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1. Introduction

In this paper, we present a Maximum Entropy Method (MEM) algorithm that acts in both the spatial and spectral domains and we show first results of applying this algorithm to data obtained with the frequency-agile solar interferometer at Owens Valley Radio Observatory (OVRO). The data are taken at 45 frequencies in the range tex2html_wrap_inline1469 and measure the Fourier components of the brightness distribution, where each frequency measures a different spatial component. The measured Fourier data are used to reconstruct an image in the spatial domain, as a function of position and frequency, to provide brightness temperature spectra at each point which can be analyzed and interpreted in terms of physical parameters such as coronal magnetic field strength and electron temperature. The number of observed Fourier components can be quite large depending on the array and the length of the observing time, but not all Fourier components will be measured which can lead to ambiguities in interpreting the data. Thus, one has to address the problem of missing information or incomplete (u v) coverage. Imaging algorithms, such as CLEAN or the standard MEM algorithm, fill in the unmeasured Fourier components by using a priori information about what the radio source is expected to look like. However, the existing algorithms do not exploit the spatial information available at adjacent frequencies in the OVRO data. These algorithms treat each frequency separately which leads to a reconstructed image consisting of 45 independent spatial maps. We present an algorithm that obtains a global solution to the visibilities in both the spatial and spectral domains.

The spatial term in the traditional least-squares MEM maximizes a spatial entropy term tex2html_wrap_inline1473, where T is the map temperature as a function of spatial position and frequency, subject to the data constraints. This ensures that the resulting image is spatially smooth and that it is positive everywhere. In our modified algorithm, we include an analogous spectral entropy term defined as tex2html_wrap_inline1477, with tex2html_wrap_inline1479 where T' is the temperature interpolated from the two neighboring frequencies at the same spatial position. This term ensures that a spectrum at a given spatial position changes only smoothly with frequency. In this paper, the algorithm is described in one spectral and two spatial dimensions, but is applied only for the case of one spatial and one spectral dimension for several reasons: (1) To simplify the development process; (2) To speed up exploration of the relevant parameter space; (3) To make presentation of the results simpler (we display the one spectral and one spatial dimension as 2-d contour plots, whereas two spatial and one spectral dimensions would require presentation of a data-cube). A subsequent paper is planned to describe the full algorithm as applied to one spectral and two spatial dimensions.

In Sect. 2, we describe the concept and its current implementation. In Sect. 3, we apply our 1-d algorithm to observations taken with the OVRO frequency-agile interferometer of active region AR 5417 near the solar limb on March 20, 1989 (vernal equinox) using the two 27-m antennas and the 40-m antenna arranged in a linear east-west array. The geometry of an east-west array on this date gives strictly 1-d spatial resolution, and so gives a good match to the 1-d algorithm. We compare the result of our MEM algorithm with the source structure shown on 1-d OVRO maps obtained using the conventional CLEAN algorithm, and with a reconstruction using only the spatial MEM term of our algorithm. Then, we use the reconstructed image to calculate brightness temperature spectra and to derive physical parameters.


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Up: A spatial and

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