An efficient technique for the detection of a Bernoulli-Gaussian process is proposed in this paper. A new property of the well-known Minimum Variance Deconvolution Filter is derived first, which can feed the detection procedure with reliable estimates of the input process. Based on this derivation, a detection procedure is built, which mainly uses simple detectors, reducing the contribution of more complex ones. The resulting detection procedure performs well and has a very low computational load. Examples are given, which illustrate the theoretical results.