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 that can be used in the reconstruction and recognition of vectorized images. The analyzed inverse problem is given by the equations $F\left ({\boldsymbol {x}_{ \boldsymbol {i}} }\right)= \boldsymbol {y}_{i}$ and $\boldsymbol {x}_{i}=F^{-1}\left ({\boldsymbol {y}_{i} }\right), i=1, \ldots, N$ , where $F\left ({\cdot }\right)$ is a linear mapping for $\boldsymbol {x}_{i}\in X\subset R^{n}, \boldsymbol {y}_{i}\in Y\subset R^{m}$ . Thus, $\boldsymbol {y}_{i}$ can be seen as a projection of image $\boldsymbol {x}_{i}$ , and $\boldsymbol {x}_{i}$ 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 $\boldsymbol {x}_{i}=F^{-1}\left ({\boldsymbol {y}_{i} }\right)$ , can be seen as an operation with associative memory, and the second one, when $\boldsymbol {x}_{i}=F^{-1}\left ({\boldsymbol {y}_{i} }\right)$ , 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 $\boldsymbol {x}_{i}$ and $\boldsymbol {y}_{i}$ . 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