How to make an image (12 bit depth) from a double matrix?

I am running a pipeline which initially imports tif images (12-bit; 0 to 4095 pixel intensity value), converts values to doubles (it still stores original pixel values i.e. 0-4095) and finally do some processing. Afterwards I need to save them again as tif files for further processing on ImageJ, but it seems transferrring matrix data into image changes the original pixel values. I used imshow to generate an image and save it using Save As in the dropdown menu on matlab figure.

Is there a way to generate/store images from matrix without changing the original pixel values of a 12 bit image?

[Isaac Kafshkanan]

img_new = img - min(img(:)); %where img = name of your image

img_new = double(img_new)/max(img_new(:))*4095;