Speckle reduction by I-divergence regularization in optical coherence tomography

For optical coherence tomography (OCT), ultrasound, synthetic-aperture radar, and other coherent ranging methods, speckle can cause spurious detail that detracts from the utility of the image. It is a problem inherent to imaging densely scattering objects with limited bandwidth. Using a method of regularization by minimizing Csiszar's I-divergence measure, we derive a method of speckle minimization that produces an image that both is consistent with the known data and extrapolates additional detail based on constraints on the magnitude of the image. This method is demonstrated on a test image and on an OCT image of a Xenopus laevis tadpole. © 2005 Optical Society of America OCIS codes: 100.3010, 110.4500. 2 (OCT), ultrasound, and synthetic-aperture radar. Natural objects usually contain detail at all scales, but most coherent ranging instruments can probe these details in only a narrow bandwidth of frequencies. The re- sult is speckle, which is caused by the seemingly random interference of scatterers within a resolution cell of the in- strument. Speckle randomizes the amplitudes of points in the image, which obscures fine features but generally al- lows coarse features to be resolved. We propose and dem- onstrate a method of regularization that removes these small-scale amplitude changes without smoothing the im- age. This is achieved by constraining the resulting recon- structed image to be consistent in a least-squares sense with the known data, while simultaneously utilizing Csiszar's I-divergence measure 3,4 to constrain and regu- larize the amplitudes of the reconstructed data. By ensur- ing that the resulting image is consistent with the known data, the detail is retained, while additional bandwidth is extrapolated to make the amplitudes of the image consis- tent with the regularization. Most natural objects, especially those biological in ori- gin, have detail at length scales from the macroscopic to the atomic. Unfortunately, because of instrument limita- tions and the attenutation of radiation by the sample, only a finite signal bandwidth can be utilized for useful resolution from the sample. The phenomenon of speckle in these imaging modalities is caused by the interference between scatterers that are too small and too close to- gether to be individually resolved. What is observed is a seemingly random modulation of the amplitude of the im- age as a result of the interference of scattered waves from these unresolved scatterers. Unfortunately, it is difficult in practice to differentiate between the features that are caused by the speckle modulation and the features of interest. Because scatter- ers are randomly placed in most natural objects, the coarse detail tends to be present in almost any frequency bandwidth that is much wider than the reciprocal of the minimum feature size one wishes to resolve. This is what enables most coherent ranging techniques to be used in practice. However, as one considers distinguishing fea- tures on the minimally resolvable scale of the instrument, it is less certain whether a certain feature is due to the random modulation of speckle or to scatterers with larger sizes.