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Register a new userMatched filter in the low-number count Poisson noise regime: an efficient and effective implementation
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Roberto Vio
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The matched filter (MF) is widely used to detect signals hidden within the noise. If the noise is Gaussian, its performances are well-known and describable in an elegant analytical form. The treatment of non-Gaussian noises is often cumbersome as in most cases there is no analytical framework. This is true also for Poisson noise which, especially in the low-number count regime, presents the additional difficulty to be discrete. For this reason in the past methods have been proposed based on heuristic or semi-heuristic arguments. Recently, an analytical form of the MF has been introduced but the computation of the probability of false detection or false alarm (PFA) is based on numerical simulations. To overcome this inefficient and time consuming approach we propose here an effective method to compute the PFA based on the saddle point approximation (SA). We provide the theoretical framework and support our findings by means of numerical simulations. We discuss also the limitations of the MF in practical applications.
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Detection of templates (e.g., sources) embedded in low-number count Poisson noise is a common problem in astrophysics. Examples include source detection in X-ray images, gamma-rays, UV, neutrinos, and search for clusters of galaxies and stellar streams. However, the solutions in the X-ray-related literature are sub-optimal -- in some cases by considerable factors. Using the lemma of Neyman-Pearson we derive the optimal statistics for template detection in the presence of Poisson noise. We demonstrate that this method provides higher completeness, for a fixed false-alarm probability value, compared with filtering the image with the point-spread function (PSF). In turn, we find that filtering by the PSF is better than filtering the image using the Mexican-hat wavelet (used by wavedetect). For some background levels, our method improves the sensitivity of source detection by more than a factor of two over the popular Mexican-hat wavelet filtering. This filtering technique can also be used also for fast PSF photometry and flare detection, and it is efficient, as well as straight forward to implement. We provide an implementation in MATLAB.
Object detection is one of the most important areas in computer vision, which plays a key role in various practical scenarios. Due to limitation of hardware, it is often necessary to sacrifice accuracy to ensure the infer speed of the detector in practice. Therefore, the balance between effectiveness and efficiency of object detector must be considered. The goal of this paper is to implement an object detector with relatively balanced effectiveness and efficiency that can be directly applied in actual application scenarios, rather than propose a novel detection model. Considering that YOLOv3 has been widely used in practice, we develop a new object detector based on YOLOv3. We mainly try to combine various existing tricks that almost not increase the number of model parameters and FLOPs, to achieve the goal of improving the accuracy of detector as much as possible while ensuring that the speed is almost unchanged. Since all experiments in this paper are conducted based on PaddlePaddle, we call it PP-YOLO. By combining multiple tricks, PP-YOLO can achieve a better balance between effectiveness (45.2% mAP) and efficiency (72.9 FPS), surpassing the existing state-of-the-art detectors such as EfficientDet and YOLOv4.Source code is at https://github.com/PaddlePaddle/PaddleDetection.
A new technique for reliably identifying point sources in millimeter/sub-millimeter wavelength maps is presented. This method accounts for the frequency dependence of noise in the Fourier domain as well as non-uniformities in the coverage of a field. This optimal filter is an improvement over commonly-used matched filters that ignore coverage gradients. Treating noise variations in the Fourier domain as well as map space is traditionally viewed as a computationally intensive problem. We show that the penalty incurred in terms of computing time is quite small due to casting many of the calculations in terms of FFTs and exploiting the absence of sharp features in the noise spectra of observations. Practical aspects of implementing the optimal filter are presented in the context of data from the AzTEC bolometer camera. The advantages of using the new filter over the standard matched filter are also addressed in terms of a typical AzTEC map.
The detection reliability of weak signals is a critical issue in many astronomical contexts and may have severe consequences for determining number counts and luminosity functions, but also for optimising the use of telescope time in follow-up observations. Because of its optimal properties, one of the most popular and widely-used detection technique is the matched filter (MF). This is a linear filter designed to maximise the detectability of a signal of known structure that is buried in additive Gaussian random noise. In this work we show that in the very common situation where the number and position of the searched signals within a data sequence (e.g. an emission line in a spectrum) or an image (e.g. a point-source in an interferometric map) are unknown, this technique, when applied in its standard form, may severely underestimate the probability of false detection. This is because the correct use of the MF relies upon a-priori knowledge of the position of the signal of interest. In the absence of this information, the statistical significance of features that are actually noise is overestimated and detections claimed that are actually spurious. For this reason, we present an alternative method of computing the probability of false detection that is based on the probability density function (PDF) of the peaks of a random field. It is able to provide a correct estimate of the probability of false detection for the one-, two- and three-dimensional case. We apply this technique to a real two-dimensional interferometric map obtained with ALMA.
Retinal blood vessels structure contains information about diseases like obesity, diabetes, hypertension and glaucoma. This information is very useful in identification and treatment of these fatal diseases. To obtain this information, there is need to segment these retinal vessels. Many kernel based methods have been given for segmentation of retinal vessels but their kernels are not appropriate to vessel profile cause poor performance. To overcome this, a new and efficient kernel based matched filter approach has been proposed. The new matched filter is used to generate the matched filter response (MFR) image. We have applied Otsu thresholding method on obtained MFR image to extract the vessels. We have conducted extensive experiments to choose best value of parameters for the proposed matched filter kernel. The proposed approach has examined and validated on two online available DRIVE and STARE datasets. The proposed approach has specificity 98.50%, 98.23% and accuracy 95.77 %, 95.13% for DRIVE and STARE dataset respectively. Obtained results confirm that the proposed method has better performance than others. The reason behind increased performance is due to appropriate proposed kernel which matches retinal blood vessel profile more accurately.
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