An enhanced block-based Compressed Sensing technique using orthogonal matching pursuit

Compressed sensing is a new paradigm to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, a new structured Wilkinson matrix is proposed as a measurement matrix to improve the performance of the block compressive sensing technique which is based on the orthogonal matching pursuit (OMP) algorithm. OMP is simpler to implement and potentially faster than linear programming algorithms but it suffers from two problems: the lack of reconstruction quality, and the need for a large number of measurements. The use of the new structured Wilkinson matrix has improved the OMP reconstruction quality, increased the compression ratio and reduced the computational time. In our experiments, the proposed method was applied to three different test images: Lenna, Barbara and heart MRI. Compared to conventional CS algorithms, the proposed method improves the reconstruction quality by approximately 10 dB with less computational time.

Multiphase flow measurements, based on tomographic imaging techniques, have made substantial progress in the past several years. In particular, ultrasonic tomographic reconstruction has shown its high potential in accurately measuring fluid fractions in a flow cross-section based on direct flow measurements. These types of measurements are very attractive as the system is nonradioactive, has direct contact to fluid, yet without flow obstruction. An ultrasonic tomographic multiphase flow meter (UTM) is being developed to capture the fluid flow rates and phase compositions in producing oil wells. The UTM aims to generate cross-sectional images of the flow inside the pipe. To recover these images, complex computations and high processing time are required, based on a limited amount of available data. For this purpose, compressive sensing (CS) reconstruction methods have shown great potential in overcoming the mentioned data quality and quantity issues. CS builds upon the fact that one can recover certain data of interest from potentially very few measurements. Many CS algorithms have been proposed in the literature. In this paper, we seek to find a suitable algorithm by comparing different CS algorithms in terms of the resulting recovered image quality. Specifically, we survey three algorithms in CS, namely basis pursuit, iterative soft thresholding (IST), and orthogonal matching pursuit (OMP). We also compare the results of the CS algorithms to that of a least-square based conventional algorithm. The numerical results show the superiority of CS recovery algorithms over the conventional approach, both qualitatively and quantitatively. The results also suggest that high image quality could potentially be achieved with less complex CS algorithms, i.e., the IST and OMP algorithms. As presented in the paper, our goal is to adapt CS reconstruction algorithms for images generated by the UTM, for the purpose of accurate quantification of oil, gas, and water phase fractions produced from different wells.

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.

Due to the bad channel environment and poor image sampling equipment, images are often contaminated by noise in the process of collection, transmission and processing. Speckle noise, which is difficult and complex to eliminate, is one of the common noise appearing in image processing. Denoising methods based on Compressed Sensing (CS) technology have been proved as useful tools in suppressing speckle noise of single-frame images. However, temporal correlation in multi-frame images has not yet been utilized. Considering that the traditional denoising methods do not work satisfactorily in speckle noise reduction, a multi-frame image speckle denoising methods based on compressed sensing using tensor model is proposed. The first step is to use the third-order tensor to represent the blocks of image sequences, then the denoising tensor model is established according to the CS theory and the corresponding optimization problem is raised. The problem is divided into three parts: the sparse representation, the tensor dictionary update and the image reconstruction. A Kruskal tensor-based Orthogonal Matching Pursuit (OMP) and Candecomp/Parafac (CP) analysis are used to solve these problems and get the denoised image. At last, simulations are conducted to compare the CS method and traditional methods. It is shown that the CS-based multi-frame speckle denoising method performs well in noise variance and can significantly enhance the visual quality of the image.

The theory of compressed sensing (CS) predicts that structured images can be sampled in a compressive manner with very few nonadaptive linear measurements, made in a proper adjacent domain. However, is such a recovery still possible with non-linear measurements, such as optical-based Fourier modulus? In this paper, we study the problem of Fourier phase retrieval required for optical Fourier CS imaging. We propose an algorithm to solve this problem, exploiting a specific TV-based regularization constraint. We demonstrate the performance of the proposed method on synthetic and real test sequences, in the context of microscopy video reconstructions.

In this paper, a complex-valued Zadoff–Chu measurement matrix is proposed and used in an image-based quantized compressive sensing (CS) scheme. The results of theoretical analysis and simulations show that the reconstruction performance generated by the proposed Zadoff–Chu measurement matrix is better than that obtained by commonly used real-valued measurement matrices. We also applied block compressive sensing (BCS) to reduce the computational complexity of CS and analyzed the effect of block size on the reconstruction performance of the method. The results of simulations revealed that an appropriate choice of block size can not only reduce the computational complexity but also improve the accuracy of reconstruction. Moreover, we studied the effect of quantization on the reconstruction performance of image-based BCS through simulations, and the results showed that analog-to-digital converters with medium resolutions are sufficient to implement quantization and achieve comparable reconstruction performance to that obtained at high resolutions, based on which an image-based BCS framework with low power consumption can thus be developed.

Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-lead Electrocardiogram (MECG) signals. This paper develops the compressed sensing theory for sparse modeling and effective multi-channel ECG compression. A basis matrix with Gaussian kernels is proposed to obtain the sparse representation of each channel, which showed the closest similarity to the ECG signals. Thereafter, the greedy orthogonal matching pursuit (OMP) method is used to obtain the sparse representation of the signals. After obtaining the sparse representation of each ECG signal, the compressed sensing theory could be used to compress the signals as much as possible. Following the compression, the compressed signal is reconstructed utilizing the greedy orthogonal matching pursuit (OMP) optimization technique to demonstrate the accuracy and reliability of the algorithm. Moreover, as the wavelet basis matrix is another sparsifying basis to sparse representations of ECG signals, the compressed sensing is applied to the ECG signals using the wavelet basis matrix. The simulation results indicated that the proposed algorithm with Gaussian basis matrix reduces the reconstruction error and increases the compression ratio.

