Orthogonal decomposition technique for ionospheric tomography

The possibility of reconstructing two‐dimensional electron‐density profiles in the ionosphere with ionospheric tomography is significant. However, due to the nature of the imaging system, there are several resolution degradation parameters. In order to compensate for these degradation parameters, a priori information must be used. This article introduces the orthogonal decomposition algorithm for image reconstruction, which uses the a priori information to generate a set of orthogonal basis functions for the source domain. This algorithm consists of two simple steps: orthogonal decomposition and recombination. In the development of the algorithm, it is shown that the degradation parameters of the imaging system result in correlations among projections of orthogonal functions. Gram–Schmidt orthogonalization is used to compensate for these correlations, producing a matrix that measures the degradation of the system. Any set of basis functions can be used, and depending upon this choice, the nature of the algorithm varies greatly. Choosing the basis functions of the source domain to be the Fourier kernels produces an algorithm capable of isolating individual frequency components of individual projections. This particular choice of basis functions also results in an algorithm that strongly resembles the direct Fourier method, but without requiring the use of inverse Fourier transforms.