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@@ -8,7 +8,7 @@ The intensity observed through optically-thin SDO/AIA filters (94 Å, 131 Å, 17
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In this equation, g_i is the DN/s/px value in the <i>i</i>th SDO/AIA channel. This intensity corresponds to the K_i(T) temperature response function, and the DEM, ξ(T), is in units of cm^-5 K^-1. The matrix formulation of this integral equation can be represented in the form, g = <b>K</b>ξ, however, this problem is an ill-posed inverse problem, and any attempt to directly recover ξ leads to significant noise amplication.
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There are numerous methods to tackle mathematical problems of this kind, and there are an increasing number of methods in the literature for recovering the differential emission measure including methods based techniques such as Tikhonov Regularisation (<a href="https://doi.org/10.1051/0004-6361/201117576">Hannah & Kontar 2012</a>), on the concept of sparsity (<a href="https://doi.org/10.1088/0004-637X/807/2/143">Cheung et al 2015</a>).
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There are numerous methods to tackle mathematical problems of this kind, and there are an increasing number of methods in the literature for recovering the differential emission measure. These include methods based techniques such as Tikhonov Regularisation (<a href="https://doi.org/10.1051/0004-6361/201117576">Hannah & Kontar 2012</a>), or on the concept of sparsity (<a href="https://doi.org/10.1088/0004-637X/807/2/143">Cheung et al 2015</a>).
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In the attached notebook (DeepEM.ipynb) we will introduce a deep learning approach for Differential Emission Measure (DEM) Inversion. <i>For this notebook</i>, `DeepEM` is a trained on one set of <i>SDO</i>/AIA observations (six optically-thin channels; 6 x N x N) and DEM solutions (in 18 temperature bins from logT = 5.5 - 7.2, 18 x N x N; [Cheung et al 2015](https://doi.org/10.1088/0004-637X/807/2/143)) at a resolution of 512 x 512 (N = 512) using a 1x1 2D Convolutional Neural Network with a single hidden layer.
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