The first part of this thesis develops methods for UWB communication. To meet the stringent regulatory body constraints, the physical layer signaling technique of the UWB transceiver should be optimally designed. We propose two signaling schemes which are variants of pulse position modulation (PPM) signaling for impulse radio (IR) UWB communication. We also discuss the detectors for the signaling schemes and evaluate the performance of these detectors.  IR-UWB can be used for precise range measurements as it provides a very high time resolution. This enables accurate time of arrival (TOA) estimations from which precise range values can be derived. We propose methods which use range information to arrive at optimal schedules for an all-to-all broadcast problem. Results indicate that throughput can be increased on average by three to ten times for typical network configurations compared to the traditional methods. Next, we discuss hypothesis testing in the context of UWB transceivers. We show that, when multiple detector outputs from a hardware platform are available, fusing the results from them can yield better performance in hypothesis testing than relying on a single detector output. In the second part of this thesis, the emphasis is placed on localization and joint estimation of location and communication parameters. Here, we focus on estimating the TOA of the signal. The wide bandwidth of the UWB signal requires high speed analog to digital converts (ADC) which makes the cost of the digital transceivers prohibitively high. To address this problem, we take two different strategies. In the first approach, we propose a multichannel receiver with each channel having a low-cost energy detector operating at a sub-Nyquist rate. In the second approach, we consider a compressive sampling based technique. Here, we propose a new acquisition front end, using which the sampling rate of the ADC can be significantly reduced. We extended the idea of compressive sampling based TOA estimation towards joint estimation of TOA and PPM symbols. Here, two signaling methods along with the algorithms are proposed based on the dynamicity of the target. They provide similar performance to the ML based estimation, however with a significant savings in the ADC resources. / <p>QC 20161205</p>

Compressed Sensing (CS) is a new paradigm in signal processing which exploits the sparse or compressible nature of the signal to significantly reduce the number of measurements, without compromising on the signal reconstruction quality. Recently, many algorithms have been reported in the literature for efficient sparse signal reconstruction. Nevertheless, it is well known that the performance of any sparse reconstruction algorithm depends on many parameters like number of measurements, dimension of the sparse signal, the level of sparsity, the measurement noise power, and the underlying statistical distribution of the non-zero elements of the signal. It has been observed that a satisfactory performance of the sparse reconstruction algorithm mandates certain requirement on these parameters, which is different for different algorithms. Many applications are unlikely to fulfil this requirement. For example, imaging speed is crucial in many Magnetic Resonance Imaging (MRI) applications. This restricts the number of measurements, which in turn affects the medical diagnosis using MRI. Hence, any strategy to improve the signal reconstruction in such adverse scenario is of substantial interest in CS. Interestingly, it can be observed that the performance degradation of the sparse recovery algorithms in the aforementioned cases does not always imply a complete failure. That is, even in such adverse situations, a sparse reconstruction algorithm may provide partially correct information about the signal. In this thesis, we study this scenario and propose a novel fusion framework and an iterative framework which exploit the partial information available in the sparse signal estimate(s) to improve sparse signal reconstruction. The proposed fusion framework employs multiple sparse reconstruction algorithms, independently, for signal reconstruction. We first propose a fusion algorithm viz. FACS which fuses the estimates of multiple participating algorithms in order to improve the sparse signal reconstruction. To alleviate the inherent drawbacks of FACS and further improve the sparse signal reconstruction, we propose another fusion algorithm called CoMACS and variants of CoMACS. For low latency applications, we propose a latency friendly fusion algorithm called pFACS. We also extend the fusion framework to the MMV problem and propose the extension of FACS called MMV-FACS. We theoretically analyse the proposed fusion algorithms and derive guarantees for performance improvement. We also show that the proposed fusion algorithms are robust against both signal and measurement perturbations. Further, we demonstrate the efficacy of the proposed algorithms via numerical experiments: (i) using sparse signals with different statistical distributions in noise-free and noisy scenarios, and (ii) using real-world ECG signals. The extensive numerical experiments show that, for a judicious choice of the participating algorithms, the proposed fusion algorithms result in a sparse signal estimate which is often better than the sparse signal estimate of the best participating algorithm. The proposed fusion framework requires toemploy multiple sparse reconstruction algorithms for sparse signal reconstruction. We also propose an iterative framework and algorithm called {IFSRA to improve the performance of a given arbitrary sparse reconstruction algorithm. We theoretically analyse IFSRA and derive convergence guarantees under signal and measurement perturbations. Numerical experiments on synthetic and real-world data confirm the efficacy of IFSRA. The proposed fusion algorithms and IFSRA are general in nature and does not require any modification in the participating algorithm(s).

