  The fidelity of radio astronomical images is generally assessed by practical
experience, i.e. using rules of thumb, although some aspects and cases have
been treated rigorously. In this paper we present a mathematical framework
capable of describing the fundamental limits of radio astronomical imaging
problems. Although the data model assumes a single snapshot observation, i.e.
variations in time and frequency are not considered, this framework is
sufficiently general to allow extension to synthesis observations. Using tools
from statistical signal processing and linear algebra, we discuss the
tractability of the imaging and deconvolution problem, the redistribution of
noise in the map by the imaging and deconvolution process, the covariance of
the image values due to propagation of calibration errors and thermal noise and
the upper limit on the number of sources tractable by self calibration. The
combination of covariance of the image values and the number of tractable
sources determines the effective noise floor achievable in the imaging process.
The effective noise provides a better figure of merit than dynamic range since
it includes the spatial variations of the noise. Our results provide handles
for improving the imaging performance by design of the array.
