Quantization Noise on Image Reconstruction Using Model-Based Compressive Sensing

Compressed Sensing (CS), as a new rapidly growing research field, promises to effectively recover a sparse signal at the rate of below Nyquist rate. This revolutionary technology strongly relies on the sparsity of the signal and incoherency between sensing basis and representation basis. Exact recovery of a sparse signal will be occurred in a situation that the signal of interest sensed randomly and the measurements are also taken based on sparsity level and log factor of the signal dimension. In this paper, compressed sensing method is proposed to reduce the noise and reconstruct the image signal. Noise reduction and image reconstruction are formulated in the theoretical framework of compressed sensing using Basis Pursuit (BP) and Compressive Sampling Matching Pursuit (CoSaMP) algorithm when random measurement matrix is utilized to acquire the data. In this research we have evaluated the performance of our proposed image enhancement methods using the quality measure peak signal-to-noise ratio (PSNR).

This paper proposes an efficient image reconstruction for compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) using Symlet 8 (sym8) wavelets with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT) which relies on computationally intensive convolution operations the LWT provides a faster sparse representation while preserving the sparsity crucial for CS. The proposed approach leverages a key insight: among the four subbands produced by the LWT namely the approximation (CA) and the detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Therefore, compressive sensing is applied exclusively to these detail subbands, while the CA subband is left uncompressed to retain essential low-frequency information. Experiments were conducted on both a natural test image (Lena) and a medical MRI scan, across image resolutions ranging from 200×200 to 512×512 pixels and sampling rates from 10% to 80%. Performance was assessed using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently demonstrate that ALISTA significantly outperforms SP and CoSaMP in both reconstruction fidelity and computational efficiency. At an 80% sampling rate, ALISTA achieves SSIM values of 0.99346 for Lena and 0.98 for the MRI image, compared to approximately 0.97 and 0.94, respectively, for the other two methods. Furthermore, ALISTA maintains remarkably low reconstruction times under 4 seconds even for 512×512-pixel images. These findings confirm that the ALISTA + LWT/sym8 combination offers the best trade-off between image quality and speed, exhibiting robustness across different image types and scales.

This paper proposes an efficient image reconstruction for compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) using Reverse Biorthogonal 6.8 (rbio6.8) wavelets with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT) which relies on computationally intensive convolution operations the LWT provides a faster sparse representation while preserving the sparsity crucial for CS. The proposed approach leverages a key insight: among the four subbands produced by the LWT namely the approximation (CA) and the detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Therefore, compressive sensing is applied exclusively to these detail subbands, while the CA subband is left uncompressed to retain essential low-frequency information. Experiments were conducted on both a natural test image (Lena) and a medical MRI scan, across image resolutions ranging from 200×200 to 512×512 pixels and sampling rates from 10% to 80%. Performance was assessed using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently demonstrate that ALISTA significantly outperforms SP and CoSaMP in both reconstruction fidelity and computational efficiency. At an 80% sampling rate, ALISTA achieves SSIM values of 0.99314 for Lena and 0.97688 for the MRI image, compared to approximately 0.97402 and 0.93577, respectively, for the other two methods. Furthermore, ALISTA maintains remarkably low reconstruction times under 4 seconds even for 512×512-pixel images. These findings confirm that the ALISTA + LWT/rbio6.8 combination offers the best trade-off between image quality and speed, exhibiting robustness across different image types and scales.

In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result.

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

A new greedy algorithm for sparse recovery

In this paper, joint compressed sensing (CS)-based estimation of transmit power, geographical location and frequency bands of active primary users (PUs) using three reconstruction algorithms, orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and iterative hard thresholding (IHT) methods is investigated. In the first simulations, the performances of OMP, CoSaMP and IHT methods are evaluated in different signal to noise ratios (SNRs) and different values of sparsity. The first experiment demonstrates that OMP is the high performance reconstruction algorithm but it needs a bit higher complexity. Moreover, two scenarios for decision-making is considered in fusion center (FC) and respected simulation results for two cases, ideal and non-ideal lossy channels between secondary users (SUs) and fusion center, are represented. Second experiments show that decision-making based on integrated reconstruction is more efficient than averaging on three separate reconstructions in both ideal and lossy channels.

Impulse detection using a shift-invariant dictionary and multiple compressions

In most scenes of through-the-wall imaging (TWI), the observation zone is spares. So the radar signals could be processed using Compressive Sensing (CS) technique. Existing greedy algorithms for CS, such as orthogonal Matching Pursuit (OMP) algorithm and Compressive Sampling Matching pursuit (CoSaMP), suffer from artifacts and low resolution respectively. To cover the shortage of existing algorithms, a modified Compressive Sampling Matching Pursuit algorithm is proposed. By using the orthogonality among selected basis-signals and backtracking strategy for basis-signals reevaluation, the proposed algorithm could reconstruct radar signal. Then the image of observation zone could be got using Delay and Sum (DAS) beamforming method. Measurement results demonstrate the effectiveness of the proposed algorithm.

