Compressive sampling for streaming signals with sparse frequency content

Compressed Sensing (CS) is a new framework to measure a signal at sub-Nyquist rate, implying that fewer measurements are needed in reduction of acquisition time, simplification of hardware, reduction of memory space required, etc. In this paper, We demonstrate that ideas from compressed sensing may be exploited in the context of real, no-spare audio signals with short-term stability and focus on two types of greedy reconstruction algorithms: matching pursuit and gradient pursuit, including MP, OMP, StOMP, CoSaMP, GP, CGP, etc. The performance of the greedy reconstruction algorithms is analyzed for original audio signals with the reconstruction time, reconstruction error, SDR, etc. It is demonstrated that the compressed sensing framework may be applied with relatively minor modifications for real audio signals with short-term stability.

Compressive Sensing (CS) is a stable and robust technique that allows for the sub-sampling of data at a given data rate: ‘compressive sampling’ or ‘compressive sensing’ at rates smaller than the Nyquist sampling rate. It makes it possible to create standalone and net-centric applications with fewer resources required in Internet of Things (IoT). CS-based signal and information acquisition/compression paradigm combines the nonlinear reconstruction algorithm and random sampling on a sparse basis that provides a promising approach to compress signal and data in information systems. In this paper, we investigates how CS can provide new insights into coexisting heterogeneous IoT environments. First, we briefly introduce the CS theory with respect to the sampling through providing a compressed sampling process with low computation costs. Then, a CS-based framework is proposed for IoT, in which the hub nodes measure, transmit, and store the sampled data into the fusion center. Then, an efficient cluster-sparse reconstruction algorithm is proposed for in-network compression aiming at more accurate data reconstruction and lower energy efficiency. Therefore, compression should be performed locally at each Access Point (AP) and reconstruction is executed jointly to consider dependencies in the acquired data by the final fusion center.

Compressive sensing (CS) theory proves that signals can be recovered from far fewer random measurements than that suggested by Nyquist-Shannon theorem. This advantage of CS is extremely useful in some data processing applications, especially in video processing. Considering that nonlocal patch-based CS methodology has achieved an impressive performance in image CS field, it motivates us to generalize the idea into the video CS filed. In this paper, by taking account of the spatiotemporal information, we propose a novel strategy to reconstruct the non-key frames of a video sequence by introducing the nonlocal similar patch group from some key frames. Experimental results illustrate that our proposed nonlocal patch-based video CS recovery algorithm can extremely exploit the information of the key frames, and achieve a better performance compared with some existing popular video CS recovery algorithms. It is noted that our idea to construct a spatiotemporal comprehensive patch group may be combined with any nonlocal patch-based CS method for video reconstruction, which leads to various of nonlocal patch-based compressive sensing video recovery algorithms.

Compressive Sensing (CS) is a new sensing modality, which compresses the signal being acquired at the time of sensing. Signals can have sparse or compressible representation either in original domain or in some transform domain. Relying on the sparsity of the signals, CS allows us to sample the signal at a rate much below the Nyquist sampling rate. Also, the varied reconstruction algorithms of CS can faithfully reconstruct the original signal back from fewer compressive measurements. This fact has stimulated research interest toward the use of CS in several fields, such as magnetic resonance imaging, high-speed video acquisition, and ultrawideband communication. This paper reviews the basic theoretical concepts underlying CS. To bridge the gap between theory and practicality of CS, different CS acquisition strategies and reconstruction approaches are elaborated systematically in this paper. The major application areas where CS is currently being used are reviewed here. This paper also highlights some of the challenges and research directions in this field.

This paper presents modification of the TwIST algorithm for Compressive Sensing MRI images reconstruction. Compressive Sensing is new approach in signal processing whose basic idea is recovering signal form small set of available samples. The application of the Compressive Sensing in biomedical imaging has found great importance. It allows significant lowering of the acquisition time, and therefore, save the patient from the negative impact of the MR apparatus. TwIST is commonly used algorithm for 2D signals reconstruction using Compressive Sensing principle. It is based on the Total Variation minimization. Standard version of the TwIST uses masked 2D Discrete Fourier Transform coefficients as Compressive Sensing measurements. In this paper, different masks and different transformation domains for coefficients selection are tested. Certain percent of the measurements is used from the mask, as well as small number of coefficients outside the mask. Comparative analysis using 2D DFT and 2D DCT coefficients, with different mask shapes is performed. The theory is proved with experimental results.

