Efficient and Stable Acoustic Tomography Using Sparse Reconstruction Methods

We study an acoustic tomography problem and propose a new inversion technique based on sparsity. Acoustic tomography observes the parameters of the medium that influence the speed of sound propagation. In the human body, the parameters that mostly influence the sound speed are temperature and density, in the ocean - temperature and current, in the atmosphere - temperature and wind. In this study, we focus on estimating temperature in the atmosphere using the information on the average sound speed along the propagation path. The latter is practically obtained from travel time measurements. We propose a reconstruction algorithm that exploits the concept of sparsity. Namely, the temperature is assumed to be a linear combination of some functions (e.g. bases or set of different bases) where many of the coefficients are known to be zero. The goal is to find the non-zero coefficients. To this end, we apply an algorithm based on linear programming that under some constrains finds the solution with minimum l0 norm. This is actually equivalent to the fact that many of the unknown coefficients are zeros. Finally, we perform numerical simulations to assess the effectiveness of our approach. The simulation results confirm the applicability of the method and demonstrate high reconstruction quality and robustness to noise

Inverse problems in acoustic tomography:theory and applications

Acoustic tomography aims at recovering the unknown parameters that describe a field of interest by studying the physical characteristics of sound propagating through the considered field. The tomographic approach is appealing in that it is non-invasive and allows to obtain a significantly larger amount of data compared to the classical one-sensor one-measurement setup. It has, however, two major drawbacks which may limit its applicability in a practical setting: the methods by which the tomographic data are acquired and then converted to the field values are computationally intensive and often ill-conditioned. This thesis specifically addresses these two shortcomings by proposing novel acoustic tomography algorithms for signal acquisition and field reconstruction. The first part of our exposition deals with some theoretical aspects of the tomographic sampling problems and associated reconstruction schemes for scalar and vector tomography. We show that the classical time-of-flight measurements are not sufficient for full vector field reconstruction. As a solution, an additional set of measurements is proposed. The main advantage of the proposed set is that it can be directly computed from acoustic measurements. It thus avoids the need for extra measuring devices. We then describe three novel reconstruction methods that are conceptually quite different. The first one is based on quadratic optimization and does not require any a priori information. The second method builds upon the notion of sparsity in order to increase the reconstruction accuracy when little data is available. The third approach views tomographic reconstruction as a parametric estimation problem and solves it using recent sampling results on non-bandlimited signals. The proposed methods are compared and their respective advantages are outlined. The second part of our work is dedicated to the application of the proposed algorithms to three practical problems: breast cancer detection, thermal therapy monitoring, and temperature monitoring in the atmosphere. We address the problem of breast cancer detection by computing a map of sound speed in breast tissue. A noteworthy contribution of this thesis is the development of a signal processing technique that significantly reduces the artifacts that arise in very inhomogeneous and absorbent tissue. Temperature monitoring during thermal therapies is then considered. We show how some of our algorithms allow for an increased spatial resolution and propose ways to reduce the computational complexity. Finally, we demonstrate the feasibility of tomographic temperature monitoring in the atmosphere using a custom-built laboratory-scale experiment. In particular, we discuss various practical aspects of time-of-flight measurement using cheap, off-the-shelf sensing devices

Risk factors associated with cardiac complication after total joint arthroplasty of the hip and knee: a systematic review

Background: Cardiac complication represents a major cause of morbidity and mortality after total joint arthroplasty, thus necessitating investigation into the associated risks in total hip arthroplasty and total knee arthroplasty. There remains a lack of clarity for many risk factors in the current literature. The aim of this systematic review is to assess the most recent published literature and identify the risk factors associated with cardiac complication in total hip arthroplasty and total knee arthroplasty. Methods: Scopus, PubMed, CINHAL, and Cochrane were searched to identify studies published since 2008 reporting on risk factors associated with cardiac complication in elective primary in total hip arthroplasty and total knee arthroplasty in patients 18years old with osteoarthritis. Reported odds ratios, hazard ratios, and relative risk were the principal summary measures collected. The included studies were too heterogeneous to enable meta-analysis. Results: Fifteen studies were included in this systematic review. Increasing age and history of cardiac disease were found by most studies to be positively associated with risk of cardiac complication. There was no strong association found between obesity and cardiac complication. The evidence for other risk factors was less clear in the examined literature, although there is suggestive evidence for male gender and cerebrovascular disease increasing risk. Conclusions: Increasing age and history of cardiac disease increases the risk of cardiac complication after total hip arthroplasty and total knee arthroplasty. Other risk factors commonly attributed to increased risk in non-cardiac surgery including hypertension and obesity require further evaluation in arthroplasty. Systematic review registration: A detailed protocol was published in the PROSPERO database (registration number CRD42018095887) for this systematic review

Produkcija makrozoobentosa u reci Rači uzvodno i nizvodno od pastrmskog ribnjaka

Biomasa (produkcija) makrozoobentosa je odabrana kao osnovni pokazatelj za praćenje promena kvantitativnog sastava naselja dna na lokalitetima uzvodno i nizvodno od pastrmskog ribnjaka u reci Rači. Istraživanje sekundarne produkcije makrozoobentosa reke Rače sa sedam lokaliteta, obavljeno je u periodu 2011. (april, jun, septembar, oktobar, decembar) i 2012. godine (februar i maj). Dominantne grupe u biomasi makrozoobentosa su Hirudinea (Annelida), Mollusca, Gammaridae (Crustacea) i Trichoptera (Insecta). Vrednosti biomase zoobentosa kretale su se u svim mesecima istraživanja u intervalu od 3,2001 g/m2, na lokalitetu RČ2 (u februaru) ,do 216,7120 g/m2, na lokalitetu RČ3 (u februaru). Biomasa faune dna najveća je u svim mesecima istraživanja na lokalitetu RČ3, koji je lociran nizvodno od pastrmskog ribnjaka. Na ovom lokalitetu biomasa makroinvertebrata se kretala od 87,8643 g/m2 (u aprilu 2011. godine) do 216,7120 g/m2 (u februaru 2012. godine)

Oversampled A/D Conversion of Non-Bandlimited Signals with Finite Rate of Innovation

We consider the problem of A/D conversion for non-bandlimitedsignals that have a finite rate of innovation, in particular, theclass of continuous periodic stream of Diracs, characterized by aset of time positions and weights. Previous research has onlyconsidered the sampling of these signals, ignoring quantization,which is necessary for any practical application (e.g. UWB,CDMA). In order to achieve accuracy under quantization, weintroduce two types of oversampling, namely, oversampling infrequency and oversampling in time. High accuracy is achieved byenforcing the reconstruction to satisfy either three convex setsof constraints related to: 1) sampling kernel, 2) quantization and3) periodic streams of Diracs which is then said to provide {\itstrong} consistency or only the first two, providing {\it weak}consistency. We propose three reconstruction algorithms, thefirst two achieving {\it weak} consistency and the third oneachieving {\it strong} consistency. For these three algorithms,respectively, the experimental MSE performance for time positionsdecreases as $O(1/{R_t^2 R_f^3})$, $O(1/{R_t^2 R_f^4})$ and$O(1/{R_t^2 R_f^5})$, where $R_t$ and $R_f$ are the oversamplingratios in time and in frequency, respectively. It is also provedtheoretically that our reconstruction algorithms satisfying {\itweak} consistency achieve an MSE performance of at least$O(1/{R_t^2 R_f^3})$

Error-Rate Dependence of Non-Bandlimited Signals with Finite Rate of Innovation

We consider the rate-distortion problem for non-bandlimited signals that have a finite rate of innovation, in particular, the class of continuous periodic stream of Diracs, characterized by a set of time positions and weights. Previous research has only considered the sampling of these signals, ignoring quantization, which is necessary for any practical application (e.g. UWB, CDMA). In order to achieve accuracy under quantization, we introduce two types of oversampling, namely, oversampling in frequency and oversampling in time. The reconstruction accuracy is measured by the MSE of the time positions. High accuracy is achieved by enforcing the reconstruction to satisfy either three convex sets of constraints related to: 1) sampling kernel, 2) quantization and 3) periodic streams of Diracs, which is then said to provide strong consistency or only the first two, providing weak consistency. We propose reconstruction algorithms for both weak and strong consistency. Regarding the rate, we also consider a threshold crossing based scheme, which is more efficient than the PCM encoding. We compare the rate- distortion behavior that is obtained from both increasing the oversampling in time and in frequency, on the one hand, and, on the other hand, from decreasing the quantization stepsize

Oversampled A/D Conversion and Error-Rate Dependence of Non-Bandlimited Signals with Finite Rate of Innovation

We study the problem of A/D conversion and error-rate dependence of a class of non-bandlimited signals which have a finite rate of innovation, particularly, a continuous periodic stream of Diracs, characterized by a finite set of time positions and weights. Previous research has only considered sampling of this type of signals, ignoring the presence of quantization, which is necessary for any practical application. We first define the concept of consistent reconstruction for these signals and introduce the operations of both: a) oversampling in frequency, determined by the bandwidth of the low pass filtering used in the signal acquisition, and b) oversampling in time, determined by the number of samples in time taken from the filtered signal. Accuracy in a consistent reconstruction is achieved by enforcing the reconstructed signal to satisfy three sets of constrains, defined by: the low-pass filtering operation, the quantization operation itself and the signal space of continuous periodic streams of Diracs. We provide two schemes to reconstruct the signal. For the first one, we prove that the mean squared error (MSE) of the time positions is of the order of O(1/R_t^2R_f^3), where R_t and R_f are the oversampling ratios in time and in frequency, respectively. For the second scheme, which has a higher complexity, it is experimentally observed that the MSE of the time positions is of the order of O(1/R_t^2R_f^5). Our experimental results show a clear advantage of consistent reconstruction over non-consistent reconstruction. Regarding the rate, we consider a threshold crossing based scheme where, as opposed to previous research, both oversampling in time and also in frequency influence the coding rate. We compare the error-rate dependence behavior that is obtained from both increasing the oversampling in time and in frequency, on the one hand, and on the other hand, from decreasing the quantization stepsize

Use of Learned Dictionaries in Tomographic Reconstruction

We study the use and impact of a dictionary in a tomographic reconstruction setup. First, we build two different dictionaries: one using a set of bases functions (Discrete Cosine Transform), and the other that is learned using patches extracted from training images, similar to the image that we would like to reconstruct. We use K-SVD as the learning algorithm. These dictionaries being local, we convert them to global dictionaries, ready to be applied on whole images, by generating all possible shifts of each atom across the image. During the reconstruction, we minimize the reconstruction error by performing a gradient descent on the image representation in the dictionary space. Our experiments show promising results, allowing to eliminate standard artifacts in the tomographic reconstruction, and to reduce the number of measurements required for the inversion. However, the quality of the results depends on the convergence of the learning process, and on the parameters of the dictionaries (number of atoms, convergence criterion, atom size, etc.). The exact influence of each of these remains to be studied

Acoustic tomography for estimating temperature and wind flow

We consider the problem of reconstructing superimposed temperature and wind flow fields from acoustic measurements. A new technique based solely on acoustic wave propagation is presented. In contrast to the usual straight ray assumption, a bent ray model is considered in order to achieve higher accuracy. We also develop a lab size experiment for temperature estimation