Smoothed L0 Research Articles

Tensor compressed video sensing reconstruction by combination of fractional-order total variation and sparsifying transform

High reconstructed performance compressed video sensing (CVS) with low computational complexity and memory requirement is very challenging. In order to reconstruct the high quality video frames with low computational complexity, this paper proposes a tensor-based joint sparseness regularization CVS reconstruction model FrTVCST (fractional-order total variation combined with sparsifying transform), in which a high-order tensor fractional-order total variation (FrTV) regularization and a tensor discrete wavelet transform (DWT) L0 norm regularization are combined. Furthermore, an approach for choosing the regularization parameter that controls the influence of the two terms in this joint model is proposed. Afterwards, a tensor gradient projection algorithm extended from smoothed L0 (SL0) is deduced to solve this combined tensor FrTV and DWT joint regularization constrained minimization problem, using a smooth approximation of the L0 norm. Compared with several state-of-the-art CVS reconstruction algorithms, such as the Kronecker compressive sensing (KCS), generalized tensor compressive sensing (GTCS), N-way block orthogonal matching pursuit (N-BOMP), low-rank tensor compressive sensing (LRTCS), extensive experiments with commonly used video data sets show the competitive performance of the proposed algorithm with respect to the peak signal-to-noise ratio (PSNR) and subjective visual quality.

Iterative Sparsification-Projection: Fast and Robust Sparse Signal Approximation

In this paper, we address recovery of sparse signals from compressed measurements, and sparse signal approximation, which have received considerable attention over the last decade. First, we revisit smoothed L0 (SL0), a well-known sparse recovery algorithm, and give some insights into it that have not been noticed previously. Specifically, we re-derive the SL0 algorithm based on proximal methods, and using recent results in solving nonconvex problems by proximal algorithms, we provide a convergence guarantee for it. In addition, inspired by this derivation, we propose a general family of algorithms, which we call iterative sparsification-projection (ISP), having SL0 as a special member. Our algorithmic framework starts with an initial guess for the unknown sparse vector, and then iteratively sparsifies it (using a fixed threshold) followed by projecting the result onto the admissible solution set. The threshold is then decreased, and the same process is repeated. The algorithm terminates when the threshold becomes sufficiently small, or another stopping criterion is satisfied. We also propose a robust projection to handle the situations with observation noise or model uncertainties. Our extensive simulations confirm the promising performance of the ISP algorithms compared with some well-known algorithms.

Image compression-encryption scheme combining 2D compressive sensing with discrete fractional random transform

Most of the existing image encryption algorithms based on compressive sensing are too complex to operate. An image compression-encryption scheme with simple operation is presented based on 2D compressive sensing and discrete fractional random transform (DFrRT). To accomplish compression and encryption simultaneously, the original image is expressed in a 2D discrete cosine domain and measured by the measurement matrices in two orthogonal directions during the encryption process, where the matrices are constructed with Logistic chaos map to control the row vectors of Hadamard matrix. Then the intermediate resulting image is re-encrypted by taking discrete fractional random transform. Decryption process includes the inverse operation of the DFrRT and the reconstruction process with the Newton Smoothed l0 Norm (NSL0) algorithm in sequence. Simulation results verify the security and the effectiveness of this scheme by taking advantages of both compressive sensing and DFrRT.

High Resolution ISAR Imaging Based on Improved Smoothed L0 Norm Recovery Algorithm

In radar imaging, a target is usually consisted of a few strong scatterers which are sparsely distributed. In this paper, an improved sparse signal recovery algorithm based on smoothed l 0 (SL0) norm method is proposed to achieve high resolution ISAR imaging with limited pulse numbers. Firstly, one new smoothed function is proposed to approximate the l 0 norm to measure the sparsity. Then a single loop step is used instead of two loop layers in SL0 method which increases the searching density of variable parameter to ensure the recovery accuracy without increasing computation amount, the cost function is undated in every loop for the next loop until the termination is satisfied. Finally, the new set of solution is projected into the feasible set. Simulation results show that the proposed algorithm is superior to the several popular methods both in terms of the reconstruction performance and computation time. Real data ISAR imaging obtained by the proposed algorithm is competitive to several other methods.

Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction.

Low-dose computed tomography (CT) reconstruction is a challenging problem in medical imaging. To complement the standard filtered back-projection (FBP) reconstruction, sparse regularization reconstruction gains more and more research attention, as it promises to reduce radiation dose, suppress artifacts, and improve noise properties. In this work, we present an iterative reconstruction approach using improved smoothed l 0 (SL0) norm regularization which is used to approximate l 0 norm by a family of continuous functions to fully exploit the sparseness of the image gradient. Due to the excellent sparse representation of the reconstruction signal, the desired tissue details are preserved in the resulting images. To evaluate the performance of the proposed SL0 regularization method, we reconstruct the simulated dataset acquired from the Shepp-Logan phantom and clinical head slice image. Additional experimental verification is also performed with two real datasets from scanned animal experiment. Compared to the referenced FBP reconstruction and the total variation (TV) regularization reconstruction, the results clearly reveal that the presented method has characteristic strengths. In particular, it improves reconstruction quality via reducing noise while preserving anatomical features.

High Resolution ISAR Imaging Based on Improved Smoothed L0 Norm Recovery Algorithm

In radar imaging, a target is usually consisted of a few strong scatterers which are sparsely distributed. In this paper, an improved sparse signal recovery algorithm based on smoothed l 0 (SL0) norm method is proposed to achieve high resolution ISAR imaging with limited pulse numbers. Firstly, one new smoothed function is proposed to approximate the l 0 norm to measure the sparsity. Then a single loop step is used instead of two loop layers in SL0 method which increases the searching density of variable parameter to ensure the recovery accuracy without increasing computation amount, the cost function is undated in every loop for the next loop until the termination is satisfied. Finally, the new set of solution is projected into the feasible set. Simulation results show that the proposed algorithm is superior to the several popular methods both in terms of the reconstruction performance and computation time. Real data ISAR imaging obtained by the proposed algorithm is competitive to several other methods.

Sparse-view computed tomography image reconstruction via a combination of L(1) and SL(0) regularization.

Low-dose computed tomography reconstruction is an important issue in the medical imaging domain. Sparse-view has been widely studied as a potential strategy. Compressed sensing (CS) method has shown great potential to reconstruct high-quality CT images from sparse-view projection data. Nonetheless, low-contrast structures tend to be blurred by the total variation (TV, L1-norm of the gradient image) regularization. Moreover, TV will produce blocky effects on smooth and edge regions. To overcome this limitation, this study has proposed an iterative image reconstruction algorithm by combining L1 regularization and smoothed L0 (SL0) regularization. SL0 is a smooth approximation of L0 norm and can solve the problem of L0 norm being sensitive to noise. To evaluate the proposed method, both qualitative and quantitative studies were conducted on a digital Shepp-Logan phantom and a real head phantom. Experimental comparative results have indicated that the proposed L1/SL0-POCS algorithm can effectively suppress noise and artifacts, as well as preserve more structural information compared to other existing methods.

Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform

Most of the existing image encryption techniques bear security risks for taking linear transform or suffer encryption data expansion for adopting nonlinear transformation directly. To overcome these difficulties, a novel image compression–encryption scheme is proposed by combining 2D compressive sensing with nonlinear fractional Mellin transform. In this scheme, the original image is measured by measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the nonlinear fractional Mellin transform. The measurement matrices are controlled by chaos map. The Newton Smoothed l0 Norm (NSL0) algorithm is adopted to obtain the decryption image. Simulation results verify the validity and the reliability of this scheme.

