Non-interferometric methods of phase estimation for application in optical tomography

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.

Wavelet based compression and denoising of optical tomography data

Two methods based on wavelet/wavelet packet expansion to denoise and compress optical tomography data containing scattered noise are presented, In the first, the wavelet expansion coefficients of noisy data are shrunk using a soft threshold. In the second, the data are expanded into a wavelet packet tree upon which a best basis search is done. The resulting coefficients are truncated on the basis of energy content. It can be seen that the first method results in efficient denoising of experimental data when scattering particle density in the medium surrounding the object was up to 12.0 x 10(6) per cm(3). This method achieves a compression ratio of approximate to 8:1. The wavelet packet based method resulted in a compression of up to 11:1 and also exhibited reasonable noise reduction capability. Tomographic reconstructions obtained from denoised data are presented. (C) 1999 Published by Elsevier Science B.V. All rights reserved,

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data. (C) 2011 Optical Society of America

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). (C) 2011 Optical Society of America

Ultrasound-modulated optical tomography: recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation

We address a certain inverse problem in ultrasound-modulated optical tomography: the recovery of the amplitude of vibration of scatterers [p(r)] in the ultrasound focal volume in a diffusive object from boundary measurement of the modulation depth (M) of the amplitude autocorrelation of light [phi(r, tau)] traversing through it. Since M is dependent on the stiffness of the material, this is the precursor to elasticity imaging. The propagation of phi(r, tau) is described by a diffusion equation from which we have derived a nonlinear perturbation equation connecting p(r) and refractive index modulation [Delta n(r)] in the region of interest to M measured on the boundary. The nonlinear perturbation equation and its approximate linear counterpart are solved for the recovery of p(r). The numerical results reveal regions of different stiffness, proving that the present method recovers p(r) with reasonable quantitative accuracy and spatial resolution. (C) 2011 Optical Society of America

Ultrasound modulated optical tomography: Young's modulus of the insonified region from measurement of natural frequency of vibration

We demonstrate a method to recover the Young's modulus (E) of a tissue-mimicking phantom from measurements of ultrasound modulated optical tomography (UMOT). The object is insonified by a dualbeam, confocal ultrasound transducer (US) oscillating at frequencies f(0) and f(0) + Delta f and the variation of modulation depth (M) in the autocorrelation of light traversed through the focal region of the US transducer against Delta f is measured. From the dominant peaks observed in the above variation, the natural frequencies of the insonified region associated with the vibration along the US transducer axis are deduced. A consequence of the above resonance is that the speckle fluctuation at the resonance frequency has a higher signal-to-noise to ratio (SNR). From these natural frequencies and the associated eigenspectrum of the oscillating object, Young's modulus (E) of the material in the focal region is recovered. The working of this method is confirmed by recovering E in the case of three tissue-mimicking phantoms of different elastic modulus values. (C) 2011 Optical Society of America

Studying the resistivity imaging of chicken tissue phantoms with different current patterns in Electrical Impedance Tomography (EIT)

A current injection pattern in Electrical Impedance Tomography (EIT) has its own current distribution profile within the domain under test. Hence, different current patterns have different sensitivity, spatial resolution and distinguishability. Image reconstruction studies with practical phantoms are essential to assess the performance of EIT systems for their validation, calibration and comparison purposes. Impedance imaging of real tissue phantoms with different current injection methods is also essential for better assessment of the biomedical EIT systems. Chicken tissue paste phantoms and chicken tissue block phantoms are developed and the resistivity image reconstruction is studied with different current injection methods. A 16-electrode array is placed inside the phantom tank and the tank is filled with chicken muscle tissue paste or chicken tissue blocks as the background mediums. Chicken fat tissue, chicken bone, air hole and nylon cylinders are used as the inhomogeneity to obtained different phantom configurations. A low magnitude low frequency constant sinusoidal current is injected at the phantom boundary with opposite and neighboring current patterns and the boundary potentials are measured. Resistivity images are reconstructed from the boundary data using EIDORS and the reconstructed images are analyzed with the contrast parameters calculated from their elemental resistivity profiles. Results show that the resistivity profiles of all the phantom domains are successfully reconstructed with a proper background resistivity and high inhomogeneity resistivity for both the current injection methods. Reconstructed images show that, for all the chicken tissue phantoms, the inhomogeneities are suitably reconstructed with both the current injection protocols though the chicken tissue block phantom and opposite method are found more suitable. It is observed that the boundary potentials of the chicken tissue block phantoms are higher than the chicken tissue paste phantom. SNR of the chicken tissue block phantoms are found comparatively more and hence the chicken tissue block phantom is found more suitable for its lower noise performance. The background noise is found less in opposite method for all the phantom configurations which yields the better resistivity images with high PCR and COC and proper IRMean and IRMax neighboring method showed higher noise level for both the chicken tissue paste phantoms and chicken tissue block phantoms with all the inhomogeneities. Opposite method is found more suitable for both the chicken tissue phantoms, and also, chicken tissue block phantoms are found more suitable compared to the chicken tissue paste phantom. (C) 2012 Elsevier Ltd. All rights reserved.

