Optimised two‐dimensional orthogonal matching pursuit algorithm via singular value decomposition

Abstract

The reconstruction algorithm is one of the core issues in applying compressed sensing theory to practical applications. Two-dimensional orthogonal matching pursuit (2DOMP) algorithm, as an extension of the traditional orthogonal matching pursuit algorithm, can be used directly for the reconstruction of two-dimensional signals. With 2D separable sampling, the memory requirements and the complexity of 2DOMP are exponentially reduced. However, in 2DOMP algorithm, the requirement of reconstruction matrix is not taken into consideration, merely measurement matrix is used directly. In this study, singular value decomposition is introduced into 2DOMP algorithm, and 2DOMP algorithm based on singular value decomposition (2DOMP-SVD) is proposed. Singular value decomposition of separable measurement matrices is used to obtain optimised separable reconstruction matrices and optimised measurements. Numerical experiments demonstrate that the proposed 2DOMP-SVD algorithm can significantly improve the success rate and robustness of reconstruction. Moreover, the separation design of the matrix can satisfy the requirements for both the measurement matrix and the reconstruction matrix individually, and is suitable for general separable linear system.