Multiple testing approaches for removing background noise from images

Images arising from low-intensity settings such as in X-ray astronomy and computed tomography scan often show a relatively weak but constant background noise across the frame. The background noise can result from various uncontrollable sources. In such a situation, it has been observed that the performance of a denoising algorithm can be improved considerably if an additional thresholding procedure is performed on the processed image to set low intensity values to zero. The threshold is typically chosen by an ad-hoc method, such as 5% of the maximum intensity. In this article, we formalize the choice of thresholding through a multiple testing approach. At each pixel, the null hypothesis that the underlying intensity parameter equals the intensity of the background noise is tested, with due consideration of the mulltiplicity factor. Pixels where the null hypothesis is not rejected, the estimated intensity will be set to zero, thus creating a sharper contrast with the background. The main difference of the present context with the usual multiple testing applications is that in our setup, the null value in the hypotheses is not known, and must be estimated from the data itself. We employ a Gaussian mixture to estimate the unknown common null value of the background intensity level. We discuss three approaches to solve the problem and compare them through simulation studies. The methods are applied on noisy X-ray images of a supernova remnant. John Thomas White SAS Institute Inc., Cary, NC, U.S.A. e-mail: [email protected] Subhashis Ghosal North Carolina State University, Raleigh, NC, U.S.A. e-mail: [email protected] ∗ Research is partially supported by NSF grant number DMS-1106570