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Register a new userFundamental Limitations of Pixel Based Image Deconvolution in Radio Astronomy
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Added by
Panagiotis Labropoulos
Publication date
2010
fields
Physics
and research's language is
English
Authors
Sarod Yatawatta
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Deconvolution is essential for radio interferometric imaging to produce scientific quality data because of finite sampling in the Fourier plane. Most deconvolution algorithms are based on CLEAN which uses a grid of image pixels, or clean components. A critical matter in this process is the selection of pixel size for optimal results in deconvolution. As a rule of thumb, the pixel size is chosen smaller than the resolution dictated by the interferometer. For images consisting of unresolved (or point like) sources, this approach yields optimal results. However, for sources that are not point like, in particular for partially resolved sources, the selection of right pixel size is still an open issue. In this paper, we investigate the limitations of pixelization in deconvolving extended sources. In particular, we pursue the usage of orthonormal basis functions to model extended sources yielding better results than by using clean components.
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Compressive sampling is a new paradigm for sampling, based on sparseness of signals or signal representations. It is much less restrictive than Nyquist-Shannon sampling theory and thus explains and systematises the widespread experience that methods such as the Hogbom CLEAN can violate the Nyquist-Shannon sampling requirements. In this paper, a CS-based deconvolution method for extended sources is introduced. This method can reconstruct both point sources and extended sources (using the isotropic undecimated wavelet transform as a basis function for the reconstruction step). We compare this CS-based deconvolution method with two CLEAN-based deconvolution methods: the Hogbom CLEAN and the multiscale CLEAN. This new method shows the best performance in deconvolving extended sources for both uniform and natural weighting of the sampled visibilities. Both visual and numerical results of the comparison are provided.
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of points. The ensuing deconvolution problem has been solved in many ways, mainly by algorithms based on CLEAN. However, such algorithms that use image pixels as basis functions have inherent limitations and by using an orthonormal basis that span the whole image, we can overcome them. The construction of such an orthonormal basis involves fine tuning of many free parameters that define the basis functions. The optimal basis for a given problem (or a given extended source) is not guaranteed. In this paper, we discuss the use of generalized prolate spheroidal wave functions as a basis. Given the geometry (or the region of interest) of an extended source and the sampling points on the visibility plane, we can construct the optimal basis to model the source. Not only does this gives us the minimum number of basis functions required but also the artifacts outside the region of interest are minimized.
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