Thermal Imaging can be really valuable to military, other users of surveillance camera and physicians. Contrary to the usual sampling process where weavers want to sample at the Nyquist rate the Compressive Sensing provides a stricter sampling condition when the signal is known to be sparse or compressible. It turned out that the Nyquist-Shannon theorem is a sufficient condition but not a necessary condition for perfect reconstruction. The compressive sensing field of interest provides a stricter sampling condition when the signal is known to be sparse or compressible. This theorem still struggles with three main problems: sparse representation, measurement matrix and reconstruction algorithm. Unfortunately, thermal image camera resolution is considerably lower than of optical cameras, mostly only 160×120 or 320×240 pixels narrow view. The 360-degree infrared surveillance would be the clear choice. Day or night, the IR Revolution 360 panoramic infrared camera provides instantaneous, long range, wide area, high resolution thermal imaging. The method utilizes double sensor thermal imaging cameras. Moreover the temporal resolution has been enhanced. This paper goal is to keep evolving with compressed sensing and thermal imaging technology.

Compressive sampling (CS), or Compressed Sensing , has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning , uses information gleaned from previous observations (e.g. , feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of compressive and adaptive sampling for regression in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near optimal. This result is remarkable since it is the first evidence that shows that compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in the presence of noise. The performance of CS schemes for signal detection is also investigated.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The Compressive Sensing (CS) allows the acquisition of signals already compressed and the posterior reconstruction with much less number of measures than the minimum required by the Nyquist theorem. A subarea of CS which improves the performance at the reconstruction stage is named Model-Based CS. Some works have been developed within this subarea. However, most of them consider only the noise generated by sparse approximation, disregarding the noise generated by the quantization stage and its influence on efficiency and robustness of CS. The objective of this study is to investigate the influence of the noise generated by the quantization stage in Model-Based CS efficiency for images with different levels of sparsity and different distributions of coefficients in the frequency domain. In this work, the image acquisition stage is implemented using the partial Fourier matrix which results in a vector of measures. Then, different steps of uniform scalar quantization are added to this vector and the image reconstruction stage is performed using the Compressive Sampling Matching Pursuit (CoSaMP) on a quadtree model. PSNR and bits rate (BR) are then used to evaluate the efficiency of CoSaMP with quantization noise. The performance of this proposed Model-Based CS using different quantization steps were slightly better than other studies using the same model in terms of PSNR, but with the advantage of obtaining smaller values of bit rate (BR maior que 2 bpp).

A novel noise reduction algorithm combined with compressive sensing (CS) and lifting wavelet transform (LWT) is proposed in this paper. This algorithm can overcome the limitations of traditional noise reduction methods based on Kalman filtering and wavelet threshold filtering. The characteristics of wavelet time-frequency distribution of the microelectromechanical system (MEMS) gyroscope are discussed to illustrate the demerit of the classical filtering methods. Noise reduction algorithm of MEMS gyroscope signal is studied in detail by combining CS theory with lifting wavelet transform. De-noising effect, time-consumption of computation as well as traditional CS reconstruction algorithms are analyzed. The results show that the signal reconstruction algorithm of conventional matching pursuit (MP) greedy algorithms contains more glitches and computation time-consumption, the basis pursuit de-noising (BPDN) algorithm is better and it has advantages of high computational efficiency and ease of implementation.

An improved random equivalent sampling (RES) approach based on compressed sensing (CS) for repetitive ultrasonic signal detection is presented. The proposed system considers recovering ultrasonic signal with high equivalent sampling frequency from samples captured using analogue-to-digital converter (ADC) clocked at a rate much lower than Nyquist rate. A basis function is constructed to realise the ultrasonic signal sparse representation, which paves the way for applying CS theory to ultrasonic signal sub-Nyquist sampling. A sampling architecture is developed, which is applicable for ultrasonic compressive detection. The CS measurement matrix is constructed in the context of RES. Experimental results indicate that, with this sampling system, an ultrasonic signal sampled at ultra-low rate, but still can be recovered with overwhelming probability.

