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It is demonstrated that in some cases it is possible to reconstruct images of fields whose local values are not scalars but are instead anisotropic. The approach taken relies upon Fourier analysis of the angular dependence and separation of scalar and non-scalar contributions by symmetry, and is applicable to anisotropies that do not have even symmetry. Although there are only a limited number of cases in which the problem can be analytically solved, there appears to be a variety of applications for which good approximations are available. The proposed algorithm, a hybrid of well known image reconstruction techniques, has been applied to calculated projections of test patterns, local regions of which having been assigned either scalar or vector behavior or both.