RANSAC-Based Signal Denoising Using Compressive Sensing

This paper deals with sparse signal reconstruction by designing a discrete-time projection neural network. Sparse signal reconstruction can be converted into an L1 -minimization problem, which can also be changed into the unconstrained basis pursuit denoising problem. To solve the L1 -minimization problem, an iterative algorithm is proposed based on the discrete-time projection neural network, and the global convergence of the algorithm is analyzed by using Lyapunov method. Experiments on sparse signal reconstruction and several popular face data sets are organized to illustrate the effectiveness and performance of the proposed algorithm. The experimental results show that the proposed algorithm is not only robust to different levels of sparsity and amplitude of signals and the noise pixels but also insensitive to the diverse values of scalar weight. Moreover, the value of the step size of the proposed algorithm is close to 1/2, thus a fast convergence rate is potentially possible. Furthermore, the proposed algorithm achieves better classification performance compared with some other algorithms for face recognition.

Full spark of even discrete cosine transforms

The conditions under which Compressed sensing (CS) succeeds depend on the structure of the measurement matrix. Researches indicated that matrices whose entries are drawn independently from certain probability distributions satisfy the restricted isometry property (RIP) and guarantee exact recovery of a sparse signal with high probability. Motivated by signal processing applications, random filtering with Toeplitz sensing matrices whose elements are drawn from the same distributions were considered and shown to also be sufficient to recover a sparse signal from reduced samples exactly with high probability. In order to achieve reduction of sampling rate in impulse radio Ultra-Wideband (IR-UWB) communication systems, the output streams of UWB channel were periodically down-sampled. Sub-sampling at the receiver leads to quasi-Toeplitz-structured measurement matrices, whose entries are UWB channel coefficients. In this paper, the feasibility of this kind of quasi-Toeplitz matrices as measurement matrices is discussed. It is shown that the quasi-Toeplitz matrices with entries drawn from logarithm normal distribution satisfy RIP with high probability and also ensures the exact reconstruction of the sparse signals. Simulation results validate their performance.

Periodic Non-uniform sampling in shift-invariant spaces is an effective method for lowrate sampling of continuous time sparse signals, but, recovery of sampled time sparse signals must be unstable in general. In the paper, the possibility of stable recovery under a combination of sufficient sparsity is proposed. The sampling and reconstruction of sparse signals were transformed into matrix and vector operations by using minimum L1 normal. Necessary condition of reconstruction is analyzed. Finally, we are taking multiband sinusoidal signals as an example to prove that the method can achieve the sampling and reconstruction of sparse signals from recovery successful rate and integer of system.

In this paper, we propose a new test response acquisition technique for high-speed devices-based on dual-frequency incoherent sub-sampling and sparse signal reconstruction. The proposed technique enables reconstruction of spectrally sparse wideband signals such as multi-tone signals and short pseudo-random bit sequences (PRBS) with enhanced time/frequency resolution as opposed to current methods. The sampling hardware utilizes dual analog-to-digital converters (ADCs) and dedicated sampling frequency synthesizers with a common frequency reference. As compared to other compressive sampling architectures [1], the proposed hardware architecture is easy to implement at low cost since it does not require accurate sampling clock phase adjustment or random timing generation. For digital signal reconstruction, the proposed technique requires less number of waveform samples than conventional equivalent-time sampling techniques. In addition, the use of an resolution-enhanced discrete Fourier transform (DFT) frame and basis pursuit algorithms minimizes spectral leakage of incoherently sub-sampled signals. This co-design of sampling hardware and signal reconstruction algorithms enables testing of spectrally sparse wideband signals with enhanced time/frequency resolution.

Sparse signal reconstruction methods are used in a wide range of applications such as compressive sensing, denoising, signal separation and general linear inverse problems. The numerical algorithms used for the sparse signal recovery frequently involve finding solutions to the least squares optimization problem with l1-norm regularization. As the l1-norm penalty is not differentiable, so it rules out the possibility of using the efficient optimization techniques that call for the derivative of the objective function. This paper presents a hyperbolic tangent based surrogate function to closely approximate the l1-norm regularization. Simultaneously, we also develop an iterative algorithm for sparse signal reconstruction using the gradient of the proposed smooth function. The algorithm can be used to recover the compressively sampled images from a reduced set of measurements. Various numerical and imaging experiments are used to illustrate the performance of the promising recovery method. It has been shown that the algorithm can be used to reconstruct the compressively sampled images from less number of acquired data, which makes fast imaging possible without compromising high spatial resolutions. The results are validated using phantom as well as original MR and microwave SAR images.

In this paper, we consider the problem of reconstructing sparse multiband wavelet signals of finite levels from their samples in Fourier domain. We show that those sparse signals are determined by their Fourier measurements on a set of size proportional to their sparsity.

Robust sensing matrix design for the Orthogonal Matching Pursuit algorithm in compressive sensing

Sparse gammatone signal model optimized for English speech does not match the human auditory filters

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

Sparse signal reconstruction via collaborative neurodynamic optimization

Smoothing inertial projection neural network for minimization [formula omitted] in sparse signal reconstruction

In this paper, three parameters of targets in bistatic multiple-input multiple-output (MIMO) radar are estimated based on sparse signal reconstruction. First, 2D scanning space in bistatic MIMO radar is divided into dense meshes, and a sparse signal model of multiple measurement vectors is constructed. Second, a constrained objective optimization function is established by using traditional $l2$ norm and is converted to an unconstrained objective optimization function. A conjugate gradient method is utilized to solve the inverse operation of a large-scale matrix and to avoid singular problems during sparse iterations. Even in 2D dense meshes of $90\times 90$ , the speed of convergence can be accelerated. The direction of arrival, the direction of departure, and the reflection coefficient of multiple targets in bistatic MIMO radar are estimated, and the 3D parameters of each target automatically match. Simulation results verify the validity and fast convergence of the proposed method.

The problem of blind super-resolution of sparse signals using arbitrary sampling and the atomic lift is studied. Using the Prolate Spheroidal Wave Functions (PSWFs) and matrix atomic norm, a new Semi-Definite Program (SDP) is proposed. Unlike the previous results, the proposed new version of SDP can localize spikes with higher precision and no need for the magnitude recovery and integer sampling schemes. Numerical simulations show that our method outperforms the recent techniques with generating a lower Normalized Mean Square Error (NMSE).

This paper proposed a new iterative method for solving nonlinear monotone equations with convex constraint and its applications in sparse signal reconstruction and image de-blurring problems. The method can be viewed as an improved adaptation of the generalized Hager-Zhang conjugate gradient method for unconstrained optimization. Unlike the latter which only converged globally for strongly convex functions when the Hager-Zhang parameter $ \theta_k $ lies in the interval $ \left(\frac{1}{4}, +\infty\right) $, the new method exhibited this attribute for nonlinear monotone and Lipschitz continuous functions without restriction for $ \theta_k $ under a more relaxed condition. The derivative-free structure of the method made it suitable for both smooth and non-smooth problems. Numerical experiments on benchmark test problems demonstrated the method's superior performance compared to some state-of-the-art algorithms. Furthermore, the algorithm was successfully applied to sparse signal recovery and image de-blurring problems in compressed sensing, confirming its practical effectiveness.