Interval estimate with probabilistic background constraints in deconvolution

We present in this article the use of probabilistic background constraints in astronomical image deconvolution to approach a solution as an interval estimate. We elaborate our objective—the interval estimate of the unknown object from observed data and our approach—Monte Carlo experiment and analysis of marginal distributions of image values. One-dimensional observation and deconvolution using the proposed approach are simulated. Confidence intervals revealing the uncertainties due to the background constraint are calculated and significance levels for sources retrieved from restored images are provided.