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Publication# Simulation of 1D ARPES Data and Measures to recover the underlying Signal

Abstract

Fourier deconvolution is a good tool to remove the blurring of images with a very high SNR. However it suffers under severe noise degradation and becomes impracticable at a SNR of 20dB. If the convolution width is very high this happens even earlier. The analysis of the frequency spectrum brings information on the data, especially on the periodicity of certain features. Furthermore it can be used to better understand other processing tools. Gaussian blur and smoothing can be used with the goal to enhance image structures at different scales. They have the effect of reducing high frequency information, corresponding to high pixel to pixel variation and usually a characteristic of noise. However it also reduces detail. In 2D better resultsmay be obtained, because diagonal pixels can be used in addition. Gaussian smoothing is certainly a useful tool in the analysis of ARPES data and it should be well integrated in other measures of data recovery. If the blurring of the signal is high it is beneficial apply some Gaussian blur before proceeding to other measures. If the blurring of the signal is low, it is better to apply Gaussian smoothing only after de-convolution measures in order to not loose information on the signal.

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Related concepts (5)

Gaussian blur

In , a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss). It is a widely used effect in graphics software, typically to reduce and reduce detail. The visual effect of this blurring technique is a smooth blur resembling that of viewing the image through a translucent screen, distinctly different from the bokeh effect produced by an out-of-focus lens or the shadow of an object under usual illumination.

Convolutional neural network

Convolutional neural network (CNN) is a regularized type of feed-forward neural network that learns feature engineering by itself via filters (or kernel) optimization. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by using regularized weights over fewer connections. For example, for each neuron in the fully-connected layer 10,000 weights would be required for processing an image sized 100 × 100 pixels.

Convolution

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function () that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity).