We propose a novel method called compressed sensing with linear-in-wavenumber sampling (k-linear CS) to retrieve an image for spectral-domain optical coherence tomography (SD-OCT). An array of points that is evenly spaced in wavenumber domain is sampled from an original interferogram by a preset k-linear mask. Then the compressed sensing based on 11 norm minimization is applied on these points to reconstruct an A-scan data. To get an OCT image, this method uses less than 20percent of the total data as required in the typical process and gets rid of the spectral calibration with numerical interpolation in traditional CS-OCT. Therefore k-linear CS is favorable for high speed imaging. It is demonstrated that the k-linear CS has the same axial resolution performance with approx30 dB higher signal-to-noise ratio (SNR) as compared with the numerical interpolation. Imaging of bio-tissue by SD-OCT with k-linear CS is also demonstrated.
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