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Performance limits and trade-offs of superresolution imaging systems

Several superresolution phenomena are re-visited in the context of the ”prior discrete Fourier transform” (PDFT). The PDFT is used to establish relationships between superresolution imaging applications, the construction of superoscillating signals and the design of superresolution filters. The condition number of the PDFT algorithm is identified as a pivotal parameter for practical applications of the PDFT to superresolution problems. Motivated by applications of the algorithm to imaging from Fourier data, a simple regularization procedure is suggested, which results in superoscillating signals representative of the constraints used for their construction. In addition, bandwidth extrapolation from oversampled data is investigated, which highlights inherent limits of superresolution signal recovery and synthesis.