Samir Kumar Biswas

Improving image quality in Electrical Impedance Tomography (EIT) using Projection Error Propagation-based Regularization (PEPR) technique: A simulation study

Abstract A Projection Error Propagation-based Regularization (PEPR) method is proposed and the reconstructed image quality is improved in Electrical Impedance Tomography (EIT). A projection error is produced due to the misfit of the calculated and measured data in the reconstruction process. The variation of the projection error is integrated with response matrix in each iteration and the reconstruction is carried out in EIDORS. The PEPR method is studied with the simulated boundary data for different inhomogeneity geometries. Simulated results demonstrate that the PEPR technique improves image reconstruction precision in EIDORS and hence it can be successfully implemented to increase the reconstruction accuracy in EIT.

Improving Conductivity Image Quality Using Block Matrix-based Multiple Regularization (BMMR) Technique in EIT: A Simulation Study

Abstract A Block Matrix based Multiple Regularization (BMMR) technique is proposed for improving conductivity image quality in Electrical Impedance Tomography (EIT). The response matrix (JTJ) has been partitioned into several sub-block matrices and the largest element of each sub-block matrix has been chosen as regularization parameter for the nodes contained by that sub-block. Simulated boundary data are generated for circular domains with circular inhomogeneities of different geometry and the conductivity images are reconstructed in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm. Conductivity images are reconstructed with BMMR technique and the results are compared with the Single-step Tikhonov Regularization (STR) and modified Levenberg-Marquardt Regularization (LMR) methods. Results show that the BMMR technique improves the impedance image and its spatial resolution for single and multiple inhomogeneity phantoms of different geometries. It is observed that the BMMR technique reduces the projection error as well as the solution error and improves the conductivity reconstruction in EIT. Results also show that the BMMR method improves the image contrast and inhomogeneity conductivity profile by reducing background noise for all the phantom configurations.

Improving the image reconstruction in Electrical Impedance Tomography (EIT) with block matrix-based Multiple Regularization (BMMR): A practical phantom study

Conductivity image reconstruction is studied with a Block Matrix based Multiple Regularization (BMMR) technique in Electrical Impedance Tomography (EIT) using practical phantoms. The response matrix (JTJ) is partitioned into several sub-block matrices and the largest element of each sub-block matrices is taken as regularization parameter for the nodes of the FEM mesh contained by that sub-block. Boundary potential data are collected from practical phantoms with different inhomogeneity configurations and the conductivity images are reconstructed in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm. Conductivity images, reconstructed with BMMR technique, are compared with the images obtained with Single-step Tikhonov Regularization (STR) and modified Levenberg-Marquardt Regularization (LMR) methods. Results show that BMMR technique reduces the reconstruction error and reconstruct the better conductivity images by improving the conductivity profile of the domain under test for all the phantoms. Image analysis showed that the BMMR method improves image contrast parameters, conductivity profiles, and spatial resolution of the reconstructed images.

Image reconstruction in electrical impedance tomography (EIT) with projection error propagation-based regularization (PEPR): a practical phantom study

Resistivity reconstruction of practical phantoms is studied with Projection Error Propagation-based Regularization (PEPR) method to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method calculates the regularization parameter as a function of the projection error produced due to the mismatch between experimental measurements and the calculated data. The regularization parameter in the reconstruction algorithm automatically adjusts its magnitude depending on the noise level present in measured data as well as the ill-posedness of the Hessian matrix. Resistivity images are reconstructed from the practical phantom data using the Electrical Impedance Diffuse Optical Reconstruction Software (EIDORS). The resistivity images reconstructed with PEPR method are compared with the Single step Tikhonov Regularization (STR) and Modified Levenberg Regularization (LMR) techniques. The results show that, the PEPR technique reduces the reconstruction errors in each iteration and improves the reconstructed images with better contrast to noise ratio (CNR), percentage of contrast recovery (PCR), coefficient of contrast (COC) and diametric resistivity profile (DRP).

