In this paper, we use Frame Theory to develop a generalized OCT image reconstruction method using redundant and non-uniformly spaced frequency domain samples that includes using non-redundant and uniformly spaced samples as special cases. We also correct an important theoretical error in the previously reported results related to OCT image reconstruction using the Non-uniform Discrete Fourier Transform (NDFT). Moreover, we describe an efficient method to compute our corrected reconstruction transform, i.e., a scaled NDFT, using the Fast Fourier Transform (FFT). Finally, we demonstrate different advantages of our generalized OCT image reconstruction method by achieving (1) theoretically corrected OCT image reconstruction directly from non-uniformly spaced frequency domain samples; (2) a novel OCT image reconstruction method with a higher signal-to-noise ratio (SNR) using redundant frequency domain samples. Our new image reconstruction method is an improvement of OCT technology, so it could benefit all OCT applications.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.