An iterative procedure for uniform resampling of a 2-D signal from its nonequally-spaced samples

An efficient technique is presented for an approximate reconstruction of a finite-energy bandlimited two-dimensional (2-D) signal from its unequally spaced samples which are located in the vicinity of uniformly distributed (with a rate at or above the Nyquist frequency) synchronous points. The signal is given by the set of its unequally spaced samples, and it suffices to find their uniformly distributed counterparts and then use the 2-D Shannon sampling theorem for signal reconstruction. A set of uniformly spaced samples is evaluated by solving a system of linear equations given by the 2-D Shannon theorem. To reduce the computational complexity caused by the large size of the system matrix and avoid the ill-conditioning that can occur if the nonuniform samples deviate too far from the synchronous points, the proposed method uses the partitioning of a given data block into very short overlapping subintervals of size 3×3. An innovative iterative procedure is applied to reduce the error caused by applying an extremely short 3×3 observation range. Repeated application of this procedure is used to update the estimated values of the uniformly spaced samples. A simulation example shows that the proposed windowing technique combined with the iterative procedure is simple, efficient, and rapidly convergent