Image convolution: a linear programming approach for filters design

Image analysis is a branch of signal analysis that focuses on the extraction of meaningful information from images through digital image processing techniques. Convolution is a technique used to enhance specific characteristics of an image, while deconvolution is its inverse process. In this work, we focus on the deconvolution process, defining a new approach to retrieve filters applied in the convolution phase. Given an image I and a filtered image I′= f(I) , we propose three mathematical formulations that, starting from I and I′, are able to identify the filter f′ that minimizes the mean absolute error between I′ and f′(I). Several tests were performed to investigate the applicability of our approaches in different scenarios. The results highlight that the proposed algorithms are able to identify the filter used in the convolution phase in several cases. Alternatively, the developed approaches can be used to verify whether a specific input image I can be transformed into a sample image I′ through a convolution filter while returning the desired filter as output.