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. (C) 2011 American Association of Physicists in Medicine. DOI: 10.1118/1.3531572]

Concise row-pruning algorithm to invert a matrix

Presented here, in a vector formulation, is an O(mn2) direct concise algorithm that prunes/identifies the linearly dependent (ld) rows of an arbitrary m X n matrix A and computes its reflexive type minimum norm inverse A(mr)-, which will be the true inverse A-1 if A is nonsingular and the Moore-Penrose inverse A+ if A is full row-rank. The algorithm, without any additional computation, produces the projection operator P = (I - A(mr)- A) that provides a means to compute any of the solutions of the consistent linear equation Ax = b since the general solution may be expressed as x = A(mr)+b + Pz, where z is an arbitrary vector. The rank r of A will also be produced in the process. Some of the salient features of this algorithm are that (i) the algorithm is concise, (ii) the minimum norm least squares solution for consistent/inconsistent equations is readily computable when A is full row-rank (else, a minimum norm solution for consistent equations is obtainable), (iii) the algorithm identifies ld rows, if any, and reduces concerned computation and improves accuracy of the result, (iv) error-bounds for the inverse as well as the solution x for Ax = b are readily computable, (v) error-free computation of the inverse, solution vector, rank, and projection operator and its inherent parallel implementation are straightforward, (vi) it is suitable for vector (pipeline) machines, and (vii) the inverse produced by the algorithm can be used to solve under-/overdetermined linear systems.

Cracks emanating from pin-loaded lugs

Pin-loaded lugs were analysed in the presence of cracks emanating from circular holes. The analysis presents a unified treatment of interference, push or clearance fit pins. Both metallic (isotropic) and composite (orthotropic) plates were dealt with. The finite element model used special singular six-noded quadrilateral elements at the crack tip. The non-linear load contact behaviour at the pin-hole interface was dealt with by an inverse technique. A modified crack closure integral (MCCI) technique was used to evaluate the strain energy release rates (SERRs) and stress intensity factors (SIFs) at the crack tips. Numerical results are presented showing the non-linear variation of SIF with applied stress, and the influence of the amount of interference or clearance and the interfacial friction on SIF.

Diffusion of sorbates in zeolites Y and A novel dependence on sorbate size and strength of sor ba t e-Zeoli t e interaction

A systematic investigation of monatomic spherical sorbates in the supercages of zeolites Y and A by molecular dynamics technique is presented. Rates of intercage diffusion, rates of cage visits, and the diffusion coefficients have been calculated as a function of the sorbate-zeolite interaction strength. These properties exhibit markedly different dependences on interaction strength for the two zeolites. The observed behavior is shown to be a consequence of the two principal mechanisms of intercage diffusion and the energetic barrier associated with them. The diffusion coefficient and other properties associated with intercage diffusion are found to be directly proportional to the reciprocal of the square of the sorbate diameter when the sorbate diameter is significantly smaller than the window diameter. As the sorbate diameter increases, a peak is observed in all the transport properties investigated including the diffusion coefficient. We call this surprising effect as the ring or levitation effect and it explains several anomalous results reported in the literature and suggests a breakdown of the geometrical criterion for diffusion of sorbates. It shows that under certain conditions nongeometrical factors play a major role and geometrical factors become secondary in the determination of the molecular sieve property. A generalized parameter has been proposed which suggests conditions under which one can expect the ring or levitation effect in any porous medium. Inverse size selectivity becomes operative under these conditions.

Effect of surface roughness on diffusion-limited charge transfer

A theory is developed for diffusion-limited charge transfer on a non-fractally rough electrode. The perturbation expressions are obtained for concentration, current density and measured diffusion-limited current for arbitrary one- and two-dimensional surface profiles. The random surface model is employed for a rough electrode\electrolyte interface. In this model the gross geometrical property of an electrochemically active rough surface - the surface structure factor-is related to the average electrode current, current density and concentration. Under short and long time regimes, various morphological features of the rough electrodes, i.e. excess area (related to roughness slope), curvature, correlation length, etc. are related to the (average) current transients. A two-point Pade approximant is used to develop an all time average current expression in terms of partial morphological features of the rough surface. The inverse problem of predicting the surface structure factor from the observed transients is also described. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how the surface roughness enhances the overall diffusion-limited charge transfer current.

Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse sinh square of the distance. This interaction contains a variable range as a parameter and can thus interpolate between the known solutions for the nearest-neighbor chain and the inverse-square chain. The energy, susceptibility, charge stiffness, and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.

Solvation dynamics, energy distribution and trapping of a light solute ion

In the theoretical treatments of the dynamics of solvation of a newly created ion in a dipolar solvent, the self-motion of the solute is usually ignored. Recently, it has been shown that for a light ion the translational motion of the ion can significantly enhance its own rate of solvation. Therefore, solvation itself may not be the rate determining step in the equilibration. Instead, the rate determining step is the search of the low energy configuration which serves to localize the light ion. In this article a microscopic calculation of the probability distribution of the interaction energy of the nascent charge with the dipolar solvent molecules is presented in order to address this problem of solute trapping. It is found that to a good approximation, this distribution is Gaussian and the second moment of this distribution is exactly equal to the half of its own solvation energy. It is shown that this is in excellent agreement with the simulation results that are available for the model Brownian dipolar lattice and for liquid acetonitrile. If the distortion of the solvent by the ion is negligible then the same relation gives the energy distribution for the solvated ion, with the average centered at the final equilibrium solvation energy. These results are expected to be useful in understanding various chemical processes in dipolar liquids. Another interesting outcome of the present study is a simple dynamic argument that supports Onsager's ''inverse snow-ball'' conjecture of solvation of a light ion. A simple derivation of the semi-phenomenological relation between the solvation time correlation function and the single particle orientation, reported recently by Maroncelli et al. (J. Phys. Chem. 97 (1993) 13), is also presented.

Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operators a-1 and a(dagger-1) by their actions on the number states. We show that the squeezed vacuum exp(1/2xia(dagger2)]\0] and squeezed first number state exp[1.2xia(dagger2)]\n = 1] are respectively the eigenstates of the operators (a(dagger-1)a) and (aa(dagger-1)) with the eigenvalue xi.

Stabilizing trench's algorithm to invert symmetric toeplitz matrices

Presented here is a stable algorithm that uses Zohar's formulation of Trench's algorithm and computes the inverse of a symmetric Toeplitz matrix including those with vanishing or nearvanishing leading minors. The algorithm is based on a diagonal modification of the matrix, and exploits symmetry and persymmetry properties of the inverse matrix.

Image reconstruction from incomplete projections data: A multiresolution modeling approach

Computerized tomography is an imaging technique which produces cross sectional map of an object from its line integrals. Image reconstruction algorithms require collection of line integrals covering the whole measurement range. However, in many practical situations part of projection data is inaccurately measured or not measured at all. In such incomplete projection data situations, conventional image reconstruction algorithms like the convolution back projection algorithm (CBP) and the Fourier reconstruction algorithm, assuming the projection data to be complete, produce degraded images. In this paper, a multiresolution multiscale modeling using the wavelet transform coefficients of projections is proposed for projection completion. The missing coefficients are then predicted based on these models at each scale followed by inverse wavelet transform to obtain the estimated projection data.

Fast computation of Legendre and Zernike moments

This paper presents recursive algorithms for fast computation of Legendre and Zernike moments of a grey-level image intensity distribution. For a binary image, a contour integration method is developed for the evaluation of Legendre moments using only the boundary information. A method for recursive calculation of Zernike polynomial coefficients is also given. A square-to-circular image transformation scheme is introduced to minimize the computation involved in Zernike moment functions. The recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments. The mathematical framework of the algorithms is given in detail, and illustrated with binary and grey-level images.

The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

The role of Compton and Raman scattering in the quasar continuum

There are three ways in which an electromagnetic wave can undergo scattering in a plasma: (i) when the scattering of radiation occurs by a single electron, it is called Compton Scattering (CS); (ii) if it occurs by a longitudinal electron plasma mode, it is called Stimulated Raman Scattering (SRS), and (iii) if it occurs by a highly damped electron plasma mode, it is called Stimulated Compton Scattering (SCS). The non-thermal continuum of quasars is believed to be produced through the combined action of synchrotron and inverse Compton processes, which are essentially single-particle processes. Here, we investigate the role of SRS and SCS in the generation of continuum radiation from these compact objects. It is shown as an example that the complete spectrum of 3C 273 can be reproduced by suitably combining SCS and SRS. The differential contributions of SCS and SRS under different values of the plasma parameters are also calculated.

Primary Sequence That Determines the Functional Overlap between Mitochondrial Heat Shock Protein 70 Ssc1 and Ssc3 of Saccharomyces cerevisiae

The evolutionary diversity of the HSP70 gene family at the genetic level has generated complex structural variations leading to altered functional specificity and mode of regulation in different cellular compartments. By utilizing Saccharomyces cerevisiae as a model system for better understanding the global functional cooperativity between Hsp70 paralogs, we have dissected the differences in functional properties at the biochemical level between mitochondrial heat shock protein 70 (mtHsp70) Ssc1 and an uncharacterized Ssc3 paralog. Based on the evolutionary origin of Ssc3 and a high degree of sequence homology with Ssc1, it has been proposed that both have a close functional overlap in the mitochondrial matrix. Surprisingly, our results demonstrate that there is no functional cross-talk between Ssc1 and Ssc3 paralogs. The lack of in vivo functional overlap is due to altered conformation and significant lower stability associated with Ssc3. The substrate-binding domain of Ssc3 showed poor affinity toward mitochondrial client proteins and Tim44 due to the open conformation in ADP-bound state. In addition to that, the nucleotide-binding domain of Ssc3 showed an altered regulation by the Mge1 co-chaperone due to a high degree of conformational plasticity, which strongly promotes aggregation. Besides, Ssc3 possesses a dysfunctional inter-domain interface thus rendering it unable to perform functions similar to generic Hsp70s. Moreover, we have identified the critical amino acid sequence of Ssc1 and Ssc3 that can ``make or break'' mtHsp70 chaperone function. Together, our analysis provides the first evidence to show that the nucleotide-binding domain of mtHsp70s plays a critical role in determining the functional specificity among paralogs and orthologs across kingdoms.