Image Reconstruction of Compressed Sensing Based on Improved Smoothed l0 Norm Algorithm

Image Reconstruction of Compressed Sensing Based on Improved Smoothed l0 Norm Algorithm

Single-snapshot DOA estimation by using Compressed Sensing

AbstractThis paper deals with the problem of estimating the directions of arrival (DOA) of multiple source signals from a single observation vector of an array data. In particular, four estimation algorithms based on the theory of compressed sensing (CS), i.e., the classicalℓ1minimization (or Least Absolute Shrinkage and Selection Operator, LASSO), the fast smoothℓ0minimization, and the Sparse Iterative Covariance-Based Estimator, SPICE and the Iterative Adaptive Approach for Amplitude and Phase Estimation, IAA-APES algorithms, are analyzed, and their statistical properties are investigated and compared with the classical Fourier beamformer (FB) in different simulated scenarios. We show that unlike the classical FB, a CS-based beamformer (CSB) has some desirable properties typical of the adaptive algorithms (e.g., Capon and MUSIC) even in the single snapshot case. Particular attention is devoted to the super-resolution property. Theoretical arguments and simulation analysis provide evidence that a CS-based beamformer can achieve resolution beyond the classical Rayleigh limit. Finally, the theoretical findings are validated by processing a real sonar dataset.

Non-negative sparse decomposition based on constrained smoothed ℓ0 norm

Sparse decomposition of a signal over an overcomplete dictionary has many applications including classification. One of the sparse solvers that has been proposed for finding the sparse solution of a spare decomposition problem (i.e., solving an underdetermined system of equations) is based on the Smoothed L0 norm (SL0). In some applications such as classification of visual data using sparse representation, the coefficients of the sparse solution should be in a specified range (e.g., non-negative solution). This paper presents a new approach based on the Constrained Smoothed L0 norm (CSL0) for solving sparse decomposition problems with non-negative constraint. The performance of the new sparse approach is evaluated on both simulated and real data. For the simulated data, the mean square error of the solution using the CSL0 is comparable to state-of-the-art sparse solvers. For real data, facial expression recognition via sparse representation is studied where the recognition rate using the CSL0 is better than other solver methods (in particular is about 4% better than the SL0).

SAR Image Compression and Reconstruction Based on Compressed Sensing

The appearance of multiplicative speckle noise in Synthetic Aperture Radar (SAR) imagery makes it very difficult to visualization and compression. This paper proposes a novel framework of Compressed Sensing (CS) to compress the SAR image. It combined the Nonsubsampled Contourlet Transform (NSCT) shrinkage method to SAR image sparse represent. And a modified Smoothed L0 norm (SL0) algorithm is used for SAR image accurate reconstruction. The experimental results show the proposed method is very effective and can get better reconstruction performances.

ISI sparse channel estimation based on SL0 and its application in ML sequence-by-sequence equalization

In this paper, which is an extended version of our work at LVA/ICA 2010 [1], the problem of Inter Symbol Interface (ISI) Sparse channel estimation and equalization will be investigated. We firstly propose an adaptive method based on the idea of Least Mean Square (LMS) algorithm and the concept of smoothed l0 (SL0) norm presented in [2] for estimation of sparse ISI channels. Afterwards, a new non-adaptive fast channel estimation method based on SL0 sparse signal representation is proposed. ISI channel estimation will have a direct effect on the performance of the ISI equalizer at the receiver. So, in this paper we investigate this effect in the case of optimal Maximum Likelihood Sequence-by-Sequence Equalizer (MLSE) [3]. In order to implement this equalizer, we first introduce an equivalent F-model for sparse channels, and then using this model we propose a new method called pre-filtered parallel Viterbi algorithm (or pre-filtered PVA) for general ISI sparse channels which has much less complexity than ordinary Viterbi Algorithm (VA) and also with no considerable loss of optimality, which we have examined by doing some experiments in Matlab/Simulink. Indeed, simulation results clearly show that the proposed concatenated estimation–equalization methods have much better performance than the usual equalization methods such as Linear Mean Square Equalization (LMSE) for ISI sparse channels, while preserving simplicity at the receiver.

Fast Sparse Multipath Channel Estimation with Smooth L0 Algorithm for Broadband Wireless Communication Systems

Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable; on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.