Colored Random Projections for Compressed Sensing

The emerging compressive sampling (CS) theory makes processing ultra-wide-band (UWB) signal at a low sampling rate possible if the underlying signal has a sparse representation in a certain basis. The feasibility of model based compressive sampling for ultra-wide-band (UWB) signal is investigated. In this paper, a multichannel compressive sampling architecture is developed to capture UWB signal at a rate much lower than Nyquist rate. The proposed framework considers sub-Nyquist sampling stream of delayed and weighted versions of a known signal with finite support in time domain. A basis function is constructed to realize sparse signal representation. To reduce the hardware cost, a segmented architecture is suggested. In addition, a joint signal recovery algorithm is presented. Experimental results indicate that, with this system, a UWB signal sampled at about 4% of Nyquist rate still can be recovered with overwhelming probability.

Compressive sensing (CS) is a signal processing technique that enables a signal that has a sparse representation in a known basis to be reconstructed using measurements obtained below the Nyquist rate. Single detector image reconstruction applications using CS have been shown to give promising results. In this study, we investigate the application of CS theory to single detector infrared (IR) rosette scanning systems which suffer from low performance compared to costly focal plane array (FPA) detectors. The single detector pseudoimaging rosette scanning system scans the scene with a specific pattern and performs processing to estimate the target location without forming an image. In this context, this generation of scanning systems may be improved by utilizing the samples obtained by the rosette scanning pattern in conjunction with the CS framework. For this purpose, we consider surface-to-air engagement scenarios using IR images containing aerial targets and flares. The IR images have been reconstructed from samples obtained with the rosette scanning pattern and other baseline sampling strategies. It has been shown that the proposed scheme exhibits good reconstruction performance and a large size FPA imaging performance can be achieved using a single IR detector with a rosette scanning pattern.

Classic signal processing theory dictates that, in order to faithfully reconstruct a band-limited signal (e.g., an image), the sampling rate must be at least twice the maximum frequency contained within the signal, i.e., the Nyquist frequency. Recent developments in applied mathematics, however, have shown that it is often possible to reconstruct signals sampled below the Nyquist rate. This new method of compressed sensing (CS) requires that the signal have a concise and extremely dense representation in some mathematical basis. Magnetic resonance imaging (MRI) is particularly well suited for CS approaches, owing to the flexibility of data collection in the spatial frequency (Fourier) domain available in most MRI protocols. With custom CS acquisition and reconstruction strategies, one can quickly obtain a small subset of the full data and then iteratively reconstruct images that are consistent with the acquired data and sparse by some measure. Successful use of CS results in a substantial decrease in the time required to collect an individual image. This extra time can then be harnessed to increase spatial resolution, temporal resolution, signal-to-noise, or any combination of the three. In this article, we first review the salient features of CS theory and then discuss the specific barriers confronting CS before it can be readily incorporated into clinical quantitative MRI studies of cancer. We finally illustrate applications of the technique by describing examples of CS in dynamic contrast-enhanced MRI and dynamic susceptibility contrast MRI.

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.

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.

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).

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.

Compressed sensing based multi-rate sub-Nyquist sampling system

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 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.

In this paper, we investigate sub-Nyquist sampling method, which can work at the sampling rate below the Nyquist rate. Nowadays, the sampling rate of the classical sub-Nyquist sampling is higher than discrete Compressed Sensing (CS), since the sparseness of the original signal is always destroyed by basis mismatch. We propose a new multi-channel co-prime sampling system along with Sparse Fourier Transform. The analog signal of each channel is firstly mixed by a series of exponential functions. Then, it is fed into integrators and commercial analog-to-digital converters (ADCs). It is noted that the frequency parameters of each subsystem are co-prime. Chinese remainder theorem (CRT) is utilized for the joint processing of all sets of samples and the reconstruction of original signals. Finally, the effects of the signal sparsity, the sampling rate and the signal to noise ratio are simulated in this system. In addition, the experimental results show that the proposed system can work at the rate lower than Random Demodulation RD), Modulated wideband converter (MWC) and their improved version.

Shannon’s Nyquist theorem has always dictated the conventional signal acquisition policies. Power system is not an exception to this. As per this theory, the sampling rate must be at least twice the maximum frequency present in the signal. Recently, compressive sampling (CS) theory has shown that the signals can be reconstructed from samples obtained at sub-Nyquist rate. Signal reconstruction in this theory is exact for “sparse signals” and is near exact for compressible signals provided certain conditions are satisfied. CS theory has already been applied in communication, medical imaging, MRI, radar imaging, remote sensing, computational biology, machine learning, geophysical data analysis, and so forth. CS is comparatively new in the area of computer based power system monitoring. In this paper, subareas of computer based power system monitoring where compressive sampling theory has been applied are reviewed. At first, an overview of CS is presented and then the relevant literature specific to power systems is discussed.

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.

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.

According to the compressed sensing (CS) theory, a signal that is sparse in a certain domain can be nearly exactly recovered from a few measurements where the sampling rate is lower than the Nyquist rate. This theory has been successfully applied to the image compression in the past few years as most image signals are highly sparse. In this paper, we apply an adaptive sampling mechanism to the reweighted block-based CS (BCS). The proposed adaptive sampling allocates the measurements to each image block according to the statistical information of the block so as to sample and recover the image more efficiently. Experimental results demonstrate that our adaptive reweighted method offers a very significant quality improvement compared with the traditional BCS schemes, including the non-reweighted and reweighted ones.