Spatially variant regularization improves diffuse optical tomography

Diffuse tomography with near-infrared light has biomedical application for imaging hemoglobin, water, lipids, cytochromes, or exogenous contrast agents and is being investigated for breast cancer diagnosis. A Newton-Raphson inversion algorithm is used for image reconstruction of tissue optical absorption and transport scattering coefficients from frequency-domain measurements of modulated phase shift and light intensity. A variant of Tikhonov regularization is examined in which radial variation is allowed in the value of the regularization parameter. This method minimizes high-frequency noise in the reconstructed image near the source-detector locations and can produce constant image resolution and contrast across the image field.     

Model-resolution based regularization improves near infrared diffuse optical tomography

Diffuse optical tomographic imaging is known to be an ill-posed problem, and a penalty/regularization term is used in image reconstruction (inverse problem) to overcome this limitation. Two schemes that are prevalent are spatially varying (exponential) and constant (standard) regularizations/penalties. A scheme that is also spatially varying but uses the model information is introduced based on the model-resolution matrix. This scheme, along with exponential and standard regularization schemes, is evaluated objectively based on model-resolution and data-resolution matrices. This objective analysis showed that resolution characteristics are better for spatially varying penalties compared to standard regularization; and among spatially varying regularization schemes, the model-resolution based regularization fares well in providing improved data-resolution and model-resolution characteristics. The verification of the same is achieved by performing numerical experiments in reconstructing 1% noisy data involving simple two- and three-dimensional imaging domains.     

Common-path interferometer for frequency-domain optical coherence tomography

A Michelson-type spectral interferometer that uses a common beam path for the reference and the sample arms is described. This optical arrangement is more compact and stable than the more commonly used dual-arm interferometer and is well suited for frequency-domain optical coherence tomography of biological samples. With a 16-bit CCD camera, the instrument has sufficient dynamic range and resolution for imaging to depths of 2 mm in scattering biological materials. Images obtained with this spectral interferometer are presented, including cross-sectional images in a Xenopus laevis tadpole.     

High-resolution frequency-domain second-harmonic optical coherence tomography

We used continuum generated in an 8.5 cm long fiber by a femtosecond Yb fiber laser to improve threefold the axial resolution of frequency domain second-harmonic optical coherence tomography (SH-OCT) to 12 microm. The acquisition time was shortened by more than 2 orders of magnitude compared to the time-domain SH-OCT. The system was applied to image biological tissue of fish scales, pig leg tendon, and rabbit eye sclera. Highly organized collagen fibrils can be visualized in the recorded images. Polarization dependence on the SH has been used to obtain polarization resolved images.     

Multi-frequency diffuse optical tomography

The performance of diffuse optical tomography (DOT) is investigated when multi-modulation frequencies are used simultaneously in the inverse problem in order to cast the forward model. The forward model used was based on the first-order Rytov approximation of the diffusion equation. Numerical measurements were generated with a finite difference approach for configurations relevant to breast optical mammography. The impact of various frequency-set characteristics was evaluated. Furthermore, the effect of sensitivity matrix preconditioning was investigated. The criteria underlying this study were based on a ‘singular value analysis’ and parameter cross-talk between absorption and scattering reconstructions. It had been shown that preconditioning the matrix was necessary to provide accurate results and an even distribution of frequencies within the larger bound. Furthermore, correlating the different criterions used demonstrated that analysis based on optimization of condition number alone was providing misleading results.     

Deterministic regularization of three-dimensional optical diffraction tomography

In this paper, we discuss a deterministic regularization algorithm to handle the missing cone problem of three-dimensional optical diffraction tomography (ODT). The missing cone problem arises in most practical applications of ODT and is responsible for elongation of the reconstructed shape and underestimation of the value of the refractive index. By applying positivity and piecewise-smoothness constraints in an iterative reconstruction framework, we effectively suppress the missing cone artifact and recover sharp edges rounded out by the missing cone, and we significantly improve the accuracy of the predictions of the refractive index. We also show the noise-handling capability of our algorithm in the reconstruction process.     

Volume image reconstruction for diffuse optical tomography

Optical tomography is a potential diagnostic method for visualizing optical properties of tissues in vivo. We present an optical tomography method that has been designed for imaging of the human testes, particularly for spectroscopic tumor differentiation. In this application we need to compute three-dimensional distributions of the optical contrast (absorption coefficient) in the tissue in real time. Thus we have given special care to elaborate an efficient inverse algorithm that takes the limitations of spatial resolution and data space point density into account. Our inverse solution is based on a linearization approach and a dedicated object space discretization. Furthermore, we introduce the concept of fuzzy voxels, which enables a reconstruction-inherent image smoothing.     

Pseudo-time particle filtering for diffuse optical tomography

We recast the reconstruction problem of diffuse optical tomography (DOT) in a pseudo-dynamical framework and develop a method to recover the optical parameters using particle filters, i.e., stochastic filters based on Monte Carlo simulations. In particular, we have implemented two such filters, viz., the bootstrap (BS) filter and the Gaussian-sum (GS) filter and employed them to recover optical absorption coefficient distribution from both numerically simulated and experimentally generated photon fluence data. Using either indicator functions or compactly supported continuous kernels to represent the unknown property distribution within the inhomogeneous inclusions, we have drastically reduced the number of parameters to be recovered and thus brought the overall computation time to within reasonable limits. Even though the GS filter outperformed the BS filter in terms of accuracy of reconstruction, both gave fairly accurate recovery of the height, radius, and location of the inclusions. Since the present filtering algorithms do not use derivatives, we could demonstrate accurate contrast recovery even in the middle of the object where the usual deterministic algorithms perform poorly owing to the poor sensitivity of measurement of the parameters. Consistent with the fact that the DOT recovery, being ill posed, admits multiple solutions, both the filters gave solutions that were verified to be admissible by the closeness of the data computed through them to the data used in the filtering step (either numerically simulated or experimentally generated).     

