Machine Learning Techniques for Computed Tomography Imaging Spectroscopy of the Solar Atmosphere

Hi everyone, thanks for joining me, today we will be talking about ‘Machine Learning Techniques for Computed Tomography Imaging Spectroscopy of the Solar Atmosphere’. This is work was done by me and my advisor Dr. Charles Kankelborg to improve the data analysis techniques for the CT imaging spectrographs developed by his research group.

We will start by going over a quick outline of my talk today. I will quickly introduce solar explosive events, phenomena that can only be observed through the technique of imaging spectroscopy. We will then investigate how traditional slit imaging spectroscopy is inadequate for a complete picture of explosive events and how CT imaging spectroscopy can address the problems of slit imaging spectroscopy. Next we will investigate a particular CT imaging spectrograph, known as MOSES and demonstrate how the current analysis techniques can be improved. Finally, we will introduce a new analysis technique based on neural networks and discuss the performance of this new technique.

Solar explosive events are a wide class of events that are characterized by transient intensity enhancement, and significant Doppler shift and/or increased Doppler width. They occur over a wide range spatial scales and likely are due to various underlying physical phenomena. This example was captured by the Interface Region Imaging Spectrograph (IRIS) on July 21st 2013. This is a particularly dramatic explosive event that is connected to an eruption, and we will use it as an example in the remainder of the presentation.

To understand how to interpret explosive events using imaging spectroscopy, I will use a cartoon firework as an example. This firework is a simple expanding spherical shell of randomly placed tracers in three dimensions x, y, and z.

When we observe explosive events from earth, the 3D event is projected onto the skyplane y, z. The result of this projection is shown in the bottom right.

As we saw in the IRIS example, explosive events are characterized by a measurable Doppler shift. To demonstrate that, we can add colors to the tracers to indicate the observed wavelength of the tracers, or according to Doppler, the velocity relative to the skyplane.

With this picture in mind, we can then define another 3D object known as the spatial-spectral cube, shown in the top right, which has the two original skyplane dimensions and a new wavelength dimension. The goal of imaging spectroscopy is to measure this spatial-spectral cube, which allows us to reconstruct the original object on the top left.

As I’m sure many of you are aware, diffraction gratings split light into many spectral orders and the nonzero spectral orders disperse long wavelengths more than short wavelengths. We can take advantage of this property to construct spectrographs, where different wavelengths of light are focused onto different parts of a detector and allow us to measure a spectral profile of a light source.

In terms of the spatial-spectral cube, imaging the m=0 spectral order is simply the skyplane image of the cube (bottom center). However imaging the nonzero spectral orders can be represented as projections at some angle through the spatial-spectral cube, where the angle depends on the dispersion of a particular grating. This can be seen in the bottom right figure. In this figure we can notice that space and wavelength become convolved together, making such an image difficult to interpret accurately.

One common way to resolve the ambiguity between space and wavelength can be resolved by using a slit spectrograph such as IRIS. In this design, the field-of-view along the ambiguous axis is restricted to a small area, allowing the imagery on the detector to be interpreted as only wavelength. This method is an effective way of precisely measuring the spectrum of an object, however it has the obvious disadvantage that it can only observe a small portion of an event at any one time. We can see in our example that rastering the slit across the event immediately makes interpretation of the original object difficult.

To address the problems with slit spectroscopy, there has been significant development in a field known as CT imaging spectroscopy, or slitless imaging spectroscopy. In this technique the spatial-spectral cube is imaged in several diffraction orders to produce several corresponding overlappogram images. Since each image is a projection through a 3D space, inverting these images back into the spatial-spectral cube can be reduced to a computed tomography problem. This is a well-studied problem, especially in the medical field where constructing 3D volumes from many 2D images is a common technique in instruments such as magnetic resonance imagers. However inversions for CT imaging spectroscopy is often more difficult, since the number of angles is often very limited, usually between 2-6 projection angles. Since a useful spatial-spectral cube contains more information than 2-6 images, this is known as an ill-posed inversion problem. The remainder of this presentation will discuss strategies to solve this ill-posed problem.

The Multi-order solar EUV Spectrograph is an example of a CT imaging spectrograph developed by our research group. This instrument is designed to mitigate the ill-posed inversion problem by using a narrow passband filter to target a single spectral line. It images this target line in three spectral orders m = -1, 0 and 1 just like in our firework example. This instrument has undergone two iterations, the first, which flew in 2006, imaged the He II 304A spectral line, and the second imaged the Ne VII 465 A spectral line and flew in 2015. The data from the 2015 flight is not as clean as the 2006 flight, so we will focus on the 2006 flight for the remainder of this presentation. Also like in our firework example, the dispersion is limited to one plane. Since the dispersion is invariant along the z axis, we are free to reduce the original 3D inversion problem to a 2D inversion problem.

This ability to reduce MOSES observations to a 2D inversion problem is very convenient because it means that we can use data from slit spectrographs such as IRIS as a synthetic sun to test our inversion schemes. An emission line observed by IRIS that is the closest approximation to the He II line observed by MOSES is probably one of the Si IV lines. For this work we chose the 1394 A line since it has the best signal out of the two Si IV lines. Making a synthetic MOSES observation out of these IRIS observations is very simple, we start by trimming and downsampling the image into the MOSES spectral resolution and range and then we can simply sum along the spectral axis and along the two diagonals. Since we reduced the dimensionality of the problem, the result is a set of three lines instead of three images.

Current inversion schemes for MOSES are based on algebraic reconstruction techniques, a common method in computed tomography. This algorithm only assumes that the result must be positive (as intensity should be). It is an iterative reconstruction technique that starts with some initial guess at the spatial-spectral cube, computes the corresponding MOSES observations by applying projections, compares the projections to the measurement, and then multiplies the guess by some correction factor to bring the projections closer to the measurement. This process continues until convergence is reached.

On the top left we can see an animation of the algorithm’s progress on inverting the spatial-spectral cube. We can immediately notice that the algorithm tends to create artifacts that we have dubbed plaid, where intensity is smeared along the projection direction. This is an artifact that is ubiquitous in limited-angle inversion algorithms and it plays havoc with our ability to extract meaningful line parameters from the inversions. We can see this problem in the remaining three plots: intensity, shift and width. The intensity is correct as it should be since we were iterating to correct for this quantity, however the shift both the shift and width are overestimated due to the plaid artifacts.

On the top left we can see an animation of the algorithm’s progress on inverting the spatial-spectral cube. We can immediately notice that the algorithm tends to create artifacts that we have dubbed plaid, where intensity is smeared along the projection direction. This is an artifact that is ubiquitous in limited-angle inversion algorithms and it plays havoc with our ability to extract meaningful line parameters from the inversions. We can see this problem in the remaining three plots: intensity, shift and width. The intensity is correct as it should be since we were iterating to correct for this quantity, however the shift both the shift and width are overestimated due to the plaid artifacts.