# How can I combine two filter kernels for image processing to create a single kernel?

Is it possible to create a single kernel which can help us to perform an 2 step image processing?

For example, I want to first perform a median filter on my image to remove salt and pepper noise and then perform a sharpen operation on it.

For this purpose, I have to perform the following operation

(image * Median_Kernel) *  sharpening kernel = final_image


I want to have a kernel which combines the effect of Median_kernel and sharpening it such that

image * combined_kernel = final_image


Is this mathematically possible? If so, could someone please explain to me how to do this mathematically?

• Yes if each kernel is just a convolution. Sharpening algorithms may or may not be, median also usually is not. Read this – joojaa Oct 10 '17 at 15:27
• It might depend on the actual kernel. Can you include the specific kernels you're talking about in the question? – Christian Rau Oct 11 '17 at 18:05
• "Kernel" is not a synonym for "filter". There is no such thing as a median kernel. – user106 Oct 12 '17 at 18:23