1,720,975 research outputs found
Autoregressive process parameters estimation from Compressed Sensing measurements and Bayesian dictionary learning
Full text linkThe main contribution of this thesis is the introduction of new techniques which allow to perform signal processing operations on signals represented by means of compressed sensing. Exploiting autoregressive modeling of the original signal, we obtain a compact yet representative description of the signal which can be estimated directly in the compressed domain. This is the key concept on which the applications we introduce rely on. In fact, thanks to proposed the framework it is possible to gain information about the original signal given compressed sensing measurements. This is done by means of autoregressive modeling which can be used to describe a signal through a small number of parameters. We develop a method to estimate these parameters given the compressed measurements by using an ad-hoc sensing matrix design and two different coupled estimators that can be used in different scenarios. This enables centralized and distributed estimation of the covariance matrix of a process given the compressed sensing measurements in a efficient way at low communication cost. Next, we use the characterization of the original signal done by means of few autoregressive parameters to improve compressive imaging. In particular, we use these parameters as a proxy to estimate the complexity of a block of a given image. This allows us to introduce a novel compressive imaging system in which the number of allocated measurements is adapted for each block depending on its complexity, i.e., spatial smoothness. The result is that a careful allocation of the measurements, improves the recovery process by reaching higher recovery quality at the same compression ratio in comparison to state-of-the-art compressive image recovery techniques. Interestingly, the parameters we are able to estimate directly in the compressed domain not only can improve the recovery but can also be used as feature vectors for classification. In fact, we also propose to use these parameters as more general feature vectors which allow to perform classification in the compressed domain. Remarkably, this method reaches high classification performance which is comparable with that obtained in the original domain, but with a lower cost in terms of dataset storage. In the second part of this work, we focus on sparse representations. In fact, a better sparsifying dictionary can improve the Compressed Sensing recovery performance. At first, we focus on the original domain and hence no dimensionality reduction by means of Compressed Sensing is considered. In particular, we develop a Bayesian technique which, in a fully automated fashion, performs dictionary learning. More in detail, using the uncertainties coming from atoms selection in the sparse representation step, this technique outperforms state-of-the-art dictionary learning techniques. Then, we also address image denoising and inpainting tasks using the aforementioned technique with excellent results. Next, we move to the compressed domain where a better dictionary is expected to provide improved recovery. We show how the Bayesian dictionary learning model can be adapted to the compressive case and the necessary assumptions that must be made when considering random projections. Lastly, numerical experiments confirm the superiority of this technique when compared to other compressive dictionary learning technique
Compressive estimation and imaging based on autoregressive models
Full text linkCompressed sensing (CS) is a fast and efficient way to obtain compact signal representations. Oftentimes, one wishes to extract some information from the available com- pressed signal. Since CS signal recovery is typically expensive from a computational point of view, it is inconvenient to first recover the signal and then extract the information. A much more effective approach consists in estimating the information directly from the signal's linear measurements. In this paper, we propose a novel framework for compressive estimation of autoregressive (AR) process parameters based on ad hoc sensing matrix construction. More in detail, we introduce a compressive least square estimator for AR(p) parameters and a specific AR(1) compressive Bayesian estimator. We exploit the proposed techniques to address two important practical problems. The first is compressive covariance estimation for Toeplitz structured covariance matrices where we tackle the problem with a novel parametric approach based on the estimated AR parameters. The second is a block-based compressive imaging system, where we introduce an algorithm that adaptively calculates the number of measurements to be acquired for each block from a set of initial measurements based on its degree of compressibility. We show that the proposed techniques outperform the state-of- the-art methods for these two problems
Secrecy Analysis of Finite-Precision Compressive Cryptosystems
Full text linkCompressed sensing (CS) has recently emerged as an effective and efficient way to encrypt data. Under certain conditions, it has been shown to provide some secrecy notions. In theory, it could be considered to be a perfect match for constrained devices needing to acquire and protect the data with computationally cheap operations. However, the theoretical results on the secrecy of compressive cryptosystems only hold under the assumption of infinite precision representation. With this work, we aim to close this gap and lay the theoretical foundations to support this practical framework. We provide theoretical upper bounds on the distinguishability of the measurements acquired through finite precision sensing matrices and experimentally validate them. Our main result is that the secrecy of a CS cryptosystem can be exponentially increased with a linear increase in the representation precision. This result confirms that the CS can be an effective secrecy layer and provides tools to use it in practical settings
