Noise-reduction algorithms for optimization-based imaging through multi-mode fiber

Abstract

Three modifications are shown to improve resolution and reduce noise amplification in endoscopic imaging through multi-mode fiber using optimization-based reconstruction (OBR). First, random sampling patterns are replaced by sampling patterns designed to have more nearly equal singular values. Second, the OBR algorithm uses a point-spread function based on the estimated spatial frequency spectrum of the object. Third, the OBR algorithm gives less weight to modes having smaller singular values. In simulations for a step-index fiber supporting 522 spatial modes, the modifications yield a 20% reduction in image error (l(2) norm) in the noiseless case, and a further 33% reduction in image error at a 22-dB shot noise-limited SNR as compared to the original method using random sampling patterns and OBR.

Design of flexible multi-mode fiber endoscope

“…Mathematically, the endoscope apparatus can be described using Eqs. (6) and (7). From the proximal end to the distal end, the transmission path through the endoscope consists of the MMF and reflector, and is described by:…”

“…Ideally, these should be measured during endoscope fabrication; they can be measured accurately as long as U is known, as seen in Eqs. (6) and (7). A possible procedure for measuring T and R is to measure U before the reflector is attached, attach the reflector while keeping the MMF unperturbed, and then measure the transmitted and reflected light to determine T and R using Eqs.…”

“…A possible procedure for measuring T and R is to measure U before the reflector is attached, attach the reflector while keeping the MMF unperturbed, and then measure the transmitted and reflected light to determine T and R using Eqs. (6) and (7). The calibration procedure is now described.…”

“…Multi-mode fiber (MMF) endoscopes are a class of endoscope that can be made much thinner than endoscopes of other designs [1], while maintaining a high resolution [2], opening up new medical applications [3]. Recent improvements in imaging speed [4,5] and signal-to-noise ratio (SNR) [6,7], as well as numerous other developments [8][9][10][11][12], bring these endoscopes closer to being practical medical devices, and biological imaging has been demonstrated in several experiments [7,10,13]. All MMF endoscopes require a calibration procedure to measure the mode coupling in the MMF before they can be used for imaging.…”

Two-photon imaging through a multimode fiber

“…In a similar fashion to scattering media [9][10][11][12][13], wavefront shaping methods using MCFs and multimode fibers (MMFs) have been able to effectively "de-pixelate" images to obtain diffraction limited resolution. Wavefront shaping methods include phase conjugation in the analog or digital domain [14][15][16][17][18][19], transmission matrix to provide wide field imaging [20][21][22][23] and iterative optimization [24][25][26][27][28][29][30]. However, these imaging approaches have been demonstrated using monochromatic light sources.…”