2023/11/06 by Mathias Hockmann, Hockmann, Mathias
Engineering · Mathematics · #42B10 (Secondary) #94A16 (Primary) 62F12 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Integrated Circuits and Semiconductor Failure Analysis #Numerical Analysis (math.NA) #Photoacoustic and Ultrasonic Imaging #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2311.03178
openalex publication_date 2023/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Already since the work by Abbe and Rayleigh the difficulty of super resolution where one wants to recover a collection of point sources from low-resolved microscopy measurements is thought to be dependent on whether the distance between the sources is below or above a certain resolution or diffraction limit. Even though there has been a number of approaches to define this limit more rigorously, there is still a gap between the situation where the task is known to be hard and scenarios where the task is provably simpler. For instance, an interesting approach for the univariate case using the size of the Cramér-Rao lower bound was introduced in a recent work by Ferreira Da Costa and Mitra. In this paper, we prove their conjecture on the transition point between good and worse tractability of super resolution and extend it to higher dimensions. Specifically, the bivariate statistical analysis allows to link the findings by the Cramér-Rao lower bound to the classical Rayleigh limit.