Fast matrix factorization algorithm for DOSY based on the eigenvalue decomposition and the difference approximation focusing on the size of observed matrix

This paper deals with an analysis problem for diffusion-ordered NMR spectroscopy (DOSY). DOSY is formulated as a matrix factorization problem of a given observed matrix. In order to solve this problem, a direct exponential curve resolution algorithm (DECRA) is well known. DECRA is based on singular value decomposition; the advantage of this algorithm is that the initial value is not required. However, DECRA requires a long calculating time, depending on the size of the given observed matrix due to the singular value decomposition, and this is a serious problem in practical use. Thus, this paper proposes a new analysis algorithm for DOSY to achieve a short calculating time. In order to solve matrix factorization for DOSY without using singular value decomposition, this paper focuses on the size of the given observed matrix. The observed matrix in DOSY is also a rectangular matrix with more columns than rows, due to limitation of the measuring time; thus, the proposed algorithm transforms the given observed matrix into a small observed matrix. The proposed algorithm applies the eigenvalue decomposition and the difference approximation to the small observed matrix, and the matrix factorization problem for DOSY is solved. The simulation and a data analysis show that the proposed algorithm achieves a lower calculating time than DECRA as well as similar analysis result results to DECRA. (author)