Most signals can be represented sparsely in a basis. Recently, Compressive Sensing Theorem which offers convex optimization algorithms based on l 1 -minimization for sparse signal recovery is often being used. In this paper, some of the iterative signal recovery algorithms alternative to l 1 -minimization solution which are Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), Iterative Hard Thresholding (IHT) and Lipschitz Iterative Hard Theresholding (LIHT) are compared in noisy and noiseless conditions with various tests. Iterative algorithms alternative to the l 1 optimization method with similar performance are verified. OMP algorithm that works at higher true reconstruction rates in noisy and noiseless conditions can be preferred instead of convex optimization methods.

In order to improve signal reconstruction accuracy, a CoSaMP (Compressive Sampling Matching Pursuit) algorithm based on peak signal to noise ratio is proposed in allusion to the disadvantages of CoSaMP algorithm. Firstly, the discrete cosine wave transform is improved to initially estimate the signal sparseness; secondly, the optimum iteration number is determined according to the peak signal to noise ratio to gradually approach to the real sparseness of the signal for signal reconstruction; finally, the simulation experiment is adopted to analyze the algorithm performance. The result shows: compared with CoSaMP algorithm and other improved CoSaMP algorithms, the proposed algorithm can not only obtain more ideal reconstruction effect, but also improve the reconstruction success probability and reduce the reconstruction time, thus having higher reconstruction efficiency.

A duplexer is necessary, but unfavourable for a frequency-division duplexing (FDD) base station, due to its bulky size, high cost and design challenges. In order to relax the performance requirement of such device, the transmitter (TX) leakage needs to be suppressed. The state-of-the-art solutions failed to provide a wideband solution for cancelling the TX leakage at RF frequency, due to the lack of delay optimization. Aiming to provide high delay estimation accuracy, this paper presents a modelling technique which is based on the compressed sampling matching pursuit (CoSaMP) algorithm for compressed sampling (CS). As a result, by using the proposed modelling technique, cancellation systems, particularly the ones that are based on the analog finite impulse response (FIR) filter structure, can be implemented to achieve wideband suppressing at RF frequencies.

Compressive sensing based multiuser detector for massive MBM MIMO uplink

A sparse global navigation satellite system (GLONASS) signal acquisition method based on compressive sensing and multiple measurement vectors is proposed. The nonsparse GLONASS signal can be represented sparsely on our proposed dictionary which is designed based on the signal feature. Then, the GLONASS signal is sensed by a normalized orthogonal random matrix and acquired by the improved multiple measurement vectors acquisition algorithm. There are 10 cycles of pseudorandom codes in a navigation message, and these 10 pseudorandom codes have the same row sparse structure. So, the acquisition probability can be raised by row sparse features theoretically. A large number of simulated GLONASS signal experiments show that the acquisition probability increases with the increase in the measurement vector column dimension. Finally, the practical availability of the new method is verified by acquisition experiments with the real record GLONASS signal. The new method can reduce the storage space and energy loss of data transmission. We hope that the new method can be applied to field receivers that need to record and transmit navigation data for a long time.

Wideband spectrum sensing is regarded as one of the key features in cognitive radio systems. Compressive sensing (CS) has recently become one of the promising techniques to deal with the Nyquist sampling rate bottleneck of wideband spectrum sensing. Theoretical analyses and simulation have shown that CS could achieve high detection probability and low false alarm for wideband spectrum sensing. However, implementation of CS on the real-time signals and real-time processing poses significant challenges due to the iterative nature of the CS algorithms. In this paper, we propose a novel adaptively regularized iterative reweighted least squares (AR-IRLS) algorithm to implement the real-time signal recovery on the CS based wideband spectrum sensing. The proposed algorithm moves estimated solutions along an exponential-linear path by regularizing weights with a series of non- increasing penalty terms, which significantly speeds up the convergence of reconstruction and provides high fidelity guarantee to cope with the varying bandwidths and power levels of occupied channels. The proposed algorithm presents robustness against different sparsity levels at low compressive ratio without degradation on the reconstruction performance, and is tested on the real-time signals over TV white space spectrum after having been validated on the simulated signals. Both the simulation and real-time experiments show that the proposed algorithm outperforms the conventional iterative reweighted least squares (IRLS) algorithms in terms of convergence speed, reconstruction accuracy, and compressive ratio requirement.