2014/05/06 by Dan Cheng, Cheng, Dan, Armin Schwartzman +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cell Image Analysis Techniques #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1405.1400
openalex publication_date 2014/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A topological multiple testing scheme is presented for detecting peaks in images under stationary ergodic Gaussian noise, where tests are performed at local maxima of the smoothed observed signals. The procedure generalizes the one-dimensional scheme of Schwartzman et al. (2011) to Euclidean domains of arbitrary dimension. Two methods are developed according to two different ways of computing p-values: (i) using the exact distribution of the height of local maxima (Cheng and Schwartzman, 2014), available explicitly when the noise field is isotropic; (ii) using an approximation to the overshoot distribution of local maxima above a pre-threshold (Cheng and Schwartzman, 2014), applicable when the exact distribution is unknown, such as when the stationary noise field is non-isotropic. The algorithms, combined with the Benjamini-Hochberg procedure for thresholding p-values, provide asymptotic strong control of the False Discovery Rate (FDR) and power consistency, with specific rates, as the search space and signal strength get large. The optimal smoothing bandwidth and optimal pre-threshold are obtained to achieve maximum power. Simulations show that FDR levels are maintained in non-asymptotic conditions. The methods are illustrated in a nanoscopy image analysis problem of detecting fluorescent molecules against the image background.