Effective Stray Light Removal for EUV Images. Paul R. Shearer, Richard A. Frazin , Anna C. Gilbert, Alfred O. Hero III (University of Michigan). Nonparametric Blind Deconvolution For EUVI-B, 171 Å. Removal of Stray Light from EUVI-B Data. The EUV Stray Light Problem.
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Paul R. Shearer, Richard A. Frazin, Anna C. Gilbert, Alfred O. Hero III (University of Michigan)
Nonparametric Blind Deconvolution For EUVI-B, 171 Å
Removal of Stray Light from EUVI-B Data
The EUV Stray Light Problem
Synthetic EUVI-B Blind Deconvolutions
To remove stray light from EUVI-B 171 Å images, we seek a physically reasonable PSF that removes all stray light from the Moon and produces physically reasonable deconvolved images. We give a precise meaning to “reasonable” by specifying a mathematical model for the images and PSF. Note that our model is nonparametric; we do not assume the PSF is given by a formula with just a few free parameters. Nonparametric modeling greatly facilitates discovery of unanticipated PSF structure.
Coronal images from all EUV telescopes (EIT, TRACE, EUVI, AIA) are contaminated with stray light caused by entrance aperture diffraction and mirror scattering. The contamination is worst in faint regions such as coronal holes, prominence cavities, and the off-limb corona. EUV stray light contamination is caused by a point spread function (PSF) which varies with wavelength band but not with time. In the time series of images for each band, each observation is theconvolution of the band’sPSF with the unknown true-emission image, plus Poisson-distributed photon noise:
Fig. 4: A synthetic blind deconvolution experiment which demonstrates that we can accurately recover EUVI-like PSFs and images from noisy, blurry observations by solving Eq. 2. In our experiment, we generated a synthetic EUVI-B 171 Å PSF and a series of 8 true-emission images. The PSF had a power-law decay profile simulating mirror scattering; each true-emission image was a real EUVI lunar transit image in which we set the Moon and off-limb to zero. We convolved the images and PSF together and added Poisson noise to generate synthetic EUVI observations. Col. 1: 1 of the 8 synthetic observations and its true-emission zero set (red). Col. 2: the true-emission image and our deconvolved image are visually indistinguishable. Col. 3: the relative deviation of the deconvolved image from the true emission (bottom) is at most 5%, comparable to the signal-to-noise ratio (top). Col. 4: Our recovered PSF closely resembles the true PSF despite our not imposing any prior formula.
Eq. 1: The EUV Stray Light Model.
To remove stray light from all images in a band, we must simultaneously determine h and u from f; this notoriously difficult and underdetermined signal processing problem is known asblind deconvolution. Our group’s ultimate goal is to remove stray light from all EUV images; here we present stray light corrections for EUVI-B 171 Å.
Fig. 5: We solved Eq. 2 using 8observations from the Feb. 25 transit series to estimate the EUVI 171 Å PSF (far right). For independent verification of the PSF’s accuracy, we deconvolved several transit series images not in the training set of 8, including the 3 shown here. We remove at least 90% of the Moon’s stray light in every image except those where the Moon is very close to the image boundary (not pictured). The sensitivity of deconvolution to boundary conditions is a common problem and a subject of our current work. Unlike the SolarSoft PSF, our PSF is highly anisotropic. The dark triangles on the sides are boundary effects.
Fig. 1:Severe stray light contamination can be directly observed in an EUVI-B lunar transit fromFeb. 25, 2007. Since the Moon (circled) is not an EUV emitter, all of its apparent emissions are in fact stray light. Since the apparent emissions of the off-limb region above and below the Moon are nearly identical to the apparent emissions from the Moon, the true emission from this region must be nearly zero. Quantitative study of this region’s emission is therefore meaningless without correction.
Eq. 2: Problem Formulation.
Fig. 3: The Inward Gradient PSF Model.
% stray light
To find the PSF and image series that best fit these conditions, we solve the optimization problem given in Eq. 2. For simplicity we replace the Poisson likelihood with a Gaussian likelihood, giving us a constrained nonlinear least squares problem. The large dimensionality, complex constraint structure, and highly ill-conditioned quadratic terms make even this simplified problem intractable by general-purpose optimization methods. To solve it, we created a novel algorithm based on recent advances in dual decomposition and proximal splitting, and applied it to 8x downsampled images (i.e. 2048x2048 EUVI-B images became 256x256).
EUVI 171 Å
Fig. 6: EUVI-B 171 Å features before deconvolution with our PSF (top) and after (bottom). To create these images, we upsampled our 256x256 PSF by 8x, and deconvolved the 2048x2048 images with the upsampled PSF. Col. 1:a coronal hole dims by up to 70% after deconvolution. Col. 2: a prominence cavity dims by up to 70%, which is 30% more than was predicted by the SolarSoft PSF (cf. Fig. 2).Col. 3: an active region brightens by 30%. Col. 4:stray light is removed to a tolerance of less than 5% over almost all of the Moon. The negative counts on the lower lunar boundary do not exceed 15% of the apparent emission, and appear to be an artifact of upsampling the 256x256 PSF to 2048x2048.
Conclusion and Ongoing Work
Fig. 2:Deconvolutions using PSFs output by SolarSoft’seuvi_psf.proutility (far right: SolarSoft 171 Å PSF) are the only stray light corrections publicly available today. They predict high levels of stray light contamination in faint coronal regions, but do not remove all stray light. Left: A SolarSoftdeconvolution predicts that a prominence cavity’s apparent emissions are 40% stray light. Right: In a Feb. 25 lunar transit observation, the SolarSoft 171 Å PSF removes only30-50% of the apparent lunar emissions. Since all apparent lunar emissions are in fact stray light, we conclude that the SolarSoft PSF removes less than half of the stray light in 171 Å images. When this light is fully removed by our method, faint regions such as the prominence cavity become much fainter than when deconvolved with SolarSoftPSFs (cf. Fig 5).