Accelerated gradient based diffuse optical tomographic image reconstruction

PURPOSE Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). METHODS DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. RESULTS Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. CONCLUSIONS We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

Design of a flexure for surface forces apparatus

We report the design of a variation of a double cantilever flexure system used for the measurement of displacement and force in surface force apparatus (SFA). The new force sensor is called dual double cantilever. The simple cantilever flexure suffers rotation, sideways deflection, and thermal expansion at the free end when loaded normally and asymmetrically. In the double cantilever these errors are minimized to a second order. In the dual double cantilever flexure the stiffness is enhanced 16 times as that of a single cantilever flexure but the rotation, sideways deflection, and thermal expansion at the free end are brought to many orders below the instrument resolutions. The new design enables the measurement of deflection by optical and capacitive sensing methods. The stiffness and the strain of the aluminum alloy [AUG1(2024)] flexure were estimated [dimensions, length (l=50.5 mm), breadth (b=10.5 mm), and thickness (t=1.2 mm)] by finite element method and were also validated experimentally. The finite element method was also used to create a map for the selection of a flexure geometry relevant to the properties of material under investigation by a SFA or a nanoindenter.

Diffuse optical tomographic imager using a single light source

Near-infrared diffuse optical tomography (DOT) technique has the capability of providing good quantitative reconstruction of tissue absorption and scattering properties with additional inputs such as input and output modulation depths and correction for the photon leakage. We have calculated the two-dimensional (2D) input modulation depth from three-dimensional (3D) diffusion to model the 2D diffusion of photons. The photon leakage when light traverses from phantom to the fiber tip is estimated using a solid angle model. The experiments are carried for single (5 and 6 mm) as well as multiple inhomogeneities (6 and 8 mm) with higher absorption coefficient in a homogeneous phantom. Diffusion equation for photon transport is solved using finite element method and Jacobian is modeled for reconstructing the optical parameters. We study the development and performance of DOT system using modulated single light source and multiple detectors. The dual source methods are reported to have better reconstruction capabilities to resolve and localize single as well as multiple inhomogeneities because of its superior noise rejection capability. However, an experimental setup with dual sources is much more difficult to implement because of adjustment of two out of phase identical light probes symmetrically on either side of the detector during scanning time. Our work shows that with a relatively simpler system with a single source, the results are better in terms of resolution and localization. The experiments are carried out with 5 and 6 mm inhomogeneities separately and 6 and 8 mm inhomogeneities both together with absorption coefficient almost three times as that of the background. The results show that our experimental single source system with additional inputs such as 2D input/output modulation depth and air fiber interface correction is capable of detecting 5 and 6 mm inhomogeneities separately and can identify the size difference of multiple inhomogeneities such as 6 and 8 mm. The localization error is zero. The recovered absorption coefficient is 93% of inhomogeneity that we have embedded in experimental phantom.

Measurement of stiffness and damping constant of self-assembled monolayers

We design and fabricate an apparatus which uses two dual double cantilever flexures to probe mechanical properties of self-assembled monolayers (SAM) under compression. The cantilevers were designed to give stiffness of the same order as the SAM. One of the cantilevers carrying the probe is vibrated sinusoidally at subresonance frequency and subnanometric amplitude while the dynamic response of the other carrying the SAM is recorded in the contact mode to yield data which could be deconvoluted to give stiffness and damping constant of the SAM under compression using a model of viscoelasticity. We validate the apparatus as well as the method of deconvolution by indenting bulk polytetrafluoroethylene and estimate mechanical properties of SAMs of different chain length and head group. The approach adopted here is able to distinguish in terms of mechanical properties a bulk polymer from a SAM and also between two SAMs of similar but subtly different structure.

A Model Based Iterative Image Reconstruction (MoBIIR) Algorithm for Conductivity Imaging in EIT Using Simulated Boundary Data

A Model Based Iterative Image Reconstruction (MoBIIR) algorithm is developed for impedance image reconstruction of Electrical Impedance Tomography (EIT). Simulated boundary data are generated for circular phantom configuration and the conductivity images are reconstructed with different regularization techniques and regularization parameters. Results show that the algorithm successfully reconstructs the conductivity distribution of the domain under test with its proper inhomogeneity and background conductivity. CNR and PCR of the reconstructed images are found high in both STR and LMR methods. Results show that the normalized projection errors in STR and LMR are same with higher value of λ where as the LMR method has low normalized projection errors compared to STR method with lower value of λ.

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.