The increasing amount of data generated by space applications poses several challenges due to limited resources available onboard: power, memory, computation, data rate. In this paper, we propose Compressed Sensing (CS) as the key tool to face those challenges via compressive imaging. This signal processing technique, only recently applied to space applications, dramatically simplifies the image acquisition featuring native compression/encryption and enabling onboard image analysis, allowing to design simpler and lighter optical systems. In this paper, we try to answer the following question: To what extent are the potential benefits of CS going to materialize in a realistic “space big data” application scenario? To this purpose, we first review compressive imaging techniques and already existing prototypes and concepts, critically discussing the technological issues involved. Then, we propose a set of instrument concepts in the application domains of space science, planetary exploration and earth observation, most suitable for a CS-based application. For the most promising of them, we go deeper into the analysis showing preliminary reconstruction performance tests.

A well-known result [1, Lemma 3.4] states that, without noise, it is better to overestimate the support of a sparse signal, since, if the estimated support includes the true support, the reconstruction is perfect. In this paper, we investigate whether this result holds also in the presence of noise. First, we derive the covariance matrix of the signal estimate when the observation matrix is Gaussian, generalizing existing results. Then, we show that, even in the noisy case, overestimating the support length is the preferred solution, as the error incurred by missing some signal components dominates the overall error variance. Finally, an upper bound of the estimated support length is provided to avoid excessive noise amplification.

In this paper, we propose new gradient-based methods for image reconstruction from partial Fourier measurements, which are commonly used in magnetic resonance imaging (MRI) or synthetic aperture radar. Compared to classical gradient recovery methods, a key improvement is obtained by formulating the gradient recovery problem as a compressed sensing problem with the additional constraint that the curl of the gradient field must be zero. Moreover, we formulate the image recovery problem as an inverse problem on graphs. Iteratively reweighted ℓ1recovery methods are proposed to recover these relative differences and the structure of the similarity graph. Finally, the image is recovered from the compressed Fourier measurements using least squares estimation. Numerical experiments demonstrate that the proposed approach outperforms the state-of-the-art image recovery methods.

Multifactor user authentication systems enhance security by augmenting passwords with the verification of additional pieces of information such as the possession of a particular device. This paper presents an innovative user authentication scheme that verifies the possession of one’s smartphone by uniquely identifying its camera. High-frequency components of the photo-response nonuniformity of the optical sensor are extracted from raw images and used as a weak physical unclonable function. A novel scheme for efficient transmission and server-side verification is also designed based on adaptive random projections and on an innovative fuzzy extractor using polar codes. The security of the system is thoroughly analyzed under different attack scenarios both theoretically and experimentally.

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 ℓ1-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 ℓ1recovery 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.

Recently, we demonstrated that random projections can provide an extremely compact representation of a camera fingerprint without significantly affecting the matching performance. In this paper, we propose a new construction that makes random projections of camera fingerprints scale-robust. The proposed method maps the compressed fingerprint of a rescaled image to the compressed fingerprint of the original image, rescaled by the same factor. In this way, fingerprints obtained from rescaled images can be directly matched in the compressed domain, which is much more efficient than existing scale-robust approaches. Experimental results on the publicly available Dresden database show that the proposed technique is robust to a wide range of scale transformations. Moreover, robustness can be further improved by providing reference scales in the database, with a small additional storage cost.

Image retrieval is the process of finding images from a large collection, satisfying a user-specified criterion. Content-based retrieval has been the traditional paradigm, in which one wishes to find images whose content is similar to a query. In this paper we explore a novel criterion for image search, based on forensic principles. We address the problem of retrieving all the photos in a collection that have been acquired by a specific device which is presented to the system as a query. This is an important forensic problem, whose solution could be very useful for detecting improper usage of pictures. We do not rely on metadata such as Exif headers because they can be unavailable, or easily manipulated, and in most cases cannot identify the specific device. We rely instead on a forensic tool called Photo Response Non-Uniformity (PRNU), which constitutes a reliable fingerprint of a camera sensor. We examine recent advances in compression of such fingerprints, which allow to address the previously unexplored image retrieval problem on large scales.

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.

Retrieving pictures from large collections according to a specific criterion is an increasingly relevant task. An important , but so far overlooked, such criterion is the retrieval of pictures acquired by a specific camera. Instead of relying on metadata , which can be absent or easily manipulated, a forensic tool is exploited, namely the photo response non-uniformity (PRNU) of the camera sensor. Recent works showed that random projections can be used to significantly compress the PRNU, enabling operation on very large scales, previously impossible due to the size of the PRNU and to the complexity of the matching operations. In this paper, we propose efficient techniques for management and retrieval of images employing the PRNU, and test them on a database of 1174 cameras and half a million pictures downloaded from the Internet.

A sparse or compressible signal can be recovered from a certain number of noisy random projections, smaller than what dictated by classic Shannon/Nyquist theory. In this paper, we derive the closed-form expression of the mean square error performance of the oracle receiver, knowing the sparsity pattern of the signal. With respect to existing bounds, our result is exact and does not depend on a particular realization of the sensing matrix. Moreover, our result holds irrespective of whether the noise affecting the measurements is white or correlated. Numerical results show a perfect match between equations and simulations, confirming the validity of the result.

