Combining images with different exposure times & ISO values

[Cheyenne]

I believe it's possible, but was wondering if it really is possible, and if so what is the technique to do so?

[Juan Conejero]

Hi Cheyenne,

Of course it's possible. With ImageIntegration, the solution to this problem is just to select an appropriate weighting algorithm (Weights parameter).

The best option seems to be the noise evaluation weighting algorithm. Basically, this algorithm performs an automatic estimation of the standard deviation of the noise for each image, assuming a Gaussian noise distribution. Noise estimates are used to derive relative weights (relative to the reference image, which is always the first one in the list of input images).

Unfortunately, the implementation of this algorithm in PI 1.5.2 has some problems that don't allow for accurate evaluations when exposure times differ significantly. The ImageIntegration module that comes with the upcoming PI 1.5.5 has all of these problems fixed, and also implements an enhanced version of the noise estimation algorithm. In all tests we have conducted, this automatic weighting system consistently leads to the highest SNR improvements with fixed rejection parameters. I hope to be able to release PI 1.5.5 within a couple days or so.

A good alternative (but less accurate) is the exposure time weighting mode. In this mode, ImageIntegration uses exposure times to derive relative weights.  Of course, in this case all images must provide EXPTIME or EXPOSURE FITS keywords. You can also try the average signal strength method; however it will fail if some of the images have gradients or are not correctly calibrated.

Let me know how it goes.

[lucchett]

Juan, I've tried this method with two images and doesn't work; it seems PI is expecting at least three images.
Am I doing something wrong?

Many thanks,
Andrea

[Juan Conejero]

Hi Andrea,

Juan, I've tried this method with two images and doesn't work; it seems PI is expecting at least three images.
Am I doing something wrong?

Not at all; ImageIntegration needs at least three images.

If you have just two images, you can use PixelMath. Assume you have both images open in PixInsight. Call one of them A and the other B. Follow these steps:

1. Use the NoiseEvaluation script to compute noise estimates for both images. Write down the noise standard deviation estimates. Let's suppose we have:

Noise estimate for image A: 2.225e-04
Noise estimate for image B: 2.708e-04

2. Open PixelMath.

3. In the Symbols field, you must define two constants with the above noise estimates, plus one variable. In this example it would be:

nA=2.225e-04, nB=2.708e-04, snB

4. In the RGB/K expression field, write this expression:

snB = nB*AvgDev(A)/AvgDev(B); A/nA/nA + B/snB/snB

This expression combines both images weighted according to their noise estimates. Weighting takes into account that the proportionality between signal and noise follows a quadratic relation. The AvgDev(A)/AvgDev(B) scales B to match the mean dispersion of A, so both noise estimates are statistically comparable.

5. The Rescale option must be enabled so you'll get an integrated image without any data clipping and maximized dynamic range usage.

6. In the Destination section, enable the "Create new image" option.

7. Apply the PixelMath process to either A or B, and you're done.

This procedure basically mimics what ImageIntegration does. Let me know how it works.

[lucchett]

hi Juan,
you always have an answer!

I've tried with Pixel math, it works but there are some issue to solve:

-there are some artifacts on the final image, especially around the stars. I've put a small preview here:

ftp://213.203.138.22/
user: astrouser
pass: astro4810
folder: public
image: image04.jpg

I think it is easier to see that to explain (straight edge on the stars..)

-the final image is quite "flat": when I try to stretch the final image the histogram become very wide and flat, not the classic gauss shape. I loose all the micro contrast and faint areas

As background, I've taken an RGB composite bin2, resampled 2x, applied a linear RGB WS, extracted the luminance. the single original frames were 300sec for a total of 30 min per channel.
the second image is a luminance bin 1, 600 sec frames for a total of 2hours.

the noise of the first image is about 2.7e-05, while the second is 1.7e-04

Can the formula be adjusted to solve the two issues?

Many thanks!!
Andrea