Random Sampling and Signal Bregman Reconstruction Based on Compressed Sensing

We consider the energy efficiency of collecting sparse data in wireless sensor networks using compressive sensing (CS). We use a sparse random matrix as the sensing matrix, which we call Sparse Random Sampling (SRS). In SRS, only a randomly selected subset of nodes, called the source nodes, are required to report data to the sink. Given the source nodes, we intend to construct a data gathering tree such that (1) it is rooted at the sink and spans every source node and (2) the minimum residual energy of the tree nodes after the data collection is maximized. We first show that this problem is NP-complete and then develop a polynomial time algorithm to approximately solve the problem. We greedily construct a sequence of data gathering trees over multiple rounds and propose a polynomial-time algorithm to collect linearly combined measurements at each round. We show that the proposed algorithm is provably near-optimal. Simulation and experimental results show that the proposed algorithm excels not only in increasing the minimum residual energy, but also in extending the network lifetime.

Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.

Compressive Sensing (CS) is a new sampling theory which allows signals to be sampled at sub-Nyquist rate without loss of information. Fundamentally, its procedure can be modeled as a linear projection on one specific sensing matrix, which, in order to guarantee the information conservation, satisfies Restricted Isometry Property (RIP). Ordinarily, this matrix is constructed by the Gaussian random matrix or Bernoulli random matrix. In previous work, we have proved that the typical chaotic sequence - logistic map can be adopted to generate the sensing matrix for CS. In this paper, we show that Toeplitz-structured matrix constructed by chaotic sequence is sufficient to satisfy RIP with high probability. With the Toeplitz-structured Chaotic Sensing Matrix (TsCSM), we can easily build a filter with small number of taps. Meanwhile, we implement the TsCSM in compressive sensing of images.

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.

Most recently, an emerging Compressed Sensing (CS) theory has brought a major breakthrough for data acquisition and recovery. It asserts that a signal, which is highly compressible in a known basis, can be reconstructed with high probability through sampling frequency which is well below Nyquist Sampling Frequency. When applying CS to Remote Sensing (RS) Video imaging, it can directly and efficiently acquire compressed image data by randomly projecting original data to obtain linear and non-adaptive measurements. In this paper, with the help of distributed video coding scheme which is a low-complexity technique for resource limited sensors, the frames of a RS video sequence are divided into Key frames (K frames) and Non-Key frames (CS frames). In other words, the input video sequence consists of many groups of pictures (GOPs) and each GOP consists of one K frame followed by several CS frames. Both of them are measured based on block, but at different sampling rates. In this way, the major encoding computation burden will be shifted to the decoder. At the decoder, the Side Information (SI) is generated for the CS frames using traditional Motion-Compensated Interpolation (MCI) technique according to the reconstructed key frames. The over-complete dictionary is trained by dictionary learning methods based on SI. These learning methods include ICA-like, PCA, K-SVD, MOD, etc. Using these dictionaries, the CS frames could be reconstructed according to sparse-land model. In the numerical experiments, the reconstruction performance of ICA algorithm, which is often evaluated by Peak Signal-to-Noise Ratio (PSNR), has been made compared with other online sparse representation algorithms. The simulation results show its advantages in reducing reconstruction time and robustness in reconstruction performance when applying ICA algorithm to remote sensing video reconstruction.

Random sampling and reconstruction of concentrated signals in a reproducing kernel space

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) can alleviate the sensing effort involved in the acquisition of three dimensional image (3D) data. The most common CS sampling schemes employ uniformly random sampling because it is universal, thus it is applicable to almost any signals. However, by considering general properties of images and properties of the acquisition mechanism, it is possible to design random sampling schemes with variable density that have improved CS performance. We have introduced the concept of non-uniform CS random sampling a decade ago for holography. In this paper we overview the non-uniform CS random concept evolution and application for coherent holography, incoherent holography and for 3D LiDAR imaging.

