A non-iterative linear algebraic algorithm for image reconstruction

The authors introduce a noniterative linear algebraic algorithm for image reconstruction. The proposed algorithm solves the system equations by approximating the inverse of a matrix with a low-order polynomial function of the matrix. The criterion for designing such a polynomial is addressed, and the performance of the new method is demonstrated. By designing an appropriate polynomial, this method retains the good performance features of the generalized matrix inversion algorithm (GMI) while eliminating the practicality prohibitive computational load associated with singular value decomposition (SVD). Because this method is noniterative and does not require SVD, its computational advantage over iterative methods and GMI is obvious. This method is also more flexible than iterative methods in the sense that it can use different polynomials for different tasks