We describe a method to estimate background noise in atom probe tomography (APT) mass spectra and to use this information to enhance both background correction and quantification. Our approach is mathematically general in form for any detector exhibiting Poisson noise with a fixed data acquisition time window, at voltages varying through the experiment. We show that this accurately estimates the background observed in real experiments. The method requires, as a minimum, the z-coordinate and mass-to-charge-state data as input and can be applied retrospectively. Further improvements are obtained with additional information such as acquisition voltage. Using this method allows for improved estimation of variance in the background, and more robust quantification, with quantified count limits at parts-per-million concentrations. To demonstrate applications, we show a simple peak detection implementation, which quantitatively suppresses false positives arising from random noise sources. We additionally quantify the detectability of 121-Sb in a standardized-doped Si microtip as (1.5 × 10−5, 3.8 × 10−5) atomic fraction, α = 0.95. This technique is applicable to all modes of APT data acquisition and is highly general in nature, ultimately allowing for improvements in analyzing low ionic count species in datasets.

A new algorithm for the removal of additive uncorrelated Gaussian noise from a digital image is presented. The algorithm is based on a data driven methodology for the adaptive thresholding of wavelet coefficients. This methodology is derived from higher order statistics of the residual image, and requires no a priori estimate of the level of noise contamination of an image.

We propose a new paradigm for no-reference image quality assessment (IQA) exploiting neurological and psychophysical properties of the human visual system (HVS)1. Physiological and psychological evidences exist that HVS has different behavioral patterns under low and high noise/artifact levels. In this paper, we propose a dual-model approach for blind IQA under near-threshold and suprathreshold noise conditions. The underlying assumption for the proposed dual-model approach is that for images with low-level near-threshold noise, HVS tries to gauge the strength of the noise, so image quality can be well approximated via measuring strength of the noise. On the other hand, for images with structures overwhelmed by high-level suprathreshold noise, perceptual quality assessment relies on a cognitive model and the HVS tries to recover meaningful contents from the noisy pixels using past experiences and prior knowledge encoded into an internal generative model of the brain. And image quality is therefore closely related to the agreement between the noisy observation and the internal generative model explainable part of the image. Specifically, under near-threshold noise condition, a noise level estimation algorithm using natural image statistics is used, while under suprathreshold condition, an active inference model based on the free-energy principle is adopted. The near- and suprathreshold models can be seamlessly integrated through a mathematical transformation between estimates from both models. The proposed dual-model algorithm has been tested on additive Gaussian noise contaminated images. Experimental results and comparative studies suggest that although being a no-reference approach, the proposed algorithm has prediction accuracy comparable with some of the best full-reference IQA methods. The dual-model perspective of IQA presented in this paper is expected to facilitate future research in the field of visual perceptual modeling.

The goal of this paper is to take steps towards estimating the frequency of terrestrial planets in the habitable zones of their host stars, using planet counts from the Kepler mission. The method is to assume that an analytical form for the underlying distribution function, numerically simulate the observing procedure, compare the simulated and real observations, and iterate the model parameters to achieve convergence in the sense of least-squares. The underlying distribution can then be extrapolated to a region of interest, here the terrestrial habitable-zone range. In this regime (small radii, long periods), the instrument noise makes such detections essentially impossible below a fairly sharply defined threshold signal level. This threshold can be estimated from the existing data. By taking this cutoff into account, the distribution of planets, as a function of radius and period, can be estimated with minimal bias. Extending this distribution to terrestrial planets in habitable-zone orbits can yield an estimate of eta-sub-Earth.