Time delay estimation (TDE) is a hot research topic in wireless location technology. Compressed sensing (CS) theory has been widely applied to image reconstruction and direction of arrival estimation since it was proposed in 2004. The sparse model can be constructed in time domain for estimating the time delay by using the CS theory. The measurement matrix plays a crucial role in the processing of signal reconstruction which is the core problem of CS theory. Therefore the research in the measurement matrix has becomes a hotspot in recent years. The existing measurement matrix is mainly divided into two categories, i.e., random measurement matrix and deterministic measurement matrix. The performance of random measurement matrix has bottlenecks. Firstly, because of the redundant measurement matrix data, the generation and storage of the random number put forward a high requirement for hardware. Secondly the random matrix can only satisfy the restricted isometry property in a statistical sense. The research of the deterministic measurement matrix is of great value under this background. The parity check matrix of low density parity check (LDPC) code has good performance in CS theory. However, the method of randomly selecting non-zero element position has a certain probability to generate a measurement matrix with a short loop structure during generating LDPC code measurement matrix. The robustness of the reconstruction performance decreases with the increase of iteration times. A novel quasi-cyclic CS algorithm based on progressive edge-growth is constructed to estimate the time delay. The purpose of this article is to deal with the need to store a large number of data in existing measurement matrix during time delay, by using the CS theory. The algorithm presented here can achieve TDE in a high precision. First, the theoretical bridge between CS and the maximum likelihood decoding is established. And the design criterion of measurement matrix based on the LDPC code is derived. The sparse measurement matrix with quasi-cyclic structure is constructed by introducing the idea of progressive edge-growth. Finally, the orthogonal matching pursuit algorithm is used to estimate the time delay. Furthermore, the computational complexity of the algorithm and the data storage of the measurement matrix are analyzed theoretically. Simulations show that the correct reconstruction probability of the proposed approach is higher than those of the Gauss random matrix and random LDPC matrix under the same dimension. Compared with the random LDPC matrix, the proposed method can improve performance at the expense of less complexity under the condition of the same data storage.

BackgroundVarious sampling techniques have been implemented to assess child restraint use practices. However, little evidence exists about the impact of selection bias. This study explored differences in demographic characteristics and...

Reconstruction of atomic force microscopy image using compressed sensing

Compressed sensing based multi-rate sub-Nyquist sampling system

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.

Compressed sensing (CS) leverages signal sparsity in transform domains to facilitate precise signal reconstruction from restricted incoherent measurements. While effectively applied in turbomachinery flow field measurements, current compressed sensing reconstruction research primarily emphasizes random sampling within limited instrumentation parameters, resulting in a significant knowledge deficit regarding high-frequency reconstruction from time-domain uniformly undersampled data. This study addresses this limitation by developing compressed sensing-enhanced temporal resolution for unsteady flow field measurements in compressor cascades. This research presents and implements a dual low-frequency uniform sampling compressive sensing approach for particle image velocimetry analysis in the near-wake areas of compressor blades. The effectiveness of the strategy was validated through comparative analysis with random sampling CS reconstruction. Second, a sensitivity analysis was performed on the principal factors influencing reconstruction accuracy in dual low-frequency sampling CS, including the orthogonal basis, compression ratio, and modal order. The dual low-frequency uniform sampling strategy is ultimately extended to multi-low-frequency sampling, hence confirming the robustness of generalized multi-frequency CS implementations. The findings indicate that the dual low-frequency uniform sampling CS technique markedly decreases the need for instrumentation frequency responsiveness while maintaining measurement reliability. This study develops a methodological framework for high-resolution physical field measurements in turbomachinery applications, providing theoretical foundations and practical implementation guidelines for CS-enhanced experimental fluid dynamics.

Capsule Using simulations in a geographical information system our results showed that systematic sampling with quadrats was the most accurate, precise and cost-effective method to survey Magellanic Penguin colonies.Aims To determine which sampling method gives better estimations of penguin abundance.Methods A virtual colony was generated deriving spatial parameters from a real survey and applying Kriging interpolation. Three sampling methods were then applied on this virtual colony: random sampling with quadrats; systematic sampling with quadrats; systematic sampling with fixed-width transects. The estimated abundance for each trial was compared to the abundance of the virtual colony to have a measure of accuracy and precision.Results Systematic sampling with quadrats estimated penguin abundance better than random or systematic sampling with transects since it achieved 100% accuracy and great precision after sampling only 2.1% of the virtual colony.Conclusion The use of a simulated colony allowed the comparison of several sampling methods traditionally used in Magellanic Penguin surveys. The results of this study are important in order to standardize sampling protocols for Magellanic Penguins and to have more comparable estimations to detect trends over time. Also, the methodological approach used here could be used to assess sampling methods for other colonial bird species.