Consider the following system model y = Ax + e, where x is n-dimensional sparse signal, y is the measurement vector in a much lower dimension m, A is the measurement matrix and e is the error in our measurements. The Dantzig selector estimates x by solving the following optimization problem minimize || x ||₁ subject to || A'(Ax - y) ||∞ ≤ ε, (DS). This is a convex program and can be recast into a linear program and solved using any modern optimization method e.g., interior point methods. We propose a fast and efficient scheme for solving the Dantzig Selector (DS), which we call "Primal-Dual pursuit". This algorithm can be thought of as a "primal-dual homotopy" approach to solve the Dantzig selector (DS). It computes the solution to (DS) for a range of successively relaxed problems, by starting with a large artificial ε and moving towards the desired value. Our algorithm iteratively updates the primal and dual supports as ε reduces to the desired value, which gives final solution. The homotopy path solution of (DS) takes with varying ε is piecewise linear. At some critical values of ε in this path, either some new elements enter the support of the signal or some existing elements leave the support. We derive the optimality and feasibility conditions which are used to update the solutions at these critical points. We also present a detailed analysis of primal-dual pursuit for sparse signals in noiseless case. We show that if our signal is S-sparse, then we can find all its S elements in exactly S steps using about "S² log n" random measurements, with very high probability.

This diploma thesis deals with separation of moving objects from static unchanging background in video sequence. In this thesis are described common method of separation and access using sparse signal representation. In the practical part of thesis was created video sequences, on which is verified the designed algorithm, implemented in Matlab, for obtaining background from damaged video frames and comparing this methods.

This diploma thesis deals with separation of moving objects from static unchanging background in video sequence. Thesis contains description of common method of separation and approach based sparse signal representation. In the practical part of thesis, there were created video sequences, which are used to verify designed algorithm implemented in Matlab interface, disegned to obtain separated background from damaged video frames.

This thesis deals with the nuclear magnetic resonance field, especially spectroscopy and spectroscopy imaging, sparse signal representation and low-rank approximation approaches. Spectroscopy imaging methods are becoming very popular in clinical praxis, however, long measurement times and low resolution prevent them from their spreading. The goal of this thesis is to improve state of the art methods by using sparse signal representation and low-rank approximation approaches. The compressed sensing technique is demonstrated on the examples of magnetic resonance imaging speedup and hyperspectral imaging data saving. Then, a new spectroscopy imaging scheme based on compressed sensing is proposed. The thesis deals also with the in vivo spectrum quantitation problem by designing the MRSMP algorithm specifically for this purpose.

We often have to face the fact that several signals are mixed together in unknown environment. The signals must be first extracted from the mixture in order to interpret them correctly. This problem is in signal processing society called blind source separation. This dissertation thesis deals with multi-channel separation of audio signals in real environment, when the source signals outnumber the sensors. An introduction to blind source separation is presented in the first part of the thesis. The present state of separation methods is then analyzed. Based on this knowledge, the separation systems implementing fuzzy time-frequency mask are introduced. However these methods are still introducing nonlinear changes in the signal spectra, which can yield in musical noise. In order to reduce musical noise, novel methods combining time-frequency binary masking and beamforming are introduced. The new separation system performs linear spatial filtering even if the source signals outnumber the sensors. Finally, the separation systems are evaluated by objective and subjective tests in the last part of the thesis.