Compressed Sensing (CS) is suitable for remote acquisition of hyperspectral images for earth observation, since it could exploit the strong spatial and spectral correlations, allowing to simplify the architecture of the onboard sensors. Solutions proposed so far tend to decouple spatial and spectral dimensions to reduce the complexity of the reconstruction, not taking into account that onboard sensors progressively acquire spectral rows rather than acquiring spectral channels. For this reason, we propose a novel progressive CS architecture based on separate sensing of spectral rows and joint reconstruction employing Total Variation. Experimental results run on raw AVIRIS and AIRS images confirm the validity of the proposed system.

In this paper we present F2OMP, a recovery algorithm for Compressed Sensing over finite fields. Classical recovery algorithms do not exploit the fact that a signal may belong to a finite alphabet, while we show that this information can lead to more efficient reconstruction algorithms. As an application, we use the proposed algorithm to recover sparse grayscale images, showing that performing CS operation over a finite field can outperform classical recovery algorithms from visual quality, memory occupation and complexity point of view.

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.

The compressed sensing paradigm allows to efficiently represent sparse signals by means of their linear measurements. However, the problem of transmitting these measurements to a receiver over a channel potentially prone to packet losses has received little attention so far. In this paper, we propose novel methods to generate multiple descriptions from compressed sensing measurements to increase the robustness over unreliable channels. In particular, we exploit the democracy property of compressive measurements to generate descriptions in a simple manner by partitioning the measurement vector and properly allocating bit-rate, outperforming classical methods like the multiple description scalar quantizer. In addition, we propose a modified version of the Basis Pursuit Denoising recovery procedure that is specifically tailored to the proposed methods. Experimental results show significant performance gains with respect to existing methods.

In this paper we address the problem of visual quality of images reconstructed from block-wise random projections. Independent reconstruction of the blocks can severely affect visual quality, by displaying artifacts along block borders. We propose a method to enforce smoothness across block borders by modifying the sensing and reconstruction process so as to employ partially overlapping blocks. The proposed algorithm accomplishes this by computing a fast preview from the blocks, whose purpose is twofold. On one hand, it allows to enforce a set of constraints to drive the reconstruction algorithm towards a smooth solution, imposing the similarity of block borders. On the other hand, the preview is used as a predictor of the entire block, allowing to recover the prediction error, only. The quality improvement over the result of independent reconstruction can be easily assessed both visually and in terms of PSNR and SSIM index.

Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. In this paper we address the application of CS to the scenario of progressive acquisition of 2D visual signals in a line-by-line fashion. This is an important setting which encompasses diverse systems such as flatbed scanners and remote sensing imagers. The use of CS in such setting raises the problem of reconstructing a very high number of samples, as are contained in an image, from their linear projections. Conventional reconstruction algorithms, whose complexity is cubic in the number of samples, are computationally intractable. In this paper we develop an iterative reconstruction algorithm that reconstructs an image by iteratively estimating a row, and correlating adjacent rows by means of linear prediction. We develop suitable predictors and test the proposed algorithm in the context of flatbed scanners and remote sensing imaging systems. We show that this approach can significantly improve the results of separate reconstruction of each row, providing very good reconstruction quality with reasonable complexity.

Abstract—Channel estimation inaccuracy is known to affect significantly the error performance of coded communication systems. This applies in particular to broadband MIMO channels, often considered in conjunction with OFDM such as in the IEEE 802.11n and 802.16 standards. The focus of this work is on an 802.11n compliant MIMO-OFDM communication system. Different channel estimation techniques (based on pilot symbol insertion) are considered and their relevant error performance is analyzed. More specifically, genie-aided, mismatched, and optimum channel estimation techniques are studied with special emphasis on the last one as far as concerns the relative error performance versus complexity trade-off in suboptimum implementation. It is shown that the optimum receiver can be implemented by limiting the channel processing to the dominant eigenmodes, in order to reduce the ensuing complexity. The approach followed in this work may be seen as an extension of previous results relevant to the narrowband MIMO channel. I.

Two receiver structures based on pilot symbol-aided channel estimation are considered for the separately-correlated Rician fading MIMO channel. 1) A mismatched receiver, which decodes the received signal by first using maximum-likelihood (ML) or minimum mean-square error (MMSE) estimation of the MIMO channel matrix, and then by assuming that the estimate is exact. 2) An optimum receiver, which does not estimate explicitly the channel matrix but jointly processes the received pilot and data samples assuming known channel distribution. The main focus is on the optimum receiver. First, the optimum detection algorithm for the separately-correlated Rician fading MIMO channel is derived. Then, an iterative implementation suitable for trellis space–time decoding is proposed in order to reduce the algorithm complexity. Numerical results are presented for a 2x2 MIMO system with Rayleigh/Rice correlated/uncorrelated fading and a simple trellis space–time code. These results show that substantial gain is available by using our proposed optimum receiver either in terms of Eb/N0 and system throughput (in both cases accounting for pilot-symbol rate reduction). Finally, the effect of parameter estimation (required by the optimum receiver) is studied and it is shown that this effect is almost unnoticeable in the case considered.