Radio tomographic imaging (RTI) is a novel device-free localization technique which utilizes the changes in radio signals caused by obstruction to enable various sensing applications. However, the deployment of these applications is hindered by the energy-expensive radio sensing techniques employed in these systems. In this thesis, we tackle this issue by introducing a novel way to realize a battery-free RTI sensor. We go through the design process and produce and evaluate a working prototype that operates on minuscule amounts of energy. Our design reduces power consumption by orders of magnitude compared to traditional RTI sensors by eliminating the energy-expensive components used in current RTI systems, enabling battery-free operation of RTI sensors. We demonstrate the efficiency and accuracy of our system in a boundary crossing scenario. We Discuss its limitations and tackle some of the security threats correlated with the deployment of such a system. / Radiotomografisk avbildning (RTA) är en ny, anordningsfri lokaliseringstekniksom utnyttjar förändringarna i radiosignaler orsakat av obstruktioner för att möjliggöraolika avkänningsapplikationer. Utvecklingen av dessa applikationer hindrasemellertid av de energiineffektiva radioavkännande tekniker som användsi dessa system. I denna avhandling behandlar vi problemet genom att introduceraen ny metod för att skapa en batterifri RTA-sensor. Vi går igenom konstruktionsprocessenoch producerar och utvärderar en arbetsprototyp som kräver minusklermängder energi. Vår design minskar energiförbrukningen signifikantjämfört med traditionella RTA-sensorer, genom att eliminera de energiineffektivakomponenterna som används i dagens RTA-system, vilket möjliggör batterifridrift av RTA-sensorer. Vi demonstrerar effektiviteten och noggrannheten hos vårtsystem i ett gränsöverskridande scenario. Vi diskuterar begränsningarna och taritu med några av de säkerhetshot som är korrelerade med utplaceringen av ettsådant system.

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Diffuse optical tomography uses near infrared (NIR) light as the probing media to re-cover the distributions of tissue optical properties with an ability to provide functional information of the tissue under investigation. As NIR light propagation in the tissue is dominated by scattering, the image reconstruction problem (inverse problem) is non-linear and ill-posed, requiring usage of advanced computational methods to compensate this. Diffuse optical image reconstruction problem is always rank-deficient, where finding the independent measurements among the available measurements becomes challenging problem. Knowing these independent measurements will help in designing better data acquisition set-ups and lowering the costs associated with it. An optimal measurement selection strategy based on incoherence among rows (corresponding to measurements) of the sensitivity (or weight) matrix for the near infrared diffuse optical tomography is proposed. As incoherence among the measurements can be seen as providing maximum independent information into the estimation of optical properties, this provides high level of optimization required for knowing the independency of a particular measurement on its counterparts. The utility of the proposed scheme is demonstrated using simulated and experimental gelatin phantom data set comparing it with the state-of-the-art methods. The traditional image reconstruction methods employ ℓ2-norm in the regularization functional, resulting in smooth solutions, where the sharp image features are absent. The sparse recovery methods utilize the ℓp-norm with p being between 0 and 1 (0 ≤ p1), along with an approximation to utilize the ℓ0-norm, have been deployed for the reconstruction of diffuse optical images. These methods are shown to have better utility in terms of being more quantitative in reconstructing realistic diffuse optical images compared to traditional methods. Utilization of ℓp-norm based regularization makes the objective (cost) function non-convex and the algorithms that implement ℓp-norm minimization utilizes approximations to the original ℓp-norm function. Three methods for implementing the ℓp-norm were con-sidered, namely Iteratively Reweigthed ℓ1-minimization (IRL1), Iteratively Reweigthed Least-Squares (IRLS), and Iteratively Thresholding Method (ITM). These results in-dicated that IRL1 implementation of ℓp-minimization provides optimal performance in terms of shape recovery and quantitative accuracy of the reconstructed diffuse optical tomographic images. Photoacoustic tomography (PAT) is an emerging hybrid imaging modality combining optics with ultrasound imaging. PAT provides structural and functional imaging in diverse application areas, such as breast cancer and brain imaging. A model-based iterative reconstruction schemes are the most-popular for recovering the initial pressure in limited data case, wherein a large linear system of equations needs to be solved. Often, these iterative methods requires regularization parameter estimation, which tends to be a computationally expensive procedure, making the image reconstruction process to be performed off-line. To overcome this limitation, a computationally efficient approach that computes the optimal regularization parameter is developed for PAT. This approach is based on the least squares-QR (LSQR) decomposition, a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution.

This thesis reports the work done towards design and fabrication of a versatile and low cost, frequency domain DOT (Diffuse Optical Tomography) Imager. A design which uses only a single fiber for the source and a single fiber bundle for the detector is reported. From near the source, to diametrically opposite to the source, the detected intensity of scattered light varies by three to four orders in magnitude, depending on the tissue/phantom absorption and scattering properties. The photo multiplier tube’s (PMT’s) gain is controlled to operate it in the linear range, thus increasing the dynamic range of detection. Increasing the dynamic range by multi channel data acquisition is also presented. Arresting the oscillations of a stepper using a negative torque braking method is also adopted in this application for increasing the speed of data acquisition. The finite element method (FEM) for obtaining photon density solution to the transport equation and the model based iterative image reconstruction (MPBIIR) algorithm are developed for verifying the experimental prototype. Simulation studies presented towards the end of this thesis work provide insight into the nature of measurements. The optical absorption reconstructed images from the simulation, verified the validity of implementation of the reconstruction method for further reconstructions from data gathered from the developed imager. A single iteration of MOBIIR to segment the region of interest (ROI) using an homogeneous measurement estimate is presented. Using the single iteration MOBIIR to obtain a relatively more accurate starting value for the optical absorption coefficient, and the reconstruction results for data obtained from tissue mimicking solid epoxy-resin phantom with a single in-homogeneity inclusion is also presented to demonstrate the imager prototype.

