Zhenghua Wu

Sufficient conditions for generalized Orthogonal Matching Pursuit in noisy case

In compressive sensing, generalized Orthogonal Matching Pursuit (gOMP) algorithm generalizes OMP algorithm by selecting N ( N ? 1 ) atoms in each iteration. In this paper, we propose restricted isometry constant based sufficient conditions for gOMP algorithm to correctly recover the support of significant components of signal when both measurement dictionary and measurement signal are contaminated with noise. Bound of estimation error is also derived. Upper bound of restricted isometry constant could be relaxed if the original sparse signal is strong decaying. When sparsity of original sparse signal is unavailable, we give a stopping criterion of gOMP algorithm to ensure correct support recovery. HighlightsSufficient conditions for generalized OMP algorithm to recover the support of sparse signal in noisy case are proposed.The sufficient conditions can be relaxed if sparse signal is strong decaying.If number of iterations is unavailable, stopping criterion for generalized OMP algorithm is derived to ensure correct support recovery.Empirical experiments verify the theoretical results proposed in this paper.

Photoacoustic image reconstruction based on Bayesian compressive sensing algorithm

The photoacoustic tomography (PAT) method, based on compressive sensing (CS) theory, requires that, for the CS reconstruction, the desired image should have a sparse representation in a known transform domain. However, the sparsity of photoacoustic signals is destroyed because noises always exist. Therefore, the original sparse signal cannot be effectively recovered using the general reconstruction algorithm. In this study, Bayesian compressive sensing (BCS) is employed to obtain highly sparse representations of photoacoustic images based on a set of noisy CS measurements. Results of simulation demonstrate that the BCS-reconstructed image can achieve superior performance than other state-of-the-art CS-reconstruction algorithms.

Total variation-regularized weighted nuclear norm minimization for hyperspectral image mixed denoising

Abstract. Many nuclear norm minimization (NNM)-based methods have been proposed for hyperspectral image (HSI) mixed denoising due to the low-rank (LR) characteristics of clean HSI. However, the NNM-based methods regularize each eigenvalue equally, which is unsuitable for the denoising problem, where each eigenvalue stands for special physical meaning and should be regularized differently. However, the NNM-based methods only exploit the high spectral correlation, while ignoring the local structure of HSI and resulting in spatial distortions. To address these problems, a total variation (TV)-regularized weighted nuclear norm minimization (TWNNM) method is proposed. To obtain the desired denoising performance, two issues are included. First, to exploit the high spectral correlation, the HSI is restricted to be LR, and different eigenvalues are minimized with different weights based on the WNNM. Second, to preserve the local structure of HSI, the TV regularization is incorporated, and the alternating direction method of multipliers is used to solve the resulting optimization problem. Both simulated and real data experiments demonstrate that the proposed TWNNM approach produces superior denoising results for the mixed noise case in comparison with several state-of-the-art denoising methods.

Measurement matrix construction algorithm for sparse signal recovery

A simple measurement matrix construction algorithm (MMCA) within compressive sensing framework is introduced. In compressive sensing, the smaller coherence between the measurement matrix and the sparse dictionary (basis) can have better signal reconstruction performance. Random measurement matrices (e.g., Gaussian matrix) have been widely used because they present small coherence with almost any sparse base. However, optimizing the measurement matrix by decreasing the coherence with the fixed sparse base will improve the CS performance greatly, and the conclusion has been well proved by many prior researchers. Based on above analysis, we achieve this purpose by adopting shrinking and Singular Value Decomposition (SVD) technique iteratively. Finally, the coherence among the columns of the optimized matrix and the sparse dictionary can be decreased greatly, even close to the welch bound. In addition, we established several experiments to test the performance of the proposed algorithm and compare with the state of art algorithms. We conclude that the recovery performance of greedy algorithms (e.g., orthogonal matching pursuit) by using the proposed measurement matrix construction method outperforms the traditional random matrix algorithm, Elads algorithm, Vahids algorithm and optimized matrix algorithm introduced by Xu.

Photoacoustic microscopy image resolution enhancement via directional total variation regularization

Photoacoustic microscopy (PAM) is recognized as a powerful tool for various microcirculation system studies. To improve the spatial resolution for the PAM images, the requirements of the system will always be increased correspondingly. Without additional cost of the system, we address the problem of improving the resolution of PAM images by integrating a deconvolution model with a directional total variation regularization. Additionally, we present a primal-dual-based algorithm to solve the associated optimization problem efficiently. Results from both test images and some PAM images studies validate the effectiveness of the proposed method in enhancing the spatial resolution. We expect the proposed technique to be an alternativeresolution enhancement tool for some important biomedical applications.

