101 research outputs found
A Stochastic Search Approach to Inverse Problems
No full textThe focus of the thesis is on the development of a few stochastic search schemes for inverse problems and their applications in medical imaging. After the introduction in Chapter 1 that motivates and puts in perspective the work done in later chapters, the main body of the thesis may be viewed as composed of two parts: while the first part concerns the development of stochastic search algorithms for inverse problems (Chapters 2 and 3), the second part elucidates on the applicability of search schemes to inverse problems of interest in tomographic imaging (Chapters 4 and 5). The chapter-wise contributions of the thesis are summarized below.
Chapter 2 proposes a Monte Carlo stochastic filtering algorithm for the recursive estimation of diffusive processes in linear/nonlinear dynamical systems that modulate the instantaneous rates of Poisson measurements. The same scheme is applicable when the set of partial and noisy measurements are of a diffusive nature. A key aspect of our development here is the filter-update scheme, derived from an ensemble approximation of the time-discretized nonlinear Kushner Stratonovich equation, that is modified to account for Poisson-type measurements. Specifically, the additive update through a gain-like correction term, empirically approximated from the innovation integral in the filtering equation, eliminates the problem of particle collapse encountered in many conventional particle filters that adopt weight-based updates. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth, first with application to filtering problems with diffusive or Poisson-type measurements and then to an automatic control problem wherein the exterminations of the associated cost functional is achieved simply by an appropriate redefinition of the innovation process.
The aim of one of the numerical examples in Chapter 2 is to minimize the structural response of a duffing oscillator under external forcing. We pose this problem of active control within a filtering framework wherein the goal is to estimate the control force that minimizes an appropriately chosen performance index. We employ the proposed filtering algorithm to estimate the control force and the oscillator displacements and velocities that are minimized as a result of the application of the control force. While Fig. 1 shows the time histories of the uncontrolled and controlled displacements and velocities of the oscillator, a plot of the estimated control force against the external force applied is given in Fig. 2.
(a) (b)
Fig. 1. A plot of the time histories of the uncontrolled and controlled (a) displacements and (b) velocities.
Fig. 2. A plot of the time histories of the external force and the estimated control force
Stochastic filtering, despite its numerous applications, amounts only to a directed search and is best suited for inverse problems and optimization problems with unimodal solutions. In view of general optimization problems involving multimodal objective functions with a priori unknown optima, filtering, similar to a regularized Gauss-Newton (GN) method, may only serve as a local (or quasi-local) search. In Chapter 3, therefore, we propose a stochastic search (SS) scheme that whilst maintaining the basic structure of a filtered martingale problem, also incorporates randomization techniques such as scrambling and blending, which are meant to aid in avoiding the so-called local traps. The key contribution of this chapter is the introduction of yet another technique, termed as the state space splitting (3S) which is a paradigm based on the principle of divide-and-conquer. The 3S technique, incorporated within the optimization scheme, offers a better assimilation of measurements and is found to outperform filtering in the context of quantitative photoacoustic tomography (PAT) to recover the optical absorption field from sparsely available PAT data using a bare minimum ensemble. Other than that, the proposed scheme is numerically shown to be better than or at least as good as CMA-ES (covariance matrix adaptation evolution strategies), one of the best performing optimization schemes in minimizing a set of benchmark functions.
Table 1 gives the comparative performance of the proposed scheme and CMA-ES in minimizing a set of 40-dimensional functions (F1-F20), all of which have their global minimum at 0, using an ensemble size of 20. Here, 10 5 is the tolerance limit to be attained for the objective function value and MAX is the maximum number of iterations permissible to the optimization scheme to arrive at the global minimum.
Table 1. Performance of the SS scheme and
Chapter 4 gathers numerical and experimental evidence to support our conjecture in the previous chapters that even a quasi-local search (afforded, for instance, by the filtered martingale problem) is generally superior to a regularized GN method in solving inverse problems. Specifically, in this chapter, we solve the inverse problems of ultrasound modulated optical tomography (UMOT) and diffraction tomography (DT). In UMOT, we perform a spatially resolved recovery of the mean-squared displacements, p r of the scattering centres in a diffusive object by measuring the modulation depth in the decaying autocorrelation of the incident coherent light. This modulation is induced by the input ultrasound focussed to a specific region referred to as the region of interest (ROI) in the object. Since the ultrasound-induced displacements are a measure of the material stiffness, in principle, UMOT can be applied for the early diagnosis of cancer in soft tissues. In DT, on the other hand, we recover the real refractive index distribution, n r of an optical fiber from experimentally acquired transmitted intensity of light traversing through it. In both cases, the filtering step encoded within the optimization scheme recovers superior reconstruction images vis-à-vis the GN method in terms of quantitative accuracies.