Iterative boundary method for diffuse optical tomography

The recent application of tomographic methods to three-dimensional imaging through tissue by use of light often requires modeling of geometrically complex diffuse-nondiffuse boundaries at the tissue-air interface. We have recently investigated analytical methods to model complex boundaries by means of the Kirchhoff approximation. We generalize this approach using an analytical approximation, the N-order diffuse-reflection boundary method, which considers higher orders of interaction between surface elements in an iterative manner. We present the general performance of the method and demonstrate that it can improve the accuracy in modeling complex boundaries compared with the Kirchhoff approximation in the cases of small diffuse volumes or low absorption. Our observations are also contrasted with exact solutions. We furthermore investigate optimal implementation parameters and show that a second-order approximation is appropriate for most in vivo investigations.     

Minimum-phase-function-based processing in frequency-domain optical coherence tomography systems

We present a simple processing technique that uses the concept of minimum-phase functions to improve frequency-domain optical coherence tomography systems. Our approach removes the autocorrelation noise and therefore increases both the accessible depth range and the recovery accuracy. To our knowledge, this is the first time that the concept of minimum-phase functions has been applied to improve optical coherence tomography.     

采用频域快速延迟线的光学相干层析系统的研制

建立了一套单模光纤型光学相干层析(OCT)成像系统。系统采用了不同于国内其他组的新型频域快速扫描延迟线(FD-ODL)和外差平衡接受技术,采取了一系列提高系统信噪比的方法,成功地实现高信噪比(113dB)、高分辨率、大成像深度的层析图像的提取,获得了纵向分辨率9μm、横向分辨率10μm、深度2.88μm的清晰的皮肤OCT图像。该系统比传统的采用时域延迟线的OCT在信噪比上高出了一个量级。     

Time-resolved Fourier optical diffuse tomography.

Time-resolved Fourier optical diffuse tomography is a novel approach for imaging of objects in a highly scattering turbid medium with use of an incident (near) plane wave. The theory of the propagation of spatial Fourier components of the scattered wave field is presented, along with a fast algorithm for three-dimensional reconstruction in a parallel planar geometry. Examples of successful reconstructions of simulated hidden absorptive or scattering objects embedded inside a human-tissue-like semi-infinite turbid medium are provided.     

Streak camera: a multidetector for diffuse optical tomography

We describe an experimental setup for time-resolved diffuse optical tomography that uses a seven-channel light guide to transmit scattered light to a streak camera. This setup permits the simultaneous measurement of the time profiles of photons reemitted at different boundary sites of the objects studied. The instrument, its main specifications, and detector-specific data analysis before image reconstruction are described. The instrumentation was tested with phantoms simulating biological tissue, and the absorption and reduced scattering images that were obtained are discussed.     

Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography

We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss-Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant.     

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.     

Robust MR image super-resolution reconstruction with cross-modal edge-preserving regularization

In this article, we propose a novel image super-resolution (SR) reconstruction method in the field of magnetic resonance imaging, which is based on a cross-modal edge-preserving regularization integrating the internal gradient prior from the target-modal image itself and the external gradient prior from the reference-modal image obtained by pre-scan in many medical imaging scenes. The reference-modal image is a high-resolution guidance image that has much shareable information such as gradient orientation on edge regions, which can be used to improve the image resolution of the target modal. In addition, to be robust against the misalignment between the target-modal image and reference-modal image, a multimodal registration is incorporated in the SR reconstruction process. In this work, the proposed SR method can be formulated as an alternating optimization problem, that is, the target-modal and reference-modal images are alternately updated through iterations. Experimental results on simulated and realistic images show the superior performance of the proposed approach over several state-of-the-art SR techniques.     

Optode positional calibration in diffuse optical tomography

Although diffuse optical tomography is a highly promising technique used to noninvasively image blood volume and oxygenation, the reconstructed data are sensitive to systemic difference between the forward model and the actual experimental conditions. In particular, small changes in optode location or in the optode-tissue coupling coefficient significantly degrade the quality of the reconstruction images. Accurate system calibration therefore is an essential part of any experimental protocol. We present a technique for simultaneously calibrating optode positions and reconstructing images that significantly improves image quality, as we demonstrate with simulations and phantom experiments.     

Noncontact fluorescence diffuse optical tomography of heterogeneous media

Fluorescence-enhanced diffuse optical tomography is expected to be useful to the collection of functional information from small animal models. This technique is currently limited by the extent of tissue heterogeneity and management of the shape of the animals. We propose an approach based on the reconstruction of object heterogeneity, which provides an original solution to the two problems. Three evaluation campaigns are described: the first two were performed on phantoms designed to test the reconstructions in highly heterogeneous media and noncontact geometries; the third was conducted on mice with lung tumors to test fluorescence yield reconstruction feasibility in vivo.     

Image correction algorithm for functional three-dimensional diffuse optical tomography brain imaging

We outline a computationally efficient image correction algorithm, which we have applied to diffuse optical tomography (DOT) image time series derived from a magnetic resonance imaging (MRI)-based brain model. Results show that the algorithm increases spatial resolution, decreases spatial bias, and only modestly reduces temporal accuracy for noise levels typically seen in experiment, and produces results comparable to image reconstructions that incorporate information from MRI priors. We demonstrate that this algorithm has robust performance in the presence of noise, background heterogeneity, irregular external and internal boundaries, and error in the initial guess. However, the algorithm introduces artifacts when the absorption and scattering coefficients of the reference medium are overestimated--a situation that is easily avoided in practice. The considered algorithm offers a practical approach to improving the quality of images from time-series DOT, even without the use of MRI priors.