Image Recognition and Reconstruction With Machine Learning: An Inverse Problem Approach

Image recognition and reconstruction are common problems in many image processing systems. These problems can be formulated as a solution to the linear inverse problem. This article presents a machine learning system model F(x(i)) = y(i )and x(i )= F-1 (y(i)),i = 1, ... ,N, where F () is a linear mapping for x(i )is an element of X subset of R-n, y(i) is an element of Y subset of R-m. Thus, y(i) can be seen as a projection of image x(i) should be reconstructed as a solution to the inverse problem. We consider image reconstruction as an inverse problem using two different schemes. The first one, when x(i )= F-1 (y(i)), can be seen as an operation with associative memory, and the second one, when x(i )= F-1 (y(i)), can be implemented by creating random vectors for training sets. Moreover, we point out that the solution to the inverse problem can be generalized to complex-valued images x(i) and y(i). In this paper, we propose a machine learning model based on a spectral processor as an alternative solution to deep learning based on optimization procedures.

Automated summary

This article presents a solution to the linear inverse problem of image recognition and reconstruction through a machine learning model based on a spectral processor. It proposes an alternative solution to deep learning based on optimization procedures and extends the solution to complex-valued images.