Fig. 3 gives a comparative cross-sectional plot through the centre of the reference and reconstructed p r images in UMOT when the ROI is at the centre of the object. Here, the anomaly is presented as an increase in the displacements and is at the centre of the ROI.
Fig. 4 shows the comparative cross-sectional plot of the reference and reconstructed refractive index distributions, n r of the optical fiber in DT.
Fig. 3. Cross-sectional plot through the center of the reference and reconstructed p r images.
Fig. 4. Cross-sectional plot through the center of the reference and reconstructed n r distributions.
In Chapter 5, the SS scheme is applied to our main application, viz. photoacoustic tomography (PAT) for the recovery of the absorbed energy map, the optical absorption coefficient and the chromophore concentrations in soft tissues. Nevertheless, the main contribution of this chapter is to provide a single-step method for the recovery of the optical absorption field from both simulated and experimental time-domain PAT data. A single-step direct recovery is shown to yield better reconstruction than the generally adopted two-step method for quantitative PAT. Such a quantitative reconstruction maybe converted to a functional image through a linear map. Alternatively, one could also perform a one-step recovery of the chromophore concentrations from the boundary pressure, as shown using simulated data in this chapter. Being a Monte Carlo scheme, the SS scheme is highly parallelizable and the availability of such a machine-ready inversion scheme should finally enable PAT to emerge as a clinical tool in medical diagnostics.
Given below in Fig. 5 is a comparison of the optical absorption map of the Shepp-Logan phantom with the reconstruction obtained as a result of a direct (1-step) recovery.
Fig. 5. The (a) exact and (b) reconstructed optical absorption maps of the Shepp-Logan phantom. The x- and y-axes are in m and the colormap is in mm-1.
Chapter 6 concludes the work with a brief summary of the results obtained and suggestions for future exploration of some of the schemes and applications described in this thesis
Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography
No full textStable and computationally efficient reconstruction methodologies are developed to solve two important medical imaging problems which use near-infrared (NIR) light as the source of interrogation, namely, diffuse optical tomography (DOT) and one of its variations, ultrasound-modulated optical tomography (UMOT). Since in both these imaging modalities the system matrices are ill-conditioned owing to insufficient and noisy data, the emphasis in this work is to develop robust stochastic filtering algorithms which can handle measurement noise and also account for inaccuracies in forward models through an appropriate assignment of a process noise.
However, we start with demonstration of speeding of a Gauss-Newton (GN) algorithm for DOT so that a video-rate reconstruction from data recorded on a CCD camera is rendered feasible. Towards this, a computationally efficient linear iterative scheme is proposed to invert the normal equation of a Gauss-Newton scheme in the context of recovery of absorption coefficient distribution from DOT data, which involved the singular value decomposition (SVD) of the Jacobian matrix appearing in the update equation. This has sufficiently speeded up the inversion that a video rate recovery of time evolving absorption coefficient distribution is demonstrated from experimental data. The SVD-based algorithm has made the number of operations in image reconstruction to be rather than. 2()ONN3()ONN
The rest of the algorithms are based on different forms of stochastic filtering wherein we arrive at a mean-square estimate of the parameters through computing their joint probability
distributions conditioned on the measurement up to the current instant. Under this, the first algorithm developed uses a Bootstrap particle filter which also uses a quasi-Newton direction within. Since keeping track of the Newton direction necessitates repetitive computation of the Jacobian, for all particle locations and for all time steps, to make the recovery computationally feasible, we devised a faster update of the Jacobian. It is demonstrated, through analytical reasoning and numerical simulations, that the proposed scheme, not only accelerates convergence but also yields substantially reduced sample variance in the estimates vis-à-vis the conventional BS filter. Both accelerated convergence and reduced sample variance in the estimates are demonstrated in DOT optical parameter recovery using simulated and experimental data.
