Tensor B-spline reconstruction of multidimensional signals from large irregularly sampled data

We present a tensor based approach for the efficient reconstruction of high-dimensional signals from large sets of irregularly sampled measurements. Using our tensor framework we analyzed the structure of the B-spline reconstruction problem and identified its important tensor properties, which were used for building a computationally and memory efficient solving algorithm. The proposed algorithm was successfully validated on 3D/4D standard datasets, where this novel tensor-based algorithm outperformed existing spline approaches. Then the algorithm was applied to a large practical problem of reconstruction of 4D medical ultrasound signal from irregularly sampled data.