Equalization and then Sharpening vs Sharpening and then Equalization This was a question from an exam of digital image processing:

"Working with low contrast images, an elective method to enhance details and improve contrast is to apply in cascade an equalization of the histogram and a sharpening filter technique.
a) Does the order of application of the methods matter? Justify
b) Which method would you use first? Justify"

Could anyone help me? I can't find a clear answer in the textbooks.
Since the Histogram Equalization isn't Linear Operator the order does matter and the result of the doing one before the other changes the final result.
Sharpening would work best when all the Dynamic Range is used.
Hence I'd first maximize the Dynamic Range by Histogram Equalization and then would apply the sharpening.
You might also think of the noise when making this choice.