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Compressed sensing in optical coherence tomography

Optical coherence tomography (OCT) is a valuable technique for non-invasive imaging in medicine and biology. In some applications, conventional time-domain OCT (TD-OCT) has been supplanted by spectral-domain OCT (SD-OCT); the latter uses an apparatus that contains no moving parts and can achieve orders of magnitude faster imaging. This enhancement comes at a cost, however: the CCD array detectors required for SD-OCT are more expensive than the simple photodiodes used in TD-OCT. We explore the possibility of extending the notion of compressed sensing (CS) to SD-OCT, potentially allowing the use of smaller detector arrays. CS techniques can yield accurate signal reconstructions from highly undersampled measurements, i.e., data sampled significantly below the Nyquist rate. The Fourier relationship between the measurements and the desired signal in SD-OCT makes it a good candidate for compressed sensing. Fourier measurements represent good linear projections for the compressed sensing of sparse point-like signals by random under-sampling of frequency-domain data, and axial scans in OCT are generally sparse in nature. This sparsity property has recently been used for the reduction of speckle in OCT images. We have carried out simulations to demonstrate the usefulness of compressed sensing for simplifying detection schemes in SD-OCT. In particular, we demonstrate the reconstruction of a sparse axial scan by using fewer than 10 percent of the measurements required by standard SD-OCT.