In the next demonstration a derivative free variant of the pseudo-dynamic ensemble Kalman filter (PD-EnKF) is developed for DOT wherein the size of the unknown parameter is reduced by representing of the inhomogeneities through simple geometrical shapes. Also the optical parameter fields within the inhomogeneities are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions). The EnKF is then 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. 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 = 0.01 mm-1 and = 1.0 mm-1respectively. We also assume=0.02 mm-1 within the inhomogeneity (for the single inhomogeneity case) and=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 from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one.
The superiority of a modified version of the PD-EnKF, which uses an ensemble square root filter, is also demonstrated in the context of UMOT by recovering the distribution of mean-squared amplitude of vibration, related to the Young’s modulus, in the ultrasound focal volume. Since the ability of a coherent light probe to pick-up the overall optical path-length change is limited to modulo an optical wavelength, the individual displacements suffered owing to the US forcing should be very small, say within a few angstroms. The sensitivity of modulation depth to changes in these small displacements could be very small, especially when the ROI is far removed from the source and detector. The contrast recovery of the unknown distribution in such cases could be seriously impaired whilst using a quasi-Newton scheme (e.g. the GN scheme) which crucially makes use of the derivative information. The derivative-free gain-based Monte Carlo filter not only remedies this deficiency, but also provides a regularization insensitive and computationally competitive alternative to the GN scheme. The inherent ability of a stochastic filter in accommodating the model error owing to a diffusion approximation of the correlation transport may be cited as an added advantage in the context of the UMOT inverse problem.
Finally to speed up forward solve of the partial differential equation (PDE) modeling photon transport in the context of UMOT for which the PDE has time as a parameter, a spectral decomposition of the PDE operator is demonstrated. This allows the computation of the time dependent forward solution in terms of the eigen functions of the PDE operator which has speeded up the forward solution, which in turn has rendered the UMOT parameter recovery computationally efficient
Stochastic Dynamical Systems : New Schemes for Corrections of Linearization Errors and Dynamic Systems Identification
No full textThis thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional
nonlinear filtering problems.
The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of
locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon-
Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own.
The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the
likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling.
The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates visà-vis those obtained through the parent filtering schemes.
In Chapter 4, we explore the possibility of unscented transformation on Gaussian random
variables, as employed within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully
treating relatively larger dimensional filtering problems.
We propose in Chapter 5 an iterated gain-based particle filter that is consistent with the form of the nonlinear filtering (Kushner-Stratonovich) equation in our attempt to treat larger dimensional filtering problems with enhanced estimation accuracy. A crucial aspect of the proposed filtering set-up is that it retains the simplicity of implementation of the ensemble Kalman filter (EnKF). The numerical results obtained via EnKF-like simulations with or without a reduced-rank unscented transformation also indicate substantively improved filter convergence.
The final contribution, reported in Chapter 6, is an iterative, gain-based filter bank
incorporating an artificial diffusion parameter and may be viewed as an extension of the iterative filter in Chapter 5. While the filter bank helps in exploring the phase space of the state variables better, the iterative strategy based on the artificial diffusion parameter, which is lowered to zero over successive iterations, helps improve the mixing property of the associated iterative update kernels and these are aspects that gather importance for
highly nonlinear filtering problems, including those involving significant initial mismatch of the process states and the measured ones. Numerical evidence of remarkably enhanced filter performance is exemplified by target tracking and structural health assessment applications.