The compressive sensing (CS) theory provides a new slight to the big-data problem led by the Shannon sampling theorem in rolling element bearings condition monitoring, where the measurement matrix of CS tends to be designed by the random matrix (RM) to preserve the integrity of signal roughly. However, when the signal to be analyzed is infected with strong noise, not only does the signal become insufficiently sparse, but the randomness of the measurement matrix will bring down the sensing efficiency, resulting in the loss of fault feature. Thus, a sensing-enhanced CS scheme based on a series of modes after VMD decomposition is proposed under this paper. The core of this scheme is as follows: (1) the principal mode of VMD with better sparsity replaces the raw signal for compressive sensing; (2) all these modes contain the time-frequency characteristics of the raw signal; (3) a new measurement matrix called mode-circulant matrix (MCM) is defined by circulating the mode matrix, and when the amount of samples is shrunk, the sensing efficiency can be enhanced greatly. Besides, considering the fault signal of rolling bearings under variable speed, there is a need to use order tracking to overcome the nonstationarity of the signal before applying CS theory. The analysis results of simulation and experiment prove that the VMD- and MCM-based CS can successfully extract the weak fault feature of rolling bearings with operating speed changing.

The emerging theory of compressed sensing (CS) has led to the remarkable result that signals having a sparse representation in some known basis can be represented (with high probability) by a small sample set, taken from random projections of the signal. Notably, this sample set can be smaller than that required by the ubiquitous Nyquist sampling theorem. Much like the generalized Nyquist sampling theorem dictates that the sampling rate can be further reduced for the representation of bandlimited signals, this paper points to similar results for the sampling density in CS. In particular, it is shown that if additional spectral information of the underlying sparse signals is known, colored random projections can be used in CS in order to further reduce the number of measurements needed. Such a priori information is often available in signal processing applications and communications. Algorithms to design colored random projection vectors are developed. Further, an adaptive CS sampling method is developed for applications where non-uniform spectral characteristics of the signal are expected but are not known a priori.

ADC (Analog to Digital Converter) which follows the Nyquist rate has changed signal processing. Most of the real time applications required too many samples if Nyquist rate is followed. This may involve more cost or even practically not feasible to build systems capable of acquiring samples at Nyquist rate. Compressive Sensing (CS) is a recent trend emerged as a better concept than Nyquist technique by enabling reconstruction of sparse signals which are acquired bellow Nyquist rate. The authors propose reconstruction of Image using Compressive Sensing Technique. Various matrices like Partial Hadmard, Bernoulli Matrix, Uniform Spherical and Random Matrix with proper threshold are used. The reconstruction time, SNR and MSE are measured. Experiments are carried on various sized image with Foreward Hadmard Transform. The experimental results show that for an image of size 256×256 the reconstruction time is 9 sec with signal to noise ratio 23 dB. For inage of size 512×512 the reconstruction time is 15 sec with signal to noise ratio as 26dB. This gives the opportunity to build CS hardware as an alternative for ADC.

The research of frame synchronisation, which processing is based on the sampling at Nyquist rate in traditional method, has been become the hot topic over the past few decades. In the light of compressed sensing theory that sampling received signals below the Nyquist rate, a frame synchronisation method with correlation rule is proposed in this paper. Firstly, the synchronisation metrics of frame synchronisation is expressed as compressed mode by developing the sparsity of the synchronisation metric amplitudes over observation window. The measurement matrix for compressive sampling is then projected, and compressive sampling for the received signal is employed according to the projected measurement matrix. Finally, we reconstruct the synchronisation metrics from the compressive sampling by utilising compressive sampling matching pursuit (CoSaMP) algorithm and obtain the estimate of frame synchronisation with the reconstructed synchronisation metrics. Compared to the traditional methods, the analysis and simulation results show that the sampling rate in proposed method is significantly reduced while obtaining comparative correct synchronisation probability when received signal-to-noise ratio (SNR) is relatively high. Simultaneously, for the reason that the correct synchronisation probability is not particularly sensitive to the iteration number of the CoSaMP algorithm for frame synchronisation, low reconstruction complexity is also obtained in the proposed method.

Compressed sensing (CS) is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, we apply the iterative hard thresholding (IHT) algorithm for compressed sensing on the speech signal. The interested speech signal is transformed to the frequency domain using Discrete Fourier Transform (DCT) and then compressed sensing is applied to that signal. The compressed signal can be reconstructed using the recently introduced Iterative Hard Thresholding (IHT) algorithm and also by the tradditional \( \ell_{1} \) minimization (basic pursuit) for comparison. It is shown that the compressed sensing can provide better root mean square error (RMSE) than the tradition DCT compression method, given the same compression ratio.