Ram Mohan Vasu

Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map

We describe a noniterative method for recovering optical absorption coefficient distribution from the absorbed energy map reconstructed using simulated and noisy boundary pressure measurements. The source reconstruction problem is first solved for the absorbed energy map corresponding to single- and multiple-source illuminations from the side of the imaging plane. It is shown that the absorbed energy map and the absorption coefficient distribution, recovered from the single-source illumination with a large variation in photon flux distribution, have signal-to-noise ratios comparable to those of the reconstructed parameters from a more uniform photon density distribution corresponding to multiple-source illuminations. The absorbed energy map is input as absorption coefficient times photon flux in the time-independent diffusion equation (DE) governing photon transport to recover the photon flux in a single step. The recovered photon flux is used to compute the optical absorption coefficient distribution from the absorbed energy map. In the absence of experimental data, we obtain the boundary measurements through Monte Carlo simulations, and we attempt to address the possible limitations of the DE model in the overall reconstruction procedure.

Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography

We suitably adapt the design of a tissue-equivalent phantom used for photoacoustic imaging to construct phantoms for optical elastography. The elastography phantom we consider should have optical properties such as scattering coefficient, scattering anisotropy factor, and refractive index; mechanical properties such as storage and loss modulus; and acoustic properties such as ultrasound velocity, attenuation coefficient, and acoustic impedance to match healthy and diseased tissues. The phantom is made of poly (vinyl alcohol) (PVA) and its mechanical, optical, and acoustic properties are tailored by physical cross-linking effected through subjecting a suitable mix of PVA stock and water to a number of freeze-thaw cycles and by varying the degree of hydrolysis in the PVA stock. The optical, mechanical, and acoustic properties of the samples prepared are measured by employing different techniques. The measured variations in the values of optical scattering coefficient, scattering anisotropy factor, and refractive index and storage modulus are found to be comparable to those in normal and diseased breast tissues. The acoustic properties such as sound speed, acoustic attenuation coefficient, and density are found to be close to the average values reported in the literature for normal breast tissue.

Wavelet based compression and denoising of optical tomography data

Abstract 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 12.0×10 6 per cm 3 . This method achieves a compression ratio of ≈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.

Reconstruction of optical properties of low-scattering tissue using derivative estimated through perturbation Monte-Carlo method

An iterative method for the reconstruction of optical properties of a low-scattering object, which uses a Monte-Carlo-based forward model, is developed. A quick way to construct and update the Jacobian needed to reconstruct a discretized object, based on the perturbation Monte-Carlo (PMC) approach, is demonstrated. The projection data is handled either one view at a time, using a propagation-backpropagation (PBP) strategy where the dimension of the inverse problem and consequently the computation time are smaller, or, when this approach failed, using all the views simultaneously with a full dataset. The main observations and results are as follows. 1. Whereas the PMC gives an accurate and quick method for constructing the Jacobian the same, when adapted to update the computed projection data, the data are not accurate enough for use in the iterative reconstruction procedure leading to convergence. 2. The a priori assumption of the location of inhomogeneities in the object reduces the dimension of the problem, leading to faster convergence in all the cases considered, such as an object with multiple inhomogeneities and data handled one view at a time (i.e., the PBP approach). 3. On the other hand, without a priori knowledge of the location of inhomogeneities, the problem was too ill posed for the PBP approach to converge to meaningful reconstructions when both absorption and scattering coefficients are considered as unknowns. Finally, to bring out the effectiveness of this method for reconstructing low-scattering objects, we apply a diffusion equation-based algorithm on a dataset from one of the low-scattering objects and show that it fails to reconstruct object inhomogeneities.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements

We propose a pseudo-dynamic form of a sub-optimal Kalman filter for elastography of plane-strain models of soft tissues under strictly static deformations and partial measurements. Since the tissue material is nearly incompressible and is thus prone to volumetric locking via standard displacement-based finite element formulations, we use a Cosserat point approach for deriving the static equilibrium equations. A pseudo-dynamical form of the equilibrium equations, with added noise and appropriate augmentation by the discretized shear modulus as additional states, is then adopted as the process equation such that its steady-state solution approaches the static response of the plane-strain model. A fictitious noise of small intensity is also added to the measurement equation and, following linearization of the process equation, a Kalman filter is applied to reconstruct the shear modulus profile. We present several numerical experiments, some of which also bring forth the relative advantages of the proposed approach over a deterministic reconstruction based on a quasi-Newton search.

