We propose a novel method called compressed sensing with linear-in-wavenumber sampling (-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 -linear mask. Then the compressed sensing based on norm minimization is applied on these points to reconstruct an A-scan data. To get an OCT image, this method uses less than 20% 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 -linear CS is favorable for high speed imaging. It is demonstrated that the -linear CS has the same axial resolution performance with higher signal-to-noise ratio (SNR) as compared with the numerical interpolation. Imaging of bio-tissue by SD-OCT with -linear CS is also demonstrated.
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