Synthetic aperture radar map aperture annealing and interpolation

A method for repairing, bridging, or extrapolating an existing aperture to improve image interpretability;

• comprising:
• determining a size of a corrupt data region embedded in or adjacent to an existing set of aperture data;
• identifying a border region of uncorrupted data contiguous with the corrupt data region;
• selecting an uncorrupt data region from the set of existing aperture data, disjoint from the border region and the corrupt data region, where the uncorrupt data region is selected to be able to completely overlay the corrupt data region and the border region at multiple translational offsets;
• forming an extended basis set of vectors, X, from a one-dimensional mapping of uncorrupted data registered to each point in the border region, for each translational offset;
• forming an auxiliary set of vectors, A, from a one-dimensional mapping of uncorrupted data registered to each point in the corrupt data region, for each translational offset;
• forming a reduced basis set of vectors, S, either by 1) picking selected translational offsets of the extended basis set, identified by peaks of a conjugate correlation between the uncorrupted data and the border region, or by 2) picking one or more top eigenvectors of a singular value decomposition (SVD) of the extended basis set, as X=UDV′, where U is m×m, with m the length of the one-dimensional mapping to each point in the border region, where D is diagonal and m×n, with n the number of translational offsets and m>=n, where V′ is the hermitian conjugate of V, an n×n matrix, and U and V are unitary, with the reduced basis set of vectors formed as S=XVtop, where Vtop is composed of the columns of V corresponding to the one or more largest diagonal values of D (top eigenvalues), and with the reduced auxiliary set of vectors formed as S′=AVtop;
• solving a linear matrix equation for a linear combination, C, of the reduced basis set, S, which minimizes an L2-norm distance from the border region;
• applying the linear combination vector, C, to the reduced auxiliary set of vectors, S′, to generate replacement data for replacing the data in the corrupt data region.