Imaging in turbid media by modified filtered back projection method using data from Monte Carlo simulation

Noninvasive diagnosis in medicine has shown considerable attention in recent years. Several methods are already available for imaging the biological tissue like X-ray computerized tomography, magentic resonance imaging and ultrasound imaging et c. But each of these methods has its own disadvantages. Optical tomography which uses NIR light is one of the emerging methods in teh field of medical imaging because it is non-invasive in nature. The only problem that occurs in using light for imaging the tissue is that it is highly scattered inside tissue, so the propagation of light in tissue is not confined to straight lines as is the case with X-ray tomography. Therefore the need arises to understand the behaviour of propagation of light in tissue. There are several methods for light interaction with tissue. Monte Carlo method is one of these methods which is a simple technique for simulation of light through tissue. The only problem faced with Monte Carlo simulation is its high computational time. Once the data is obtained using Monte Carlo simulation, it need to be inverted to obtain the reconstruction of tissue image. There are standard methods of reconstruction like algebraic reconstruction method, filtered backprojection method etc. But these methods can not be used as such in the case when light is used as probing radiations because it is highly scattered inside the tissue. The standard filtered backprojection method has been modified so that the zigzag path of photons is taken into consideration while back projecting the data. This is achieved by dividing the tissue domain in a square grid and storing the average path traversed in each grid element. It has been observed that the reconstruction obtained using this modification is much better than the result in case of standard filtered backprojection method.

Optical tomographic microscope for quantitative imaging of phase objects

We describe a tomographic microscope, for imaging phase objects, that makes use of the transport-of-intensity equation to estimate the phase of the transmitted light through the object. The wave-front data from optical fibers are reconstructed with an algorithm that incorporates correction for the ray bending. The reconstructed refractive-index cross sections of the fibers are found to be in agreement with the available values specified in the catalogs.

Construction of a phase-inverting grating and its use in a deblurring filter

A method of generating phase-inverting grids for use in image deblurring is described. We have also made an amplitude filter for correcting motion blurred images. This was used along with the phase-inverting grid to deblur motion blurred pictures. Experimental results are presented. It is shown that increasing the noise term in a Wiener filter helps in the reduction of noise but occasions loss of resolving power.

Diffuse optical tomography through solving a system of quadratic equations: theory and simulations

This paper discusses the iterative solution of the nonlinear problem of optical tomography. In the established forward model-based iterative image reconstruction (MOBIIR) method a linear perturbation equation containing the first derivative of the forward operator is solved to obtain the update vector for the optical properties. In MOBIIR, the perturbation equation is updated by recomputing the first derivative after each update of the optical properties. In the method presented here a nonlinear perturbation equation, containing terms up to the second derivative, is used to iteratively solve for the optical property updates. Through this modification, reconstructions with reasonable contrast recovery and accuracy are obtained without the need for updating the perturbation equation and therefore eliminating the outer iteration of the usual MOBIIR algorithm. To improve the performance of the algorithm the outer iteration is reintroduced in which the perturbation equation is recomputed without re-estimating the derivatives and with only updated computed data. The system of quadratic equations is solved using either a modified conjugate gradient descent scheme or a two-step linearized predictor-corrector scheme. A quick method employing the adjoint of the forward operator is used to estimate the derivatives. By solving the nonlinear perturbation equation it is shown that the iterative scheme is able to recover large contrast variations in absorption coefficient with improved noise tolerance in data. This ability has not been possible so far with linear algorithms. This is demonstrated by presenting results of numerical simulations from objects with inhomogeneous inclusions in absorption coefficient with different contrasts and shapes.