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

Ultrasound Assisted Optical Tomography: Estimation of phase Shift experienced by photon on transit through US insonified region for detection of breast tumor

A Monte Carlo model of ultrasound modulation of multiply scattered coherent light in a highly scattering media has been carried out for estimating the phase shift experienced by a photon beam on its transit through US insonified region. The phase shift is related to the tissue stiffness, thereby opening an avenue for possible breast tumor detection. When the scattering centers in the tissue medium is exposed to a deterministic forcing with the help of a focused ultrasound (US) beam, due to the fact that US-induced oscillation is almost along particular direction, the direction defined by the transducer axis, the scattering events increase, thereby increasing the phase shift experienced by light that traverses through the medium. The phase shift is found to increase with increase in anisotropy g of the medium. However, as the size of the focused region which is the region of interest (ROI) increases, a large number of scattering events take place within the ROI, the ensemble average of the phase shift (Delta phi) becomes very close to zero. The phase of the individual photon is randomly distributed over 2 pi when the scattered photon path crosses a large number of ultrasound wavelengths in the focused region. This is true at high ultrasound frequency (1 MHz) when mean free path length of photon l(s) is comparable to wavelength of US beam. However, at much lower US frequencies (100 Hz), the wavelength of sound is orders of magnitude larger than l(s), and with a high value of g (g 0.9), there is a distinct measurable phase difference for the photon that traverses through the insonified region. Experiments are carried out for validation of simulation results.

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. (c) 2012 Optical Society of America

Correlation of Calcification on Excised Aortic Valves by Micro-Computed Tomography with Severity of Aortic Stenosis

Background and aim of the study: The quantification of incidentally found aortic valve calcification on computed tomography (CT) is not performed routinely, as data relating to the accuracy of aortic valve calcium for estimating the severity of aortic stenosis (AS) is neither consistent nor validated. As aortic valve calcium quantification by CT is confounded by wall and coronary ostial calcification, as well as motion artifact, the ex-vivo micro-computed tomography (micro-CT) of stenotic aortic valves allows a precise measurement of the amounts of calcium present. The study aim, using excised aortic valves from patients with confirmed AS, was to determine if the amount of calcium on micro-CT correlated with the severity of AS. Methods: Each of 35 aortic valves that had been excised from patients during surgical valve replacement were examined using micro-CT imaging. The amount of calcium present was determined by absolute and proportional values of calcium volume in the specimen. Subsequently, the correlation between calcium volume and preoperative mean aortic valve gradient (MAVG), peak transaortic velocity (V-max), and aortic valve area (AVA) on echocardiography, was evaluated. Results: The mean calcium volume across all valves was 603.2 +/- 398.5 mm(3), and the mean ratio of calcium volume to total valve volume was 0.36 +/- 0.16. The mean aortic valve gradient correlated positively with both calcium volume and ratio (r = 0.72, p <0.001). V-max also correlated positively with the calcium volume and ratio (r = 0.69 and 0.76 respectively; p <0.001). A logarithmic curvilinear model proved to be the best fit to the correlation. A calcium volume of 480 mm(3) showed sensitivity and specificity of 0.76 and 0.83, respectively, for a diagnosis of severe AS, while a calcium ratio of 0.37 yielded sensitivity and specificity of 0.82 and 0.94, respectively. Conclusion: A radiological estimation of calcium amount by volume, and its proportion to the total valve volume, were shown to serve as good predictive parameters for severe AS. An estimation of the calcium volume may serve as a complementary measure for determining the severity of AS when aortic valve calcification is identified on CT imaging. The Journal of Heart Valve Disease 2012;21:320-327

Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography

Purpose: To optimize the data-collection strategy for diffuse optical tomography and to obtain a set of independent measurements among the total measurements using the model based data-resolution matrix characteristics. Methods: The data-resolution matrix is computed based on the sensitivity matrix and the regularization scheme used in the reconstruction procedure by matching the predicted data with the actual one. The diagonal values of data-resolution matrix show the importance of a particular measurement and the magnitude of off-diagonal entries shows the dependence among measurements. Based on the closeness of diagonal value magnitude to off-diagonal entries, the independent measurements choice is made. The reconstruction results obtained using all measurements were compared to the ones obtained using only independent measurements in both numerical and experimental phantom cases. The traditional singular value analysis was also performed to compare the results obtained using the proposed method. Results: The results indicate that choosing only independent measurements based on data-resolution matrix characteristics for the image reconstruction does not compromise the reconstructed image quality significantly, in turn reduces the data-collection time associated with the procedure. When the same number of measurements (equivalent to independent ones) are chosen at random, the reconstruction results were having poor quality with major boundary artifacts. The number of independent measurements obtained using data-resolution matrix analysis is much higher compared to that obtained using the singular value analysis. Conclusions: The data-resolution matrix analysis is able to provide the high level of optimization needed for effective data-collection in diffuse optical imaging. The analysis itself is independent of noise characteristics in the data, resulting in an universal framework to characterize and optimize a given data-collection strategy. (C) 2012 American Association of Physicists in Medicine. http://dx.doi.org/10.1118/1.4736820]

Zero-crossing approach to high-resolution reconstruction in frequency-domain optical-coherence tomography

We address the problem of high-resolution reconstruction in frequency-domain optical-coherence tomography (FDOCT). The traditional method employed uses the inverse discrete Fourier transform, which is limited in resolution due to the Heisenberg uncertainty principle. We propose a reconstruction technique based on zero-crossing (ZC) interval analysis. The motivation for our approach lies in the observation that, for a multilayered specimen, the backscattered signal may be expressed as a sum of sinusoids, and each sinusoid manifests as a peak in the FDOCT reconstruction. The successive ZC intervals of a sinusoid exhibit high consistency, with the intervals being inversely related to the frequency of the sinusoid. The statistics of the ZC intervals are used for detecting the frequencies present in the input signal. The noise robustness of the proposed technique is improved by using a cosine-modulated filter bank for separating the input into different frequency bands, and the ZC analysis is carried out on each band separately. The design of the filter bank requires the design of a prototype, which we accomplish using a Kaiser window approach. We show that the proposed method gives good results on synthesized and experimental data. The resolution is enhanced, and noise robustness is higher compared with the standard Fourier reconstruction. (c) 2012 Optical Society of America

Prior image-constrained l(1)-norm-based reconstruction method for effective usage of structural information in diffuse optical tomography

A novel approach that can more effectively use the structural information provided by the traditional imaging modalities in multimodal diffuse optical tomographic imaging is introduced. This approach is based on a prior image-constrained-l(1) minimization scheme and has been motivated by the recent progress in the sparse image reconstruction techniques. It is shown that the proposed framework is more effective in terms of localizing the tumor region and recovering the optical property values both in numerical and gelatin phantom cases compared to the traditional methods that use structural information. (C) 2012 Optical Society of America

Minimal residual method provides optimal regularization parameter for diffuse optical tomography

The inverse problem in the diffuse optical tomography is known to be nonlinear, ill-posed, and sometimes under-determined, requiring regularization to obtain meaningful results, with Tikhonov-type regularization being the most popular one. The choice of this regularization parameter dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. An automated method for optimal selection of regularization parameter that is based on regularized minimal residual method (MRM) is proposed and is compared with the traditional generalized cross-validation method. The results obtained using numerical and gelatin phantom data indicate that the MRM-based method is capable of providing the optimal regularization parameter. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). DOI: 10.1117/1.JBO.17.10.106015]