The thesis is finally wound up in Chapter 7 by summarizing these developments and
briefly outlining the future research direction
Bibliographics for the 983 eprints in the live archives of E-LIS : trends and status report up to 7th July 2004, based on author-self-archiving metadata
No full textThe priority for ideas and philosophy related to "Network Theory" have been traced back and documented by Braun(2004),and credit goes to Karinthy(1929).The IT has empowered to realise it, as the most practical phenomena and it is no more a humour. The OAI (Open Archives Initiatives)and ACIS (Academic Contributor Information System)are progressive in the direction ,which may lead to realise the "Collective Genius" at global level. Focus of present study is on Author-Self-Archiving (A-S-A)Metadata of the 983 Eprints in the Live Archives of the E-LIS (EPrints of Library and Information Science),which were approved till 7th July 2004.The A-S-A Metadata was used for librametric analysis. Self-explanatory bibliographics are illustrated.The highlights include: Conference papers (34%); highest approval, June 2004 (28%); published archives (76%);not refereed (52%); not in public domain (60%); highest self-archiving-author (De Robbio, Antonella).The Nos. of EPrints having single JITA domain specifications were: Theoretical and general aspects of libraries and information(27); Information use and sociology of information(80);Users,literacy and reading(13);Libraries as physical collections(30);Publishing and legal issues(57);Management(13);Industry, profession and education(36);Information sources, supports, channels(113) ; Information treatment for information services, Information functions and techniques (101); Technical services libraries, archives and museums(25); Housing technologies(1); Information technology and library technology(92); and Inter-domainery (395) i.e. having specifications of two or more than two JITA classes
Light diffusion from non-spherical particles: rotational diffusion micro-rheology using ultrasound-assisted diffusing-wave spectroscopy
No full text
Mechanical property distribution from optical measurement of resonant ultrasound spectrum
No full textQuantitative vibro-acoustography from measurement of modal frequencies: characterisation of isotropic and orthotropic tissue-like objects
No full textScientometric portrait of Nobel laureate Leland H. Hartwell
No full textLeland H. Hartwell was honoured with the Nobel Prize in Physiology or Medicine (2001) at his 62 years age and at 41 years of research publishing career. The first contribution of the author was in 1961 at the age of 22. The number of his contributions in a year peaked in 1997 when it touched 8. He had 108 publications during 1961 – 2001 in domains: Molecular Biology of Cell Cycle Regulation (43), Genetics of Cell Division (48), Genomic Re-arrangement and DNA Repair (9), Molecular Genetics of Yeast Cell Fission (5), and Drug Target Interaction (3) which were analysed for authorship pattern with his 101 collaborators. Most active researchers having number of publications with Leland H. Hartwell were : Weinert, T. A. (10), Garvik, B. M. (8), McLaughlin, C. S. (8), Jenness, D. D. (5). His productivity coefficient was 0.76 which clearly indicates that his productivity increased after 50 percentile age. Highest collaboration coefficient (1) for Leland H. Hartwell was found during 1963-1965, 1968-1969, 1977, 1981-1983, 1985-1990, 1996 and 1998-2001. Journals have been the most preferred channel of communication where, as many as 96 papers out of 108 have been published. The core journals publishing his papers were: Cell (14), Genetics (12), Mol. Cell Biol. (8), J. Bactariol. (7), J. Cell Biol. ( 7), Science (7) J. Mol. Biol.(6), Exp. Cell Res. (5), and Proc. Nat. Acad. Sci.(5). Publication density is 2.63 and Publication concentration is 14.63. Most prolific keywords in titles of publications were: Saccharomyces cerevisiae , Yeast , Cell division cycle , RAD9, DNA Damage , Genes , Cell cycle, Genetic control , Check point (s) , Cell division , Mutant of Yeast
Is Jesus a Hindu? S.C. Vasu and Multiple Madhva Misrepresentations
No full textMisperceptions and misrepresentations are frequently linked to complicated dynamics between those who are misperceived and those who do the misperceiving. Oftentimes such dynamics are manifestations of underlying social, political, or, in the cases described in this issue of the Hindu-Christian Studies Bulletin, religious differences. The Hindu and the Christian traditions share a long history of mutual misrepresentations and misperceptions. Many of the authors in this issue of the Bulletin may offer detailed analyses of such misperceptions as they have been described by virtuoso Hindu thinkers such as Ram Mohan Roy, Gandhi-ji, and, in more recent times, BJP activists. In contrast, I will explore a case where mutual misperceptions have established a peculiar dynamic by focusing on the misperceptions that the Madhva school of Vedanta has been influenced by Christian beliefs. There is a theory that the Christian influence in Madhva Vedanta has resulted in a lively and provocative dialogue, one that is not only based on mutual misrepresentations by Christians and Hindus of one another but that actually serves to reinforce such misrepresentations
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