Confocal, multi-photon, and wide-field endomicroscopy often use coherent fiber-optic bundles to facilitate in vivo imaging. The narrow diameter and flexibility of these bundles allow excellent tissue access, but fabrication processes place a practical limit on fiber packing density, restricting the number of resolvable points in an image. Furthermore, the hexagonal packing of discrete fibers creates inter-fiber gaps that prevent some regions of the object from being imaged. We have combined compressed sensing (CS) principles with dispersive optics to simultaneously address these two fundamental limitations of the fiber bundle architecture. We previously reported a CS approach to improve the spatial resolution of bundle based imaging systems by recovering multiple resolvable points within each fiber (Dumas et al., Proc. SPIE 2018). This manuscript will discuss and integrate approaches for recovering object details that lie behind inter-fiber gaps with our CS-based method for resolving intra-fiber detail. First, we show that modifying our CS model to consider the whole field of view rather than a discrete point for each fiber can partially recover inter-fiber detail. Next, we outline how a dispersive component at the distal end of the bundle can be used to spectrally shift object detail such that information from all locations on the sample are transmitted through the bundle. We then implement image compounding techniques with our CS approach to produce a more continuous image. We demonstrate that our platform can produce images of biological samples with 65,536 resolved pixels using a fiber bundle with only 3,700 fiber cores.
Endomicroscopy techniques such as confocal, multi-photon, and wide-field imaging have all been demonstrated using coherent fiber-optic imaging bundles. While the narrow diameter and flexibility of fiber bundles is clinically advantageous, the number of resolvable points in an image is conventionally limited to the number of individual fibers within the bundle. We are introducing concepts from the compressed sensing (CS) field to fiber bundle based endomicroscopy, to allow images to be recovered with more resolvable points than fibers in the bundle. The distal face of the fiber bundle is treated as a low-resolution sensor with circular pixels (fibers) arranged in a hexagonal lattice. A spatial light modulator is located conjugate to the object and distal face, applying multiple high resolution masks to the intermediate image prior to propagation through the bundle. We acquire images of the proximal end of the bundle for each (known) mask pattern and then apply CS inversion algorithms to recover a single high-resolution image. We first developed a theoretical forward model describing image formation through the mask and fiber bundle. We then imaged objects through a rigid fiber bundle and demonstrate that our CS endomicroscopy architecture can recover intra-fiber details while filling inter-fiber regions with interpolation. Finally, we examine the relationship between reconstruction quality and the ratio of the number of mask elements to the number of fiber cores, finding that images could be generated with approximately 28,900 resolvable points for a 1,000 fiber region in our platform.
Compressive sensing (CS) has proven to be a viable method for reconstructing high-resolution signals using low-resolution measurements. Integrating CS principles into an optical system allows for higher-resolution imaging using lower-resolution sensor arrays. In contrast to prior works on CS-based imaging, our focus in this paper is on imaging through fiber-optic bundles, in which manufacturing constraints limit individual fiber spacing to around 2 μm. This limitation essentially renders fiber-optic bundles as low-resolution sensors with relatively few resolvable points per unit area. These fiber bundles are often used in minimally invasive medical instruments for viewing tissue at macro and microscopic levels. While the compact nature and flexibility of fiber bundles allow for excellent tissue access in-vivo, imaging through fiber bundles does not provide the fine details of tissue features that is demanded in some medical situations. Our hypothesis is that adapting existing CS principles to fiber bundle-based optical systems will overcome the resolution limitation inherent in fiber-bundle imaging. In a previous paper we examined the practical challenges involved in implementing a highly parallel version of the single-pixel camera while focusing on synthetic objects. This paper extends the same architecture for fiber-bundle imaging under incoherent illumination and addresses some practical issues associated with imaging physical objects. Additionally, we model the optical non-idealities in the system to get lower modelling errors.
We are investigating compressive sensing architectures for applications in endomicroscopy, where the narrow diameter
probes required for tissue access can limit the achievable spatial resolution. We hypothesize that the compressive sensing
framework can be used to overcome the fundamental pixel number limitation in fiber-bundle based endomicroscopy by
reconstructing images with more resolvable points than fibers in the bundle. An experimental test platform was
assembled to evaluate and compare two candidate architectures, based on introducing a coded amplitude mask at either a
conjugate image or Fourier plane within the optical system. The benchtop platform consists of a common illumination
and object path followed by separate imaging arms for each compressive architecture. The imaging arms contain a
digital micromirror device (DMD) as a reprogrammable mask, with a CCD camera for image acquisition. One arm has
the DMD positioned at a conjugate image plane (“IP arm”), while the other arm has the DMD positioned at a Fourier
plane (“FP arm”). Lenses were selected and positioned within each arm to achieve an element-to-pixel ratio of 16
(230,400 mask elements mapped onto 14,400 camera pixels). We discuss our mathematical model for each system arm
and outline the importance of accounting for system non-idealities. Reconstruction of a 1951 USAF resolution target
using optimization-based compressive sensing algorithms produced images with higher spatial resolution than bicubic
interpolation for both system arms when system non-idealities are included in the model. Furthermore, images generated
with image plane coding appear to exhibit higher spatial resolution, but more noise, than images acquired through
Fourier plane coding.
State-of-the-art sparse recovery methods often rely on the restricted isometry property for their theoretical guarantees. However, they cannot explicitly incorporate metrics such as restricted isometry constants within their recovery procedures due to the computational intractability of calculating such metrics. This paper formulates an iterative algorithm, termed yet another matching pursuit algorithm (YAMPA), for recovery of sparse signals from compressive measurements. YAMPA differs from other pursuit algorithms in that: (i) it adapts to the measurement matrix using a threshold that is explicitly dependent on two computable coherence metrics of the matrix, and (ii) it does not require knowledge of the signal sparsity. Performance comparisons of YAMPA against other matching pursuit and approximate message passing algorithms are made for several types of measurement matrices. These results show that while state-of-the-art approximate message passing algorithms outperform other algorithms (including YAMPA) in the case of well-conditioned random matrices, they completely break down in the case of ill-conditioned measurement matrices. On the other hand, YAMPA and comparable pursuit algorithms not only result in reasonable performance for well-conditioned matrices, but their performance also degrades gracefully for ill-conditioned matrices. The paper also shows that YAMPA uniformly outperforms other pursuit algorithms for the case of thresholding parameters chosen in a clairvoyant fashion. Further, when combined with a simple and fast technique for selecting thresholding parameters in the case of ill-conditioned matrices, YAMPA outperforms other pursuit algorithms in the regime of low undersampling, although some of these algorithms can outperform YAMPA in the regime of high undersampling in this setting.
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