Image reconstruction scheme that combines modified Newton method and efficient initial guess estimation for optical tomography of finger joints

A one-step method for quantitative microwave-induced thermoacoustic tomography

BACKGROUND

Electrical conductivity directly correlates with tissue functional information such as blood and water contents, and quantitative extraction of tissue conductivity is of significant importance for disease detection and diagnosis using microwave-induced thermoacoustic tomography (TAT).

OBJECTIVE

The existing quantitative TAT (qTAT) approaches capable of extracting tissue conductivity require two steps for the recovery of conductivity. Such two steps approaches depend on an accurate knowledge of the microwave energy loss distribution in tissue and offer a slow computational convergence rate. The purpose of this study is to develop a new algorithm to reconstruct tissue conductivity with higher reconstruction accuracy and greater computational efficiency.

METHODS

We propose an improved qTAT method for direct recovery of tissue conductivity from thermoacoustic data measured along the boundary with only one step without the dependence of microwave energy loss information. The feasibility of our one-step qTAT method is validated in both simulated and tissue-mimicking phantom experiments with single-target and multi-target configurations with different contrast levels.

RESULTS

Compared with the previous two-step methods, our one-step qTAT method improves the accuracy of conductivity recovery with approximately one-fold reduction in the mean absolute error (MAE) and root mean square error (RMSE) with p-values greater than 0.05. In addition, the convergence rate is improved by more than two folds for the one-step method.

CONCLUSIONS

The study demonstrates that new method can quantitatively reconstruct conductivity of tissue more accurately and efficiently over the existing qTAT methods, leading to potentially enhanced accuracy for disease detection and diagnosis.

Back-propagation neural network-based reconstruction algorithm for diffuse optical tomography

Diffuse optical tomography (DOT) is a promising noninvasive imaging modality and is capable of providing functional characteristics of biological tissue by quantifying optical parameters. The DOT image reconstruction is ill-posed and ill-conditioned, due to the highly diffusive nature of light propagation in biological tissues and limited boundary measurements. The widely used regularization technique for DOT image reconstruction is Tikhonov regularization, which tends to yield oversmoothed and low-quality images containing severe artifacts. It is necessary to accurately choose a regularization parameter for Tikhonov regularization. To overcome these limitations, we develop a noniterative reconstruction method, whereby optical properties are recovered based on a back-propagation neural network (BPNN). We train the parameters of BPNN before DOT image reconstruction based on a set of training data. DOT image reconstruction is achieved by implementing a single evaluation of the trained network. To demonstrate the performance of the proposed algorithm, we compare with the conventional Tikhonov regularization-based reconstruction method. The experimental results demonstrate that image quality and quantitative accuracy of reconstructed optical properties are significantly improved with the proposed algorithm.

A partial reconstruction scheme for continuous wave diffuse optical tomography with reflection geometry

Image quality and photon measurement with good SNR (signal to noise ratio) in continuous wave diffuse optical tomography depend on the source detector density and sensitivity of photo detector. For large volume objects, it is difficult to obtain detectable light intensity with good SNR over the whole boundary. As an alternative, instead of the full boundary, the measurements are taken over a semi circle as in reflection geometry and a partial reconstruction scheme for the same is proposed in this paper. The cross-sectional optical parameters are reconstructed for different half of the sample with modified boundary conditions and finally the average of all the reconstructions are considered as the final reconstructed image. Simulation and experimental results have been illustrated to validate the proposed method. The main advantage of this scheme is to improve signal to noise ratio which controls the quality of reconstruction in actual phantoms. The use of continuous wave measurement makes the system cost effective as well.

A systematic investigation of reflectance diffuse optical tomography using nonlinear reconstruction methods and continuous wave measurements

We conducted a systematic investigation of the reflectance diffuse optical tomography using continuous wave (CW) measurements and nonlinear reconstruction algorithms. We illustrated and suggested how to fine-tune the nonlinear reconstruction methods in order to optimize target localization with depth-adaptive regularizations, reduce boundary noises in the reconstructed images using a logarithm based objective function, improve reconstruction quantification using transport models, and resolve crosstalk problems between absorption and scattering contrasts with the CW reflectance measurements. The upgraded nonlinear reconstruction algorithms were evaluated with a series of numerical and experimental tests, which show the potentials of the proposed approaches for imaging both absorption and scattering contrasts in the deep targets with enhanced image quality.

A calibration-free, one-step method for quantitative photoacoustic tomography

PURPOSE

Recently reported quantitative photoacoustic tomography (PAT) has significantly expanded the utilities of PAT because it allows for recovery of tissue optical absorption coefficient which directly correlates with tissue physiological information. However, the recovery of optical absorption coefficient by the existing quantitative PAT approaches strongly depends on the accuracy of absorbed energy density distribution, and on the knowledge of accurate strength and distribution of incident light source. The purpose of this study is to develop a new algorithm for the reconstruction of optical absorption coefficient that does not depend on these initial parameters.

METHODS

Here the authors propose a novel one-step reconstruction approach that can directly recover optical absorption coefficient from photoacoustic measurements along boundary domain. The authors validate the method using simulation and phantom experiments.

RESULTS

The authors have demonstrated experimental evidence that it is possible to directly recover optical absorption coefficient maps using boundary photoacoustic measurements coupled with the photon diffusion equation in just one step. The authors found that the method described is able to quantitatively reconstruct absorbing objects with different sizes and optical contrast levels.

