Double-Sparsity Recovery for ADC-Distorted Compressive Sensing

Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.

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 process of converting an analog, or continuous time, signal into a digital signal is known as analog‐to‐digital conversion (ADC). Many signals are inherently analog. Examples of analog signals obtained from a transducer abound. Other analog signals are inherently electrical, such as those obtained from biomedical electromyography or electroencephalography electrodes. In many cases, it is deemed desirable to process a signal by a microprocessor or computer to extract information, or to store the signal in some digital storage medium such as a hard drive, a floppy disk, or a CD ROM. If the original signal is in analog format, in such cases, it is necessary to convert the analog signal into an equivalent digital signal. This article describes the process of ADC. It introduces the topic and describes the operation of two of the most common methods of accomplishing ADC: the successive approximation ADC and the flash ADC. The sampling theorem is stated and proved, aliasing is described, and quantization noise is discussed. Oversampling is described, and the resultant improvements in ADC performance are documented. Then delta‐sigma ADCs are introduced and described. Conventional first‐order and second‐order delta‐sigma ADCs are described and evaluated. Performance comparisons among simple oversampling, first‐order delta‐sigma, and second‐order delta‐sigma ADCs are documented. The article concludes with an example of a higher order delta‐sigma ADC performance evaluation.

Digital-to-analog converter (DAC) circuit component errors create non-uniform quantization code widths and nonlinear distortion in the DAC's output. In this project, a low complexity 8-bit digital-to-analog converter with partial randomization dynamic element matching (DEM) technique is designed to eliminate pulse shape, timing, and amplitude errors arising from component mismatches as sources of nonlinear distortion in high-resolution DACs. The benefit of this technique is that it gives significantly reduced hardware complexity with no reduction in performance. Simulation results show that nonlinear distortion is greatly suppressed with partial randomization DEM, which offers considerable additional reduction in hardware complexity. In conclusion, this study showed another technique which intends to increase the accuracy and spectral purity of the output signal in data converters.

In the process of signal and image acquisition and transmission, there is not only the additive white Gaussian noise interference, but also the non-Gaussian noise interference. The performance of a standard reconstruction algorithm, known as compressed sensing, can be significantly reduced if it is used to recover the signal affected by non-Gaussian noise. In this paper, LpLq-ADMM algorithm $(p \in(0,2), q \in(0,1))$ based on alternating direction method of multipliers is proposed to improve the reconstruction accuracy and the robustness of signal and image restoration in impulsive SαS (symmetric α-stable) noise. Lp-norm is used as the loss function term to enhance the data restoration ability in SαS noise and Lq-norm is used as the generalized non-convex penalty term to guarantee the sparsity of the signal. In order to efficiently solve the cost function model with minimum non-convex and nonsmooth, reduce the computational complexity of the objective function and improve the processing ability of high-dimensional data, in this paper, the alternating direction method of multipliers (ADMM) is used to solve the cost function model. The appropriate p and q values are selected via numerical simulation experiments to achieve the optimal reconstruction accuracy and robustness of sparse signals in SαS noise. The reconstruction probability of sparse signals and image recovery performance are analyzed under the optimal p and q values. The simulation results show that LpLq-ADMM algorithm has great noise suppression ability to SαS noise, and its Peak Signal to Noise Ratio (PSNR) and signal recovery probability is higher than other recovery algorithms.

Patch-based weighted SCAD prior for compressive sensing

In this paper, we deal with the signal recovery problem in compressed sensing, that is, the problem of estimating the original signal from its linear measurements. Recovery algorithms can be mainly classified into two types, optimization based algorithms and statistical modeling based algorithms. Basis pursuit (BP) or basis pursuit denoising (BPDN) is one of the most widely used optimization based recovery algorithms, that minimizes the $\ell_{1}$ norm of the signal or its coefficients in some basis under the constraint that its linear transform is equal to or close to the observation signal. There are various extensions of those algorithms depending on the problem structure. When the original signal is an image, the objective function is often the sum of the $\ell_{1}$ norm of the coefficients of the signal in some basis and a total variation (TV) of the image. It can be considered that it requires the image to be sparse in both the specific transform domain and finite differences at the same time. In this paper, we propose a statistical model that represents those sparsities and the signal recovery algorithm based on the variational method. One of the advantages of the statistical approach is that we can utilize the posterior information of the original signal and it is known that it can be used to construct the compressed sensing measurements adaptively. The proposed recovery algorithm and adaptive construction of the compressed sensing measurements are validated on numerical experiments.

Low-cost underwater wireless optical communication (UOWC) systems are attractive for high-speed connections among unmanned vehicles or devices in various underwater applications. Here we demonstrate a high-speed and low-cost UOWC system using a low-resolution digital to analog converter (DAC), a single-pixel mini-sized light-emitting diode (mini-LED), and digital pre-compensation (DPC). The enabled DPC scheme comprises digital pre-distortion (DPD), digital pre-emphasis (DPE), and digital resolution enhancer (DRE), which pre-compensate for mini-LED nonlinearity, the bandwidth limitation of the mini-LED and avalanche photodiode detector, and DAC resolution limitation, respectively. The simulation results show that the in-band signal-to-quantization noise ratio can be increased by 6.8 dB using DRE based on a 4-bit DAC. To further improve the system capacity, we tune the level of DPE in order to optimize the trade-off between the residual inter-symbol interference and signal-to-noise ratio. With the combination of optimized DPE and DRE, we obtain a 21.1% higher data rate compared with full DPE only and demonstrate the transmission of 6.9 Gb/s PAM-8 signal over a 2-m distance underwater based on a single-pixel mini-LED and 4-bit DAC. This paper reports a cost-effective UOWC system first using a low-resolution DAC and DPC, which offers a promising path toward low-cost underwater optical wireless networks.

