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Highlights • Recovery with multiple prior information via solving n-l1 minimization is proposed. • Theoretical measurement bounds required by the n-l1 minimization are established. • The derived bounds of the n-l1 minimization are sharper. • The proposed n-l1 minimization outperforms the state-of-the-art algorithms. Abstract We address the problem of reconstructing a sparse signal from compressive measurements with the aid of multiple known correlated signals. We propose a reconstruction algorithm with multiple side information signals (RAMSI), which solves an n − ℓ 1 minimization problem by weighting adaptively the multiple side information signals at every iteration. In addition, we establish theoretical bounds on the number of measurements required to guarantee successful reconstruction of the sparse signal via weighted n − ℓ 1 minimization. The analysis of the derived bounds reveals that weighted n − ℓ 1 minimization can achieve sharper bounds and significant performance improvements compared to classical compressed sensing (CS). We evaluate experimentally the proposed RAMSI algorithm and the established bounds using numerical sparse signals. The results show that the proposed algorithm outperforms state-of-the-art algorithms—including classical CS, ℓ 1 -ℓ 1 minimization, Modified-CS, regularized Modified-CS, and weighted ℓ 1 minimization—in terms of both the theoretical bounds and the practical performance. [ABSTRACT FROM AUTHOR]

This paper considers online robust principal component analysis (RPCA) in time-varying decomposition problems such as video foreground-background separation. We propose a compressive online RPCA algorithm that decomposes recursively a sequence of data vectors (e.g., frames) into sparse and low-rank components. Different from conventional batch RPCA, which processes all the data directly, our approach considers a small set of measurements taken per data vector (frame). Moreover, our algorithm can incorporate multiple prior information from previous decomposed vectors via proposing an $n$ - $\ell _{1}$ minimization method. At each time instance, the algorithm recovers the sparse vector by solving the $n$ - $\ell _{1}$ minimization problem—which promotes not only the sparsity of the vector but also its correlation with multiple previously recovered sparse vectors—and, subsequently, updates the low-rank component using incremental singular value decomposition. We also establish theoretical bounds on the number of measurements required to guarantee successful compressive separation under the assumptions of static or slowly changing low-rank components. We evaluate the proposed algorithm using numerical experiments and online video foreground-background separation experiments. The experimental results show that the proposed method outperforms the existing methods. [ABSTRACT FROM AUTHOR]

Large-scale data collection by means of wireless sensor network and Internet-of-Things technology poses various challenges in view of the limitations in transmission, computation, and energy resources of the associated wireless devices. Compressive data gathering based on compressed sensing has been proven a well-suited solution to the problem. Existing designs exploit the spatiotemporal correlations among data collected by a specific sensing modality. However, many applications, such as environmental monitoring, involve collecting heterogeneous data that are intrinsically correlated. In this paper, we propose to leverage the correlation from multiple heterogeneous signals when recovering the data from compressive measurements. To this end, we propose a novel recovery algorithm—built upon belief-propagation principles—that leverages correlated information from multiple heterogeneous signals. To efficiently capture the statistical dependencies among diverse sensor data, the proposed algorithm uses the statistical model of copula functions. Experiments with heterogeneous air-pollution sensor measurements show that the proposed design provides significant performance improvements against the state-of-the-art compressive data gathering and recovery schemes that use classical compressed sensing, compressed sensing with side information, and distributed compressed sensing. [ABSTRACT FROM PUBLISHER]

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via \ell 1 - \ell 1 and \ell 1 - \ell 2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, \ell 1 - \ell 1 minimization improves the performance of CS dramatically. In contrast, \ell 1 - \ell 2 minimization has a performance very similar to classical CS, and brings no significant benefits. In addition, we use the insight provided by our bounds to design practical schemes to improve prior information. All our findings are illustrated with experimental results. [ABSTRACT FROM PUBLISHER]

This work explores an innovative strategy for increasing the efficiency of compressed sensing applied on mm-wave SAR sensing using multiple weighted side information. The approach is tested on synthetic and on real non-destructive testing measurements performed on a 3D-printed object with defects while taking advantage of multiple previous SAR images of the object with different degrees of similarity. The tested algorithm attributes autonomously weights to the side information at two levels: (1) between the components inside the side information and (2) between the different side information. The reconstruction is thereby almost immune to poor quality side information while exploiting the relevant components hidden inside the added side information. The presented results prove that, in contrast to common compressed sensing, good SAR image reconstruction is achieved at subsampling rates far below the Nyquist rate. Moreover, the algorithm is shown to be much more robust for low quality side information compared to coherent background subtraction. [ABSTRACT FROM AUTHOR]

• We design a novel deep neural network that unfolds an iterative algorithm for sparse approximation from 1-bit measurements. The resulting network architecture resembles that of deep residual learning, implying that the model has the potential to be deeply trained. • We show that DeepFPC offers higher signal reconstruction accuracy and speed than the iterative FPC-l1 algorithm. • We apply DeepFPC in the DOA estimation problem and show that it outperforms the state-of-the-art FPC-l1 and deep convolution network (DCN) methods. In this paper, we introduce a novel deep neural network, coined DeepFPC, and investigate its application to tackling the problem of direction-of-arrival (DOA) estimation. DeepFPC is designed by unfolding the iterations of the fixed-point continuation algorithm with one-sided ℓ 1 -norm (FPC-ℓ 1), which has been proposed for solving the 1-bit compressed sensing problem. The network architecture resembles that of deep residual learning and incorporates prior knowledge about the signal structure (i.e., sparsity), thereby offering interpretability by design. Once DeepFPC is properly trained, a sparse signal can be recovered fast and accurately from quantized measurements. The proposed model is then applied in DOA estimation and is shown to outperform state-of-the-art solutions; namely, the iterative FPC-ℓ 1 algorithm and the deep convolution network (DCN) model. [ABSTRACT FROM AUTHOR]