You can use a combination of the is Null tool and Con to fill NoData values from one raster with values from another. It will look like this:

Is Null, which you run on the mask image, calculates a new raster, with value of 1 meaning it has NoData value, 0 otherwise

The Con function allows you to return a result based on a condition. In this case, the condition is: if the result of the is Null function is 1, return the value from your enhanced image raster, otherwise return the value from your other mask image.