Stable, non-iterative, object reconstruction from incomplete data using prior knowledge

Abstract

The non-uniqueness and instability of object reconstruction from incomplete data can only be resolved by a priori constraints restricting the set of admissible solutions. A successful approach is to choose the object consistent with the data and of minimum norm in a weighted Hilbert space [1,2]. The weight is chosen to reflect our prior knowledge of the solution. The algorithm involves the solution of a set of linear equations with Toeplitz structure which can be efficiently solved in a finite number of steps by the Levinson recursion [3]. We show the equivalence between this method and Miller regularisation [4,5] for ill-posed problems. Experimental results demonstrating the effectiveness of the method are shown in the presentation [see also ref. 2].