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High-resolution astronomical images can be reconstructed from several blurred and noisy low-resolution images using a computational process known as superresolution reconstruction. Superresolution reconstruction is closely related to image deconvolution, except that the low-resolution images are not registered and their relative translations and rotations must be estimated in the process. The novelty of our approach to the superresolution problem is the use of wavelets and related multiresolution methods within an expectation-maximization reconstruction process to improve the accuracy and visual quality of the reconstructed image. Simulations demonstrate the effectiveness of the proposed method, including its ability to distinguish between tightly grouped stars with a small set of observations.
Many of the image reconstruction algorithms used for radio astronomical observations are two or more decades old. What in 1983 took a few hours of a million dollar machine can now be done on a thousand dollar machine in a few seconds. Data rates are increasing, of course, and the expectations for the sophistication of processing have sky-rocketed. However, there remains the point that our wonderful new telescopes are not well served by the aging image reconstruction methodology. I will discuss some of the current challenges and how they might be addressed, drawing particularly upon the considerable advances in other imaging modalities.
Aperture synthesis radio telescopes measure the Fourier transform of the sky brightness distribution. However the Point Spread Function (PSF) of such telescopes has significant and widespread side-lobes. Raw images (also called 'dirty image') made using such telescopes therefore need to be deconvolved.
The problem of deconvolution can be thought of as a search algorithm for a function P(x) in the image space which, when passed through the telescope measurement equation, fits the observed data. Most algorithms in use now, gain in speed by setting P(x) to a delta function at the location of each pixel in the image (zero correlation scale). The convolution of the PSF with P(x), which is the dominant cost in a search algorithm, in this case reduces to a shift-and-scale operation. Such algorithms however search only for the amplitude of each pixel in the image and are insensitive to finite correlation lengths in the image. These algorithms are therefore not optimal for extended emission (emission at a number of spatial scales). They use more parameters to represent an extended source than is necessary, resulting in deconvolution errors. For example, ideally a two dimensional Gaussian source can be represented by 6 parameters (the amplitude, variance, position angle and location of the Gaussian) rather than with one parameter per pixel (the amplitude for each pixel). This results in breaking-up of the source or striping. With the increase in telescope sensitivity, such errors can limit the achievable dynamic range in the images.
In this paper we present an iterative scale sensitive deconvolution algorithm for radio interferometric imaging, which attempts to minimize the degrees of freedom used to represent the signal (spatially correlated pixels). We demonstrate that the algorithm is indeed sensitive to the local scale in the image. Performance issues and comparisons of the results with other successful deconvolution algorithms will also be discussed.
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