Measurements, Models, Systems and Design

531 s.

Efficient Space-Time Sampling with Pixel-wise Coded Exposure for High Speed Imaging

Cameras face a fundamental tradeoff between spatial and temporal resolution. Digital still cameras can capture images with high spatial resolution, but most high-speed video cameras have relatively low spatial resolution. It is hard to overcome this tradeoff without incurring a significant increase in hardware costs. In this paper, we propose techniques for sampling, representing and reconstructing the space-time volume in order to overcome this tradeoff. Our approach has two important distinctions compared to previous works: (1) we achieve sparse representation of videos by learning an over-complete dictionary on video patches, and (2) we adhere to practical hardware constraints on sampling schemes imposed by architectures of current image sensors, which means that our sampling function can be implemented on CMOS image sensors with modified control units in the future. We evaluate components of our approach - sampling function and sparse representation by comparing them to several existing approaches. We also implement a prototype imaging system with pixel-wise coded exposure control using a Liquid Crystal on Silicon (LCoS) device. System characteristics such as field of view, Modulation Transfer Function (MTF) are evaluated for our imaging system. Both simulations and experiments on a wide range of scenes show that our method can effectively reconstruct a video from a single coded image while maintaining high spatial resolution

Towards Fast and High-quality Biomedical Image Reconstruction

Department of Computer Science and EngineeringReconstruction is an important module in the image analysis pipeline with purposes of isolating the majority of meaningful information that hidden inside the acquired data. The term ???reconstruction??? can be understood and subdivided in several specific tasks in different modalities. For example, in biomedical imaging, such as Computed Tomography (CT), Magnetic Resonance Image (MRI), that term stands for the transformation from the, possibly fully or under-sampled, spectral domains (sinogram for CT and k-space for MRI) to the visible image domains. Or, in connectomics, people usually refer it to segmentation (reconstructing the semantic contact between neuronal connections) or denoising (reconstructing the clean image). In this dissertation research, I will describe a set of my contributed algorithms from conventional to state-of-the-art deep learning methods, with a transition at the data-driven dictionary learning approaches that tackle the reconstruction problems in various image analysis tasks.clos

Wavelet based design of digital multichannel communications systems

The huge penetration of the personal communications systems in the market is constantly presenting new challenges to the research, aimed at satisfying people's needs and requirements for effective communication systems. At present, the cellular telephone network is perhaps the most evident example of communication system that has had a great impact on the lives of ordinary people and, at the same time, is the subject of interest of many researchers both at academic and industrial level. For the future, one of the main challenges in telecommunications will be the provision of ubiquitous broadband tetherless integrated services to mobile users. Such a pretentious goal cannot be achieved without a continuous research facing such problems as service quality, complete mobility support, and affordable complexity that are still open problems. However, present telecommunication problems are not only a matter of implementation or development of new services, exploiting a totally assessed doctrine. In order to respond to the mobility of the users personal communication systems have to deal with the wireless communication channel whereby mobility and non-stationarity of the propagation conditions require a stochastic description of the channel parameters. While this fact can be viewed as strong limitation to the development of a solid theory whose validity can be assesed in practice, on the other hand allows for an investigation and study of novel communication schemes, sometimes encompassing basic aspects of digital communications. This thesis, is the result of a research work that has investigated one of the basic building block of every communication systems, the modulation scheme, and the design of the pulse shape carrying the digital information. We have studied the design of multichannel communication scheme exploiting the mathematical theory of wavelets. Such a theory, developed recently, has had a great impact in many fields of engineering and of other scientific disciplines. In particular, wavelet theory has become very popular in the signal processing area; in fact it is a flexible toolbox for signal analysis allowing effective representation of signals for features extraction purposes. The main features that make wavelet waveforms suitable to be used as shaping pulses for modulation are their substantial compact support both in the time and frequency domains, and the fact that they are ISI-free pulses over frequency flat channels. The study presented in this thesis is focused on application of wavelet theory to design high-efficiency multichannel communication schemes and to the performance evaluation over linear and non-linear channels. We present a general method to design wavelet based multichannel communication schemes that we denoted Wavelet Orthogonal Frequency Division Multiplexing (WOFDM). We show that such schemes, having a largerspectral efficiency for a small number of channels, are a valid alternative to the classical OFDM. Potential advantage of wavelet modulation are shown presenting other applications examined in this thesis: a joint use of WOFDM and Trellis Coded Modulation to shape the power spectrum in order to match a frequency selective channel and minimize distortion, and application to spread spectrum modulation. Particular attention has been devoted to the timing recovery problem in multichannel communication schemes, exploiting the timing information of the different subchannels to improve the error variance in estimation of the sampling instant leading to a reduction of the adjacent channels interferenc

Two Studies in Representation of Signals

The thesis consists of two parts. In the first part deals with a multi-scale approach to vector quantization. An algorithm, dubbed reconstruction trees, is proposed and analyzed. Here the goal is parsimonious reconstruction of unsupervised data; the algorithm leverages a family of given partitions, to quickly explore the data in a coarse-to-fine multi-scale fashion. The main technical contribution is an analysis of the expected distortion achieved by the proposed algorithm, when the data are assumed to be sampled from a fixed unknown probability measure. Both asymptotic and finite sample results are provided, under suitable regularity assumptions on the probability measure. Special attention is devoted to the case in which the probability measure is supported on a smooth sub-manifold of the ambient space, and is absolutely continuous with respect to the Riemannian measure of it; in this case asymptotic optimal quantization is well understood and a benchmark for understanding the results is offered. The second part of the thesis deals with a novel approach to Graph Signal Processing which is based on Matroid Theory. Graph Signal Processing is the study of complex functions of the vertex set of a graph, based on the combinatorial Graph Laplacian operator of the underlying graph. This naturally gives raise to a linear operator, that to many regards resembles a Fourier transform, mirroring the graph domain into a frequency domain. On the one hand this structure asymptotically tends to mimic analysis on locally compact groups or manifolds, but on the other hand its discrete nature triggers a whole new scenario of algebraic phenomena. Hints towards making sense of this scenario are objects that already embody a discrete nature in continuous setting, such as measures with discrete support in time and frequency, also called Dirac combs. While these measures are key towards formulating sampling theorems and constructing wavelet frames in time-frequency Analysis, in the graph-frequency setting these boil down to distinguished combinatorial objects, the so called Circuits of a matroid, corresponding to the Fourier transform operator. In a particularly symmetric case, corresponding to Cayley graphs of finite abelian groups, the Dirac combs are proven to completely describe the so called lattice of cyclic flats, exhibiting the property of being atomistic, among other properties. This is a strikingly concise description of the matroid, that opens many questions concerning how this highly regular structure relaxes into more general instances. Lastly, a related problem concerning the combinatorial interplay between Fourier operator and its Spectrum is described, provided with some ideas towards its future development

Recent Applications in Graph Theory

Graph theory, being a rigorously investigated field of combinatorial mathematics, is adopted by a wide variety of disciplines addressing a plethora of real-world applications. Advances in graph algorithms and software implementations have made graph theory accessible to a larger community of interest. Ever-increasing interest in machine learning and model deployments for network data demands a coherent selection of topics rewarding a fresh, up-to-date summary of the theory and fruitful applications to probe further. This volume is a small yet unique contribution to graph theory applications and modeling with graphs. The subjects discussed include information hiding using graphs, dynamic graph-based systems to model and control cyber-physical systems, graph reconstruction, average distance neighborhood graphs, and pure and mixed-integer linear programming formulations to cluster networks