In this paper, we present a novel method for the acquisition and compression of hyperspectral images based on two concepts - distributed source coding and compressive sensing. Compressive sensing (CS) is a signal acquisition method that samples at sub Nyquist rates which is possible for signals that are sparse in some transform domain. Distributed source coding (DSC) is a method to encode correlated sources separately and decode them together in an attempt to shift complexity from the encoder to the decoder. Distributed compressive sensing (DCS) is a new framework suggested for jointly sparse signals which we apply to the correlated bands of hyperspectral images. We compressively sense each band of the hyperspectral image individually and can then recover the bands separately or using a joint recovery method. We use the Orthogonal Matching Pursuit (OMP) for individual recovery and Simultaneous Orthogonal Matching Pursuit (SOMP) for joint decoding and compare the two methods. The latter is shown to perform consistently better showing that the Distributed Compressive Sensing method that exploits the joint sparsity of the hyperspectral image is much better than individual recovery.

Iterative selection and correction based adaptive greedy algorithm for compressive sensing reconstruction

Iterative Nearest Neighbors

The transmission of high-volume multimedia content (e.g., images) is challenging for a resource-constrained wireless multimedia sensor network (WMSN) due to energy consumption requirements. Redundant image information can be compressed using traditional compression techniques at the cost of considerable energy consumption. Fortunately, compressed sensing (CS) has been introduced as a low-complexity coding scheme for WMSNs. However, the storage and processing of CS-generated images and measurement matrices require substantial memory. Block compressed sensing (BCS) can mitigate this problem. Nevertheless, allocating a fixed sampling to all blocks is impractical since each block holds different information. Although solutions such as adaptive block compressed sensing (ABCS) exist, they lack robustness across various types of images. As a solution, we propose a holistic WMSN architecture for image transmission that performs well on diverse images by leveraging saliency and standard deviation features. A fuzzy logic system (FLS) is then used to determine the appropriate features when allocating the sampling, and each corresponding block is resized using CS. The combined FLS and BCS algorithms are implemented with smoothed projected Landweber (SPL) reconstruction to determine the convergence speed. The experiments confirm the promising performance of the proposed algorithm compared with that of conventional and state-of-the-art algorithms.

An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS) theory in Cognitive Wireless Sensor Network (C-WSN). Local sensing information is collected via energy detection with Analog-to-Information Converter (AIC) at massive cognitive sensors, and sparse representation is considered with the exploration of spatial temporal correlation structure of detected signals. Adaptive measurement matrix is designed in AMS, which is based on maximum energy subset selection. Energy subset is calculated with sparse transformation of sensing information, and maximum energy subset is selected as the row vector of adaptive measurement matrix. In addition, the measurement matrix is constructed by orthogonalization of those selected row vectors, which also satisfies the Restricted Isometry Property (RIP) in CS theory. Orthogonal Matching Pursuit (OMP) reconstruction algorithm is implemented at sink node to recover original information. Simulation results are performed with the comparison of Random Measurement Scheme (RMS). It is revealed that, signal reconstruction effect based on AMS is superior to conventional RMS Gaussian measurement. Moreover, AMS has better detection performance than RMS at lower compression rate region, and it is suitable for large-scale C-WSN wideband spectrum sensing.

We investigate ultra-wideband (UWB) channel estimation based on compressive sampling (CS), where the orthogonal matching pursuit (OMP) algorithm is employed to recover the channel waveform from noisy measurements. In order to boost the robustness of OMP in the presence of additive Gaussian noise (AWGN), we propose a weighted OMP (WOMP) algorithm. For a given sparse dictionary, weighting factors are assigned to the atoms and a weighted matching process is performed by WOMP. Simulation results show that the proposed WOMP is more robust than the original OMP and can be used to gain better channel estimation precision.

The compressive sensing (CS) framework states that a signal that has a sparse representation in a known basis may be reconstructed from samples obtained at a sub-Nyquist sampling rate. The Fourier domain is widely used in CS applications due to its inherent properties. Sparse signal recovery applications using a small number of Fourier transform coefficients have made solutions to large-scale data recovery problems, including image recovery problems, more practical. The sparse reconstruction of 2D images is performed using the sampling patterns generated by taking the general frequency characteristics of the images into account. In this work, instead of forming a general sampling pattern for infrared (IR) images, a special sampling pattern is obtained by gathering a database to extract the frequency characteristics of IR sea-surveillance images. Experimental results show that the proposed sampling pattern provides better sparse recovery results compared to the widely used patterns proposed in the literature. It is also shown that, together with a certain image dataset, the sampling pattern generated by the proposed scheme can be generalized for various image sparse recovery applications.

The upcoming wireless communication technologies increase the demand for spectrum, the dynamic spectrum allocation technique is a promising solution for the spectrum allocation. Spectrum sensing plays a key role in dynamic spectrum allocation, scanning through a wideband for the detection of spectrum holes which poses a problem of very high sampling rate and compressive sensing (CS) uses sub-Nyquist samples to addresses this problem. This paper proposes how orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and stage wise orthogonal matching pursuit (StOMP) signal reconstruction algorithms can be used for detection of spectrum holes. Simulation results reveal that the probability of detection of these algorithms is very high for the detection problem than for the estimation problem.KeywordsCognitive radioOrthogonal matching pursuitSpectrum sensingCompressive sensingWide band signal