2019), natural language processing (Behera et al. In addition to the problems mentioned above, convolution has applications that include probability (Harikrishna and Amuthan 2020, Shrivastava 2019), statistics (Wang et al.
In the convolution, for real-valued functions, contrary to the cross-correlation operator, f( x) or g( x) is reflected about the y-axis. Convolution is a mathematical operation that, given two functions f and g, produces a third one that expresses how the shape of one is modified by the other. One of the basic techniques used for image processing is the convolution and its inverse, the deconvolution (Nussbaumer 2012). Feature extraction problems are closely related to artificial vision, finding applications in object detection and recognition, motion tracking, identity recognition, and numerous other problems related to automatic photograph and video processing (Bovik 2010, Alpaydin 2009). On signal analysis problems, denoising algorithms are fundamental to improve the quality of the data in particular, in image analysis, the denoising process is essential to improve the image quality (Chen and Fomel 2015). In recent years, numerous works on image processing have dealt with image denoising and feature extraction problems. 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. The results highlight that the proposed algorithms are able to identify the filter used in the convolution phase in several cases. Several tests were performed to investigate the applicability of our approaches in different scenarios.
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 \(f'(I)\). In this work, we focus on the deconvolution process, defining a new approach to retrieve filters applied in the convolution phase. Convolution is a technique used to enhance specific characteristics of an image, while deconvolution is its inverse process. Image analysis is a branch of signal analysis that focuses on the extraction of meaningful information from images through digital image processing techniques.