its susceptibility to noise. The choice of CLEAN variant depends on the specific characteristics of the data and the desired outcome.