CONCLUSIONS

Compared to the authors' previous two-step methods, the reconstruction results obtained here show that the one-step scheme can significantly improve the accuracy of absorption coefficient recovery.

Optical imaging modalities for biomedical applications

Optical photographic imaging is a well known imaging method that has been successfully translated into biomedical applications such as microscopy and endoscopy. Although several advanced medical imaging modalities are used today to acquire anatomical, physiological, metabolic, and functional information from the human body, optical imaging modalities including optical coherence tomography, confocal microscopy, multiphoton microscopy, multispectral endoscopy, and diffuse reflectance imaging have recently emerged with significant potential for non-invasive, portable, and cost-effective imaging for biomedical applications spanning tissue, cellular, and molecular levels. This paper reviews methods for modeling the propagation of light photons in a biological medium, as well as optical imaging from organ to cellular levels using visible and near-infrared wavelengths for biomedical and clinical applications.

Combined domain-decomposition and matrix-decomposition scheme for large-scale diffuse optical tomography

Image reconstruction in diffuse optical tomography (DOT) is, in general, posed as a model-based, nonlinear optimization problem, which requires repeated use of the three-dimensional (3D) forward and inverse solvers. To cope with the computation and storage problem for some applications, such as breast tumor diagnosis, it is preferable to develop a subdomain-based parallel computation scheme. In this study, we propose a two-level image reconstruction scheme for 3D DOT, which combines the Schwarz-type domain-decomposition (DD)-based forward calculation and the matrix-decomposition (MD)-based inversion. In the forward calculation, the solution to the diffusion equation is initially obtained using a whole-domain finite difference method at a coarse grid, and then updated with a parallel DD scheme at a fine grid. The inversion procedure starts with the wavelet-decomposition-based reconstruction at a coarse grid, and then follows with a Levenberg-Marquardt least-squares solution at a fine grid, where an MD strategy is adopted for the relevant linear inversion. It is demonstrated that the combination of the DD-based forward solver and MD-based inversion allows for coarse-grain parallel implementation of both the forward and inverse issues and effectively reduces computation and storage loads for the large-scale problem. Also, both numerical simulations and phantom experiments show that MD-based linear inversion is superior to the row-fashioned algebraic reconstruction technique.

Direct-current-based image reconstruction versus direct-current included or excluded frequency-domain reconstruction in diffuse optical tomography

We study the level of image artifacts in optical tomography associated with measurement uncertainty under three reconstruction configurations, namely, by using only direct-current (DC), DC-excluded frequency-domain, and DC-included frequency-domain data. Analytic and synthetic studies demonstrate that, at the same level of measurement uncertainty typical to optical tomography, the ratio of the standard deviation of mu(a) over mu(a) reconstructed by DC only is at least 1.4 times lower than that by frequency-domain methods. The ratio of standard deviations of D (or mu(s)') over D (or mu(s)') reconstructed by DC only are slightly lower than those by frequency-domain methods. Frequency-domain reconstruction including DC generally outperforms that excluding DC, but as the amount of measurements increases, the difference between the two diminishes. Under the condition of a priori structural information, the performances of three reconstruction configurations are seemingly equivalent.

Comparison of diffusion approximation and higher order diffusion equations for optical tomography of osteoarthritis

In this study, a simplified spherical harmonics approximated higher order diffusion model is employed for 3-D diffuse optical tomography of osteoarthritis in the finger joints. We find that the use of a higher-order diffusion model in a stand-alone framework provides significant improvement in reconstruction accuracy over the diffusion approximation model. However, we also find that this is not the case in the image-guided setting when spatial prior knowledge from x-rays is incorporated. The results show that the reconstruction error between these two models is about 15 and 4%, respectively, for stand-alone and image-guided frameworks.

A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography

In this work, we derived three-dimensional simplified spherical harmonics approximated higher order diffusion equations. We also solved the higher order diffusion equations using a finite element method and compared the solutions from the first-order diffusion equation and Monte Carlo simulations. We found that the conducted model is able to improve the first-order diffusion solution in a transport-like homogeneous or heterogeneous medium. Reconstructed images based on the higher order diffusion model are also presented. We conclude that the developed higher order diffusion model is able to accurately describe light propagation in biological tissues and to offer improved image reconstruction.

Tomographic x-ray-guided three-dimensional diffuse optical tomography of osteoarthritis in the finger joints

We describe a multimodality imaging approach that combines x-ray tomosynthesis with near-infrared diffuse optical tomography (DOT) for high-resolution imaging of osteoarthritis in the finger joints. In this approach, we take advantage of high resolution x-ray imaging particularly of the bones and incorporate the fine structural maps obtained from x ray as a priori information into DOT reconstructions. To realize this multi-modality approach, we constructed a hybrid imaging platform that integrated a C-arm-based x-ray tomosynthetic system with a multichannel optic-fiber-based DOT system. We also implemented improved hybrid regularization-based reconstruction algorithms that have shown to be especially effective for high-resolution modality-guided DOT. Initial evaluation of our x-ray-guided DOT reconstruction approach in the finger joints shows that spatial resolution of DOT can be enhanced dramatically when the three-dimensional geometry of bones is known a priori. In particular, the improved quantitative capability of imaging absorption and scattering coefficients of the joint tissues allows for more accurate diagnosis of osteoarthritis over x-ray radiography or DOT alone.