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Highlights • Paper provides a framework for probabilistic compressive sensing. • The paper aims to address two short-comings of the traditional formulations: the ad-hoc manner for tuning sparsity levels in signal reconstructions, and the lack of uncertainty quantification. • The key idea being presented is that the problem of probabilistic output can be addressed by use of the Relevance Vector Machine (RVM). This is sparse Bayesian regression model, for which fast optimisation methods have already been developed. • It is also highlighted that for a probabilistic output to be meaningful, it is better to use data-driven, as opposed to model-based dictionaries, as this captures the covariance structure of original data sets better. • The motivation for this development lies in the compression of ultrasound signals, for engineering applications. Thus, the method is demonstrated, and illustrations are drawn from an ultrasound Non-Destructive-Test (NDT) data set. Abstract The field of Compressive Sensing (CS) has provided algorithms to reconstruct signals from a much lower number of measurements than specified by the Nyquist-Shannon theorem. There are two fundamental concepts underpinning the field of CS. The first is the use of random transformations to project high-dimensional measurements onto a much lower-dimensional domain. The second is the use of sparse regression to reconstruct the original signal. This assumes that a sparse representation exists for this signal in some known domain, manifested by a dictionary. The original formulation for CS specifies the use of an l 1 penalised regression method, the Lasso. Whilst this has worked well in literature, it suffers from two main drawbacks. First, the level of sparsity must be specified by the user, or tuned using sub-optimal approaches. Secondly, and most importantly, the Lasso is not probabilistic; it cannot quantify uncertainty in the signal reconstruction. This paper aims to address these two issues; it presents a framework for performing compressive sensing based on sparse Bayesian learning. Specifically, the proposed framework introduces the use of the Relevance Vector Machine (RVM), an established sparse kernel regression method, as the signal reconstruction step within the standard CS methodology. This framework is developed within the context of ultrasound signal processing in mind, and so examples and results of compression and reconstruction of ultrasound pulses are presented. The dictionary learning strategy is key to the successful application of any CS framework and even more so in the probabilistic setting used here. Therefore, a detailed discussion of this step is also included in the paper. The key contributions of this paper are a framework for a Bayesian approach to compressive sensing which is computationally efficient, alongside a discussion of uncertainty quantification in CS and different strategies for dictionary learning. The methods are demonstrated on an example dataset from collected from an aerospace composite panel. Being able to quantify uncertainty on signal reconstruction reveals that this grows as the level of compression increases. This is key when deciding appropriate compression levels, or whether to trust a reconstructed signal in applications of engineering and scientific interest. [ABSTRACT FROM AUTHOR]

• The compression sampling and reconstruction of road roughness signal were realized. • The proposed ISA-SPA reconstruction method can adaptively match sparsity. • SA-GSM-SPA reconstruction method matched sparsity accurately and consumed less time. • The method presented in the paper was validated on hard pavement and soft pavement. • Sparsity matching equaled to extremal process of convex function approximately. To significantly reduce the storage space of collected road roughness signals and improve the collection rate, the work investigates the compressive sampling and reconstruction of road roughness signals based on compressive sensing theory. Moreover, to overcome the limitations of the classical signal reconstruction method in the case of unknown sparsity, two sparsity adaptive compressive signal reconstruction methods namely those based on the improved simulated annealing (I-SA) algorithm and the golden section method (GSM) are respectively proposed and compared. Both simulated and measured road roughness signals are used to verify the validity of the novel reconstruction methods and the feasibility of road roughness compression and collection. The research results show that the proposed ISA-SPA method (the sparsity adaptive reconstruction method based on the I-SA) completes the sparsity matching optimization with high reconstruction precision (R 2 = 0.9884), but has a high time consumption (about 16.09 s). Moreover, the proposed SA-GSM-SPA method (the sparsity adaptive reconstruction method based on the GSM) has a fast rate of calculation while inheriting the good sparsity estimation result and high reconstruction precision of the ISA-SPA method. [ABSTRACT FROM AUTHOR]

Abstract: We consider the reconstruction problem in compressed sensing in which the observations are recorded in a finite number of bits. They may thus contain quantization errors (from being rounded to the nearest representable value) and saturation errors (from being outside the range of representable values). Our formulation has an objective of weighted – type, along with constraints that account explicitly for quantization and saturation errors, and is solved with an augmented Lagrangian method. We prove a consistency result for the recovered solution, stronger than those that have appeared to date in the literature, showing in particular that asymptotic consistency can be obtained without oversampling. We present extensive computational comparisons with formulations proposed previously, and variants thereof. [Copyright &y& Elsevier]

Peak-to-average power ratio (PAPR) is the main challenge of the conventional and optical orthogonal frequency division multiplexing (OFDM) systems. In this paper, we implement the clipping technique to reduce the high PAPR of DC-biased optical OFDM (DCO-OFDM) signals. Then, the clipped peaks are sent to the receiver as extra data because of possessing valuable information to reconstruct the original transmission signal. Since the subtraction of the original and clipped signal is sparse, we compress the signal using the compressive sensing approach at the transmitter and the Bayesian algorithm at the receiver to reconstruct the original signal. Computer simulation results show the PAPR reduction performance of the clipping technique and the effectiveness of the suggested reconstruction approach in terms of bit error rate performance. [ABSTRACT FROM AUTHOR]

• Improve compressive sensing used for crack segmentation in practical applications. • Replace sparsity constraint in compressive sensing by deep generative models. • Reduce size of training data with imperfect generative model capturing cracks well. • Achieve high segmentation accuracy and robustness to noise with the proposed method. In a structural health monitoring (SHM) system that uses digital cameras to monitor cracks of structural surfaces, techniques for reliable and effective data compression are essential to ensure a stable and energy-efficient crack images transmission in wireless devices, e.g., drones and robots with high definition cameras installed. Compressive sensing (CS) is a signal processing technique that allows accurate recovery of a signal from a sampling rate much smaller than the limitation of the Nyquist sampling theorem. Different from the popular approach of simultaneously training encoder and decoder using neural network models, the CS theory ensures a high probability of accurate signal reconstruction based on random measurements that is shorter than the length of the original signal under a sparsity constraint. Such method is particularly useful when measurements are expensive, such as wireless sensing of civil structures, because its hardware implementation allows down sampling of signals during the sensing process. Hence, CS methods can achieve significant energy saving for the sensing devices. However, the strong assumption of the signals being highly sparse in an invertible space is relatively hard to guarantee for many real images, such as image of cracks. In this paper, we present a new approach of CS that replaces the sparsity regularization with a generative model that is able to effectively capture a low dimension representation of targeted images. We develop a recovery framework for automatic crack segmentation of compressed crack images based on this new CS method. We demonstrate the remarkable performance of our method that takes advantage of the strong capability of generative models to capture the necessary features required in the crack segmentation task even the backgrounds of the generated images are not well reconstructed. The superior performance of our recovery framework is illustrated by comparisons to three existing CS algorithms. Furthermore, we show that our framework is potentially extensible to other common problems in automatic crack segmentation, such as defect recovery from motion blurring and occlusion. [ABSTRACT FROM AUTHOR]