Compressive Bayesian K-SVD
Full text linkCompressed Sensing (CS) is an established way to perform efficient dimensionality reduction during a signal’s acquisition process. However, the common transform bases used in CS to represent a signal often lead to a compressible representation that is not optimal in terms of compactness. In this paper we present a novel dictionary learning algorithm designed to work with CS data. Following our approach, dictionaries learned directly from the signal’s random projections are specifically suited to the signal class of interest, resulting in very sparse representations. Moreover, since the proposed method lays its foundation in a Bayesian dictionary learning algorithm, no prior information such as the signals’ sparsity is needed because it is inferred directly from the data. We show the superiority of our approach by comparing it with a state-of-the-art CS dictionary learning algorithm
Autoregressive Process Parameter Estimation from Compressed Sensing Measurements
Full text linkIn this paper we introduce a least squares estimator of the regression coefficients of an autoregressive process acquired by means of Compressed Sensing (CS). Unlike common CS problems in which we only know that the signal is sparse, using the proposed autoregressive model we can gain knowledge about the structure of the original signal without recovering it. This problem is addressed by introducing an ad-hoc sensing matrix able to preserve the structure of the regression. We numerically validate the performance of this matrix. Moreover, we present applications that naturally exploit this additional information we can directly obtain from the compressed data, and particularly power spectral density estimation from CS measurement
Distributed covariance estimation for compressive signal processing
Full text linkIn this paper we present a novel technique for the distributed estimation of the covariance matrix of an additive colored noise process affecting Compressed Sensing (CS) measurements. The main application is in wireless sensor networks, where nodes sense signals in CS format in order to save energy in the computation and transmission stages. The proposed technique enables a variety of compressive signal processing operations to be performed at each node directly on the linear measurements, such as detection, exploiting the knowledge of the noise statistics, thereby achieving improved performance. The parametric approach we introduce promises to yield good results while keeping the communication cost low. Hence, we validate our technique by evaluating the error on the estimated covariance matrix, and by including it in a compressive detection tas
Compressed Sensing for Privacy-Preserving Data Processing
No full textThe objective of this book is to provide the reader with a comprehensive survey of the topic compressed sensing in information retrieval and signal detection with privacy preserving functionality without compromising the performance of the embedding in terms of accuracy or computational efficiency. The reader is guided in exploring the topic by first establishing a shared knowledge about compressed sensing and how it is used nowadays. Then, clear models and definitions for its use as a cryptosystem and a privacy-preserving embedding are laid down, before tackling state-of-the-art results for both applications. The reader will conclude the book having learned that the current results in terms of security of compressed techniques allow it to be a very promising solution to many practical problems of interest. The book caters to a broad audience among researchers, scientists, or engineers with very diverse backgrounds, having interests in security, cryptography and privacy in information retrieval systems. Accompanying software is made available on the authors’ website to reproduce the experiments and techniques presented in the book. The only background required to the reader is a good knowledge of linear algebra, probability and information theory
Adversarial Learning of Mappings Onto Regularized Spaces for Biometric Authentication
Full text linkWe present AuthNet: a novel framework for generic biometric authentication which, by learning a regularized mapping instead of a classification boundary, leads to higher performance and improved robustness. The biometric traits are mapped onto a latent space in which authorized and unauthorized users follow simple and well-behaved distributions. In turn, this enables simple and tunable decision boundaries to be employed in order to make a decision. We show that, differently from the deep learning and traditional template-based authentication systems, regularizing the latent space to simple target distributions leads to improved performance as measured in terms of Equal Error Rate (EER), accuracy, False Acceptance Rate (FAR) and Genuine Acceptance Rate (GAR). Extensive experiments on publicly available datasets of faces and fingerprints confirm the superiority of AuthNet over existing methods
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