I was looking at the Galleries in the NASA Scientific Visualization Studio and in the banner they show an image from SDO - the Solar Dynamics Observatory. I've posted it below along with a cropped, reversed tone of the green channel.
I see these "echoes" - really just periodic tire-tread-like little blip-artifacts (blipifacts) from time to time when there are certain bright events. They do seem to have a roughly cartesian distribution, spreading out away from the bright spot along all four diagonals. The vertical "spike" suggests the CCD axis is aligned to (x, y), so maybe it is vane-related? Does the instrument have a secondary supported by vanes?
What are they?
UPDATE: I found a photomontage of a bright event shown with six different wavelength bands. It's the Cinco de Mayo Flare of May 5, 2015. Many show the same effect, but different wavelengths have different patterns - strongly suggesting this is interference or diffraction, not electronic. There is always a short-period "tire-tread" combined with a long period envelope - maybe a dozen blips, then nothing, then a dozen blips... It reminds me of the diffraction pattern from a square array of points.
Image: The "Cinco de Mayo Flare" 05-05-2015: www.nasa.gov/feature/goddard/nasas-sdo-observes-cinco-de-mayo-solar-flare
HMI Continumum | 171Å upper transiti | 304Å Chromosph | 193Å Corona/Flare | 131Å Flaring reg.
You can use this guide to compare the artificial color-coding to get the actual UV wavelength for each image. From here.