How to combine two images with different gains in Matlab/ C++

Question

I have two images, both taken at the same time from the same detector.

Both images have 11 bit resolution (yes, its odd but that is the case here). The difference between the two images is that one image as been amplified by a factor of 1 and the other has been amplified by a factor of 10.

How can I take these two 11 bit images, and combine their pixel values to get a single 16 bit image? Basically, this increases the dynamic range of the final image.

I am fairly new to image processing. I know there is a solution for this, since other systems do this on the fly pixel-by-pixel in an FPGA. I was just hoping to be able to do this in Matlab post processing instead of live. I know doing bitwise operations in Matlab can be kinda difficult, but we do have an educational license with every toolbox available.

As mentioned below, this look an awful lot like HDR processing. The goal isn't artistic, rather data preservation. This is eventually going to be put in C++ and flown on an autonomous flight computer and running standard bloated HDR software on the fly would kill our timing requirements

Thanks for the help!

As a side note, I'd like to be able to do this for any combination of gains. ie 2x and 30x, 4x and 8x ect. In my gut I feel like this is a deceptively simple algorithm or interpolation, but I just don't know where to start.

Gains

Since there is some confusion on what the gains mean, I'll try to explain. The image sensor (CMOS) being used on our custom camera has the capability to simultaneously output two separate images, both taken from the same exposure. It can do this because the sensor has 2 different electrical amplifiers along its data path.

In photography terms, it would be like your DSLR being able to take a picture using 2 different ISO values at the same time.

Sorry for the confusion

Answer 1

The problems you pose is known as "High Dynamic Range Imaging" and "Tone Mapping". I suggest you start with those Wikipedia articles, then drill down to the bibliography cited therein.

You don't provide enough details about your imagery to give a more specific answer. What is the "gain" you mention? Did you crank up the sensor's gain (to what ISO-equivalent number?), or did you use a longer exposure time? Are the 11-bit pixel values linear or already gamma-compressed?