On sampling functions and Fourier reconstruction methods
نویسندگان
چکیده
Random sampling can lead to algorithms where the Fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band-limited. Conversely, regular sampling often hampers the Fourier data recovery methods. However, two-dimensional (2D) signals which are band-limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes the mixing between the unknown spectrum of the well-sampled signal and aliasing artifacts. This concept can be easily extended to higher dimensions and used to define potential strategies for acquisition-guided Fourier reconstruction. In this paper we derive the wavenumber response of various sampling operators and investigate sampling conditions for optimal Fourier reconstruction using synthetic and real data examples.
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