A computer-implemented method of interpolating seismic data, comprising: forming a plurality of pairwise Hankel tensors T H from acquired seismic data, a respective pairwise Hankel tensor for each of a plurality of originally collected frequency slices S; performing tensor completion on each of said pairwise Hankel tensors to recover a plurality of interpolated frequency slices; and combining said plurality of interpolated frequency slices with said originally collected frequency slices to form a set of seismic trace data of a geographical area of interest, wherein said step of forming a plurality of pairwise Hankel tensors comprises: determining the number of spatial dimensions D of each of said plurality of frequency slices S; determining a length of each of said spatial dimensions D, wherein for each dimension i of said plurality of frequency slices, i = 1..., D each dimension is L(i) in length; specifying a pairwise Hankel tensor number of modes as 2 D; specifying a length of each of said pairwise Hankel tensor modes as L(i) / 2 + 1 for a first and any odd number of said tensor modes, (L(i) + 1)/2 for a second and any even number of said pairwise Hankel tensor modes, and further wherein if any tensor mode length is a fraction said fractional tensor mode length is reduced to a next lowest whole number; and specifying a value for any particular pairwise Hankel tensor element T H (j 1, j 2, j 3, j 4,...,j m, j n) according to the following expression- S j 1 + j 2 − 1, j 3 + j 4 − 1,..., j m + j n − 1, wherein m = 2 D -1, n = 2D, and j 's range over all possible values for said pairwise Hankel tensor. forming a plurality of pairwise Hankel tensors T H from acquired seismic data, a respective pairwise Hankel tensor for each of a plurality of originally collected frequency slices S; performing tensor completion on each of said pairwise Hankel tensors to recover a plurality of interpolated frequency slices; and combining said plurality of interpolated frequency slices with said originally collected frequency slices to form a set of seismic trace data of a geographical area of interest, wherein said step of forming a plurality of pairwise Hankel tensors comprises: determining the number of spatial dimensions D of each of said plurality of frequency slices S; determining a length of each of said spatial dimensions D, wherein for each dimension i of said plurality of frequency slices, i = 1..., D each dimension is L(i) in length; specifying a pairwise Hankel tensor number of modes as 2 D; specifying a length of each of said pairwise Hankel tensor modes as L(i) / 2 + 1 for a first and any odd number of said tensor modes, (L(i) + 1)/2 for a second and any even number of said pairwise Hankel tensor modes, and further wherein if any tensor mode length is a fraction said fractional tensor mode length is reduced to a next lowest whole number; and specifying a value for any particular pairwise Hankel tensor element T H (j 1, j 2, j 3, j 4,...,j m, j n) according to the following expression- S j 1 + j 2 − 1, j 3 + j 4 − 1,..., j m + j n − 1, wherein m = 2 D -1, n = 2D, and j 's range over all possible values for said pairwise Hankel tensor. determining the number of spatial dimensions D of each of said plurality of frequency slices S; determining a length of each of said spatial dimensions D, wherein for each dimension i of said plurality of frequency slices, i = 1..., D each dimension is L(i) in length; specifying a pairwise Hankel tensor number of modes as 2 D; specifying a length of each of said pairwise Hankel tensor modes as L(i) / 2 + 1 for a first and any odd number of said tensor modes, (L(i) + 1)/2 for a second and any even number of said pairwise Hankel tensor modes, and further wherein if any tensor mode length is a fraction said fractional tensor mode length is reduced to a next lowest whole number; and specifying a value for any particular pairwise Hankel tensor element T H (j 1, j 2, j 3, j 4,...,j m, j n) according to the following expression- S j 1 + j 2 − 1, j 3 + j 4 − 1,..., j m + j n − 1, wherein m = 2 D -1, n = 2D, and j 's range over all possible values for said pairwise Hankel tensor.