Image reconstruction from a complete set of geometric and complex moments

•Image reconstructing ability from its complete set of geometric and complex moments.•Establishing relationships between the original and blurred images in a moment domain.•Proposing an algorithm to recover the image from degraded image.

An image can be reconstructed from the finite set of its orthogonal moments. Since geometric and complex moment kernels do not satisfy orthogonality criterion, direct image reconstruction using them is deemed to be difficult. In this paper, we propose a technique to reconstruct an image from either geometric moments (GMs) or complex moments (CMs). We utilize a relationship between GMs and Stirling numbers of the second kind. Then, by using the invertibility property of the Stirling transform, the original image can be reconstructed from its complete set of either geometric or complex moments. Further, based on previous works on blur effects on a moment domain and using the proposed reconstruction methods, a formulation is shown to obtain an estimated original image from the degraded image moments and the blur parameter. The reconstruction performance of the proposed methods on blur images is presented to validate the theoretical framework.