Biomedical optical imaging is capable of providing functional information of the soft bi-ological tissues, whose applications include imaging large tissues, such breastand brain in-vivo. Biomedical optical imaging uses near infrared light (600nm-900nm) as the probing media, givin ganaddedadvantageofbeingnon-ionizingimagingmodality. The tomographic technologies for imaging large tissues encompasses diffuse optical tomogra-phyandphotoacoustictomography. Traditional image reconstruction methods indiffuse optical tomographyemploysa �2-norm based regularization, which is known to remove high frequency no is either econstructed images and make the mappearsmooth. Hence as parsity based image reconstruction has been deployed for diffuse optical tomography, these sparserecov-ery methods utilize the �p-norm based regularization in the estimation problem with 0≤ p<1. These sparse recovery methods, along with an approximation to utilizethe �0-norm, have been used forther econstruction of diffus eopticaltomographic images.The comparison of these methods was performed by increasing the sparsityinthesolu-tion. Further a model resolution matrix based framework was proposed and shown to in-duceblurinthe�2-norm based regularization framework for diffuse optical tomography. This model-resolution matrix framework was utilized in the optical imaged econvolution framework. A basis pursuitdeconvolution based on Split AugmentedLagrangianShrink-ageAlgorithm(SALSA)algorithm was used along with the Tikhonovregularization step making the image reconstruction into a two-step procedure. This new two-step approach was found to be robust with no iseandwasabletobetterdelineatethestructureswhichwasevaluatedusingnumericalandgelatinphantom experiments. Modern diffuse optical imaging systems are multi-modalin nature, where diffuse optical imaging is combined with traditional imaging modalitiessuc has Magnetic Res-onanceImaging(MRI),or Computed Tomography(CT). Image-guided diffuse optical tomography has the advantage of reducingthetota lnumber of optical parameters beingreconstructedtothenumber of distinct tissue types identified by the traditional imaging modality, converting the optical image-reconstruction problem fromunder-determined innaturetoover-determined. In such cases, the minimum required measurements might be farless compared to those of the traditional diffuse optical imaging. An approach to choose these measurements optimally based on a data-resolution matrix is proposed, and it is shown that it drastically reduces the minimum required measurements (typicalcaseof240to6) without compromising the image reconstruction performance. In the last part of the work , a model-based image reconstruction approaches in pho-toacoustic tomography (which combines light and ultra sound) arestudied as it is know that these methods have a distinct advantage compared to traditionalanalytical methods in limited datacase. These model-based methods deployTikhonovbasedregularizationschemetoreconstruct the initial pressure from the boundary acoustic data. Again a model-resolution for these cases tend to represent the blurinduced by the regularization scheme. A method that utilizes this blurringmodelandper forms the basis pursuit econ-volution to improve the quantitative accuracy of the reconstructed photoacoustic image is proposed and shown to be superior compared to other traditional methods. Moreover, this deconvolution including the building of model-resolution matrixis achievedvia the Lanczosbidiagonalization (least-squares QR) making this approach computationally ef-ficient and deployable inreal-time. Keywords Medical imaging, biomedical optical imaging, diffuse optical tomography, photoacous-tictomography, multi-modalimaging, inverse problems,sparse recovery,computational methods inbiomedical optical imaging.

The 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.

Diffuse optical tomography is a promising imaging modality that provides functional information of the soft biological tissues, with prime imaging applications including breast and brain tissue in-vivo. This modality uses near infrared light( 600nm-900nm) as the probing media, giving an advantage of being non-ionizing imaging modality. The image reconstruction problem in diffuse optical tomography is typically posed as a least-squares problem that minimizes the difference between experimental and modeled data with respect to optical properties. This problem is non-linear and ill-posed, due to multiple scattering of the near infrared light in the biological tissues, leading to infinitely many possible solutions. The traditional methods employ a regularization term to constrain the solution space as well as stabilize the solution, with Tikhonov type regularization being the most popular one. The choice of this regularization parameter, also known as hyper parameter, dictates the reconstructed optical image quality and is typically chosen empirically or based on prior experience. In this thesis, a simple back projection type image reconstruction algorithm is taken up, as they are known to provide computationally efficient solution compared to regularized solutions. In these algorithms, the hyper parameter becomes equivalent to filter factor and choice of which is typically dependent on the sampling interval used for acquiring data in each projection and the angle of projection. Determining these parameters for diffuse optical tomography is not so straightforward and requires usage of advanced computational models. In this thesis, a computationally efficient simplex Method based optimization scheme for automatically finding this filter factor is proposed and its performances is evaluated through numerical and experimental phantom data. As back projection type algorithms are approximations to traditional methods, the absolute quantitative accuracy of the reconstructed optical properties is poor .In scenarios, like dynamic imaging, where the emphasis is on recovering relative difference in the optical properties, these algorithms are effective in comparison to traditional methods, with an added advantage being highly computationally efficient. In the second part of this thesis, this hyper parameter choice for traditional Tikhonov type regularization is attempted with the help of Least-Squares QR-decompisition (LSQR) method. The established techniques that enable the automated choice of hyper parameters include Generalized Cross-Validation(GCV) and regularized Minimal Residual Method(MRM), where both of them come with higher over head of computation time, making it prohibitive to be used in the real-time. The proposed LSQR algorithm uses bidiagonalization of the system matrix to result in less computational cost. The proposed LSQR-based algorithm for automated choice of hyper parameter is compared with MRM methods and is proven to be computationally optimal technique through numerical and experimental phantom cases.