There are a number of ways to test for the absence/presence of a spatial signal in a completely observed fine-resolution image. One of these is a powerful nonparametric procedure called enhanced false discovery rate (EFDR). A drawback of EFDR is that it requires the data to be defined on regular pixels in a rectangular spatial domain. Here, we develop an EFDR procedure for possibly incomplete data defined on irregular small areas. Motivated by statistical learning, we use conditional simulation (CS) to condition on the available data and simulate the full rectangular image at its finest resolution many times (M, say). EFDR is then applied to each of these simulations resulting in M estimates of the signal and M statistically dependent p-values. Averaging over these estimates yields a single, combined estimate of a possible signal, but inference is needed to determine whether there really is a signal present. We test the original null hypothesis of no signal by combining the (Formula pr