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Recently, biometric recognition has become a significant field of research. The concept of cancelable biometrics (CB) has been introduced to address security concerns related to the handling of sensitive data. In this paper, we address unconstrained face verification by proposing a deep cancelable framework called BiometricNet+ that employs random projections (RP) to conceal face images and compressive sensing (CS) to reconstruct measurements in the original domain. Our lightweight design enforces the properties of unlinkability, revocability, and non-invertibility of the templates while preserving face recognition accuracy. We compare facial features by learning a regularized metric: at training time, we jointly learn facial features and the metric such that matching and non-matching pairs are mapped onto latent target distributions; then, for biometric verification, features are randomly projected via random matrices changed at every enrollment and query and reconstructed before the latent space mapping is computed. We assess the face recognition accuracy of our framework on challenging datasets such as LFW, CALFW, CPLFW, AgeDB, YTF, CFP, and RFW, showing notable improvements over state-of-the-art techniques while meeting the criteria for secure cancelable template design. Since our method requires no fine-tuning of the learned features, it can be applied to pre-trained networks to increase sensitive data protection. [ABSTRACT FROM AUTHOR]

Compressed 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. [ABSTRACT FROM AUTHOR]

Compressed 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. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new gradient-based methods for image recovery from a small collection of spectral coefficients of the Fourier transform, which is of particular interest for several scanning technologies, such as magnetic resonance imaging. Since gradients of a medical image are much more sparse or compressible than the corresponding image, classical \ell 1 -minimization methods have been used to recover these relative differences. The image values can then be obtained by integration algorithms imposing boundary constraints. Compared with classical gradient recovery methods, we propose two new techniques that improve reconstruction. First, we cast the gradient recovery problem as a compressed sensing problem taking into account that the curl of the gradient field should be zero. Second, inspired by the emerging field of signal processing on graphs, we formulate the gradient recovery problem as an inverse problem on graphs. Iteratively reweighted \ell 1 recovery methods are proposed to recover these relative differences and the structure of the similarity graph. Once the gradient field is estimated, the image is recovered from the compressed Fourier measurements using least squares estimation. Numerical experiments show that the proposed approach outperforms the state-of-the-art image recovery methods. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) is a fast and efficient way to obtain compact signal representations. Oftentimes, one wishes to extract some information from the available compressed 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. [ABSTRACT FROM PUBLISHER]

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed measurements, and exploiting network communication, each node aims at reconstructing the support and the non-zero values of its observed signal. In the literature, distributed greedy algorithms have been proposed to tackle this problem, among which the most reliable ones require a large amount of transmitted data, which barely adapts to realistic network communication constraints. In this paper, we address the problem through a reweighted \ell 1 soft thresholding technique, in which the threshold is iteratively tuned based on the current estimate of the support. The proposed method adapts to constrained networks, as it requires only local communication among neighbors, and the transmitted messages are indices from a finite set. We analytically prove the convergence of the proposed algorithm and we show that it outperforms the state-of-the-art greedy methods in terms of balance between recovery accuracy and communication load. [ABSTRACT FROM AUTHOR]

Distributed optimization in multi-agent systems under sparsity constraints has recently received a lot of attention. In this paper, we consider the in-network minimization of a continuously differentiable nonlinear function which is a combination of local agent objective functions subject to sparsity constraints on the variables. A crucial issue of in-network optimization is the handling of the communications, which may be expensive. This calls for efficient algorithms, that are able to reduce the number of required communication links and transmitted messages. To this end, we focus on asynchronous and randomized distributed techniques. Based on consensus techniques and iterative hard thresholding methods, we propose three methods that attempt to minimize the given function, promoting sparsity of the solution: asynchronous hard thresholding (AHT), broadcast hard thresholding (BHT), and gossip hard thresholding (GHT). Although similar in many aspects, it is difficult to obtain a unified analysis for the proposed algorithms. Specifically, we theoretically prove the convergence and characterize the limit points of AHT in regular networks under some proper assumptions on the functions to be minimized. For BHT and GHT, instead, we characterize the fixed points of the maps that rule their dynamics in terms of stationary points of original problem. Finally, we illustrate the implementation of our techniques in compressed sensing and present several numerical results on performance and number of transmissions required for convergence. [ABSTRACT FROM PUBLISHER]

In this paper, the security of the compressed sensing (CS) framework as a form of data confidentiality is analyzed. Two important properties of one-time random linear measurements acquired using a Gaussian independent identically distributed matrix are outlined: 1) the measurements reveal only the energy of the sensed signal and 2) only the energy of the measurements leaks information about the signal. An important consequence of the above facts is that CS provides information theoretic secrecy in a particular setting. Namely, a simple strategy based on the normalization of the Gaussian measurements achieves, at least in theory, perfect secrecy, enabling the use of CS as an additional security layer in privacy preserving applications. In the generic setting in which CS does not provide information theoretic secrecy, two alternative security notions linked to the difficulty of estimating the energy of the signal and distinguishing equal-energy signals are introduced. Useful bounds on the mean square error of any possible estimator and the probability of error of any possible detector are provided and compared with the simulations. The results indicate that CS is in general not secure according to cryptographic standards, but may provide a useful built-in data obfuscation layer. [ABSTRACT FROM PUBLISHER]

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics. [ABSTRACT FROM PUBLISHER]

We consider correlated and distributed sources without cooperation at the encoder. For these sources, we derive the best achievable performance in the rate-distortion sense of any distributed compressed sensing scheme, under the constraint of high-rate quantization. Moreover, under this model we derive a closed-form expression of the rate gain achieved by taking into account the correlation of the sources at the receiver and a closed-form expression of the average performance of the oracle receiver for independent and joint reconstruction. Finally, we show experimentally that the exploitation of the correlation between the sources performs close to optimal and that the only penalty is due to the missing knowledge of the sparsity support as in (non distributed) compressed sensing. Even if the derivation is performed in the large system regime, where signal and system parameters tend to infinity, numerical results show that the equations match simulations for parameter values of practical interest. [ABSTRACT FROM AUTHOR]