Compressive sampling photoacoustic tomography based on edge expander codes and TV regularization

A new photoacoustic (PA) signal sampling and image reconstruction method, called compressive sampling PA tomography (CSPAT), is recently proposed to make low sampling rate and high-resolution PA tomography possible. A key problem within the CSPAT framework is the design of optic masks. We propose to use edge expander codes-based masks instead of the conventional random distribution masks, and efficient total variation (TV) regularization-based model to formulate the associated problem. The edge expander codes-based masks, corresponding to non-uniform sampling schemes, are validated by both theoretical analysis and results from computer simulations. The proposed method is expected to enhance the capability of CSPAT for reducing the number of measurements and fast data acquisition.

Blind Source Separation based on Compressed Sensing

Blind Source Separation (BSS) is an important issue in the coherent processing of multi-dimensional data. To recover and separate the sources from underdetermined mixtures, some prior information like sparse representation is required. The principle is very similar to the new technique named Compressed Sensing (CS), which asserts that one can recover a sparse signal from a limited number of random projections. In this paper, the relationship between BSS and CS is studied by equivalent transformation, then we propose the linear operator by which the relationship between the sources and the mixtures is modeled in two ways: RIP and incoherence, and give some instructive conclusions for the operator design. Numerical simulation applying the FOOMP algorithm and a operator we propose are conducted to demonstrate the good performance of the whole framework.

Compressive Sampling Photoacoustic Microscope System based on Low Rank Matrix Completion

Abstract Photoacoustic Microscopy (PAM) has developed into a powerful tool for deep tissue imaging with a better spatial resolution. But the data acquisition time in PAM is so long that it is a great challenge for real time imaging. In this paper, a new PAM data acquisition and image recovery method, called Compressive Sampling PAM System based on Low Rank Matrix Completion (CSLRM-PAM) is proposed to obtain a high-resolution PAM image with relatively low sampling rates. In order to successfully set up a CSLRM-PAM system, the two key problems which we need to keep focus on are design of the compressive sampling scheme and the corresponding image recovery algorithm. In this paper, two compressive sampling schemes based on expander graphs are proposed to replace the conventional point-by-point scanning scheme to implement fast data acquisition. Then, the low rank matrix completion is utilized to obtain high-resolution PAM image directly from the compressive sampling data. The effectiveness of the proposed scheme is validated using both numerical analysis and PAM experiments. In contrast with the conventional system, the proposed CSLRM-PAM system is able to dramatically decrease the total sampling points for a relatively high-resolution PAM image and to implement accelerated data acquisition.

Non-destructive photoacoustic detecting method for high-speed rail surface defects

The rail defect detection is vital to the rapid development of high-speed rail. A new, easily available nondestructive testing method which applies the photoacoustic detection technology is proposed here for the rail defect detection. Based on the ultrasonic sensor, a real-time photoacoustic imaging system for the rail non-destructive testing is established. The model of the system and its numerical solution are built first, and then the corresponding experiments and analysis are conducted. The photoacoustic image with damage characteristics can be reconstructed through the photoacoustic signals which excited by pulsed laser and then reflected back from the rail surface. According to the reconstructed image, the damage information such as the appearance, extension trend, and the depth of the rail defect can be effectively identified. It has been proved that the established photoacoustic detecting method for high-speed rail surface detection is an effective and non-destructive detecting technology.

Single-image super-resolution using directional total variation regularization and alternating direction method of multiplier solver

Abstract. Single-image super-resolution (SR) is one of the most important and challenging issues in image processing. To produce a high-resolution image from a low-resolution image, one of the conventional approaches is to leverage regularization to overcome the limitations caused by the modeling. However, conventional regularizers such as total variation always neglect the high-level structures in the data. To overcome the drawback, we propose to explore the underlying information for the images with structured edges by using directional total variation. An alternating direction method of a multiplier-based algorithm is presented to effectively solve the resulting optimization problem. Computer simulations on several texture images such as a leaf image have been used to demonstrate the effectiveness and improvement of the proposed method on SR reconstruction, both qualitatively and quantitatively. Furthermore, the effect of parameter selection is also discussed for the proposed method.