In the past decade, the compressive sensing (CS) based ISAR imaging methods have gained much interest due to the capability of obtaining high-quality images with under-sampled data. However, both the performance and the application of CS ISAR imaging methods are limited by sparse representations and iterative reconstruction algorithms where the former may be hard to find and the latter may lead to low imaging efficiency. The deep-network (DN) based image reconstruction methods appeared in recent years have been shown to be able to dramatically reduce the computational complexity and ensure the image reconstruction at the same time. The Deep-ADMM-Net (DAN) is a network constructed by iterative steps of the traditional optimization algorithm, Alternating Direction Method of Multipliers (ADMM). The mainly characteristic of DAN is that it is interpretable and efficient. We propose a DAN based ISAR imaging method. The well trained DAN can reconstruct high-quality ISAR image using much fewer measurements than CS based imaging methods. Experimental results show that our proposed imaging method is superior to the existing CS method in both image reconstruction quality and computational efficiency

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.

Due to the large swath of available bandwidth, millimeter wave (mmWave) spectrum is potentially suitable to meet enhanced network capacity requirements of future generation communication systems. However, the high Analog to Digital Converter (ADC) sampling rate required to process wide band signals in the mmWave regime results in significant power consumption in the receiver hardware. In this work, an Orthogonal Frequency Division Multiplexing (OFDM) based subsampling architecture is proposed to achieve power efficient receiver design. Subbanding in association with orthogonal spreading codes using subsampling technique reduces the high sampling rate requirement of the receiver. Power consumption in the receiver is further reduced by utilizing low resolution ADC with minimal degradation in Bit Error Rate (BER) performance. In addition to this, OFDM transmission with reduced number of Fast Fourier transform (FFT) points alleviates the multi-path effects significantly, and improves the spectral efficiency. The combined effect of ADC bit resolution and subsampling on the system error performance and power consumption is studied.

A software-defined radio (SDR) for ultrawideband (UWB) communication systems places several stringent requirements on the analog-to-digital converter (ADC). One alternative to using a single ADC is to sample the received signal with an array of lower speed ADCs that were driven by interleaved sampling clocks; however, mismatches among the ADCs will result in signal distortion. This paper makes three important contributions to overcoming this problem: 1) analytical quantification of the impact of ADC gain, offset, and timing mismatches on the performance of a time-interleaved sampling ADC array for UWB signals; 2) demonstration of the efficacy of using a pilot-based matched-filter architecture to mitigate the impact of timing mismatches in the presence of multipath; and 3) implementation of an 8-ADC time-interleaved UWB SDR testbed that operates at an effective sampling frequency of 6.4 GHz. In addition, our findings allow for the design specification of the number of pilots required to obtain a desired system performance. The simulation and measured performance results from this paper demonstrate that ADC mismatches can be controlled to within plusmn10%, yielding acceptable levels of distortion and bit-error-rate (BER) performance on the UWB SDR testbed. Both analytical and simulation results also demonstrate the efficacy of a pilot-based matched filter in mitigating the impact of timing mismatch errors, even in the presence of multipath.

In this paper, a novel transceiver for the Ultra-Wideband (UWB) communication based on emerging theory of compressed sensing (CS) is exploited. The proposed approach of this article is to apply the CS theory for UWB communication to solve the bottleneck of the sampling at the receiver. CS appears to be a natural solution to solve this problem. Our major contribution is to exploit the sparsity of the transmitted image and the channel itself as a part of CS measurement process. According to this basis, in the receiver, the sampling rate will decrease more than traditional sampling systems, and hence, simplify of analog-to-digital converter (ADC). Extensive simulation show that the proposed model can successfully recover original images with the number of samples required less than 10% of Nyquist rate. Finally, in the case of taking into of impact of noise, BER performance of the proposed model compared to the traditional model are also presented in this paper.

In this paper, the issue of gridless compressed sensing (CS)-based direction-of-departure (DOD) and direction-of- arrival (DOA) estimation for bistatic multiple-input multiple- output (MIMO) radar is investigated with one snapshot, and an alternating direction method of multipliers (ADMM) for 2D parameter estimation using decoupled atomic norm minimization (DANM) is proposed. In the proposed algorithm, the decoupled atom set and atomic norm for DOD and DOA estimation are defined, then the atomic norm is transformed into a semi-definite programming (SDP) minimization problem. To decrease the computational complexity of solving SDP using interior point method based SDPT3 solver in CVX toolbox, the DANM with ADMM is deduced, which can greatly decrease the running time, especially in the presence of large scale arrays. Finally, the DOD and DOA are obtained via shift-invariance parameter estimation. It overcomes the grid-mismatch effect of grid-partition of the conventional CS methods, and outperforms the traditional subspace-based methods. Numerical simulations are presented to demonstrate the estimation performance of the proposed algorithm.

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.