Dongjie Bi

A Sparsity Basis Selection Method for Compressed Sensing

This letter presents a new sparsity basis selection compressed sensing method (SBSCS) for improving signal reconstruction from compressed sensing (CS) measurements. Based on the observation that different classes of transform cause different sparsity expressions and better sparsity expression leads to better signal recovery, the proposed SBSCS method searches the best class of transform and basis in a set of redundant tree-structured dictionaries by nesting sparsity maximization within the CS minimization. The SBSCS method adaptively selects the class of transform and basis with the best sparsity measure at each ℓ1 iteration and converges quickly to the final class of transform and basis. Numerical experiments show that the proposed SBSCS method improves the quality of signal recovery over the existing best basis compressed sensing method (BBCS) proposed by Peyré in 2010.

Efficient 2-D synthetic aperture radar image reconstruction from compressed sampling using a parallel operator splitting structure

This paper investigates an efficient compressed sensing (CS) approach that can be used to reconstruct 2-D millimeter-wave synthetic aperture radar (SAR) images from under-sampled measurements. This approach minimizes a linear combination of four terms corresponding to a least squares data fitting, ? 1 norm regularization, total variation (TV) and a bounding operator. Although the strong convergence of this approach cannot be guaranteed, this approach always converges to a stable structural similarity (SSIM) value with a combination of a parallel operator splitting structure and a FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) updating stage. Simulation and experimental results demonstrate the superior performance of the proposed approach in terms of both efficiency and computation complexity.

Analog Circuits Soft Fault Diagnosis Using Rényi's Entropy

An analog circuit soft fault diagnosis method using Rényi’s entropy is proposed. This method focuses on extracting the entropy information contained in the probability density function (PDF) of the output of the circuit under test (CUT), which is sensitive to the parameters of circuits. Firstly, using the Lagrange multiplier method with Rényi’s entropy deduces PDF. Then the parameter α of Rényi’s entropy is estimated adaptively by employing the output of CUT through the maximum likelihood estimation method. Finally, the value of Rényi’s entropy can be calculated using the PDF and α parameter. The divergence between the Rényi’s entropy corresponding to the fault and fault free circuits is adopted to detect the fault. The method can detect soft fautls, including the single fault and multiple faults, without complicated models and mass of data, and also without interrupting the inherent connections. We conduct experiments respectively on two circuits that are implemented on an actual circuit board. The effectiveness of the proposed method is demonstrated by the result of the experiment.

A Splitting Bregman-Based Compressed Sensing Approach for Radial UTE MRI

A splitting Bregman-based compressed-sensing (CS) approach (CS-SplitBerg), using the nonuniform fast Fourier transform, is proposed to reconstruct radial magnetic resonance (MR) images from undersampled k- space measurements. Using the splitting Bregman framework, the proposed CS-SplitBerg approach takes fully into account the measurement noise and exploits the combined sparsity of MR images, i.e., ℓ1- norm and total variation regularization. With convergence guaranteed, the CS-SplitBerg approach uses the Bregman update process and some auxiliary variables to relax the constrained optimization problem to a sequence of easily solved unconstrained minimization problems. Experimental results using both a phantom example and a mouse cardiac example demonstrate that, under different undersampling rates, the CS-SplitBerg approach performs better than the CS-CG approach, which was introduced in our previous work. With an affordable computational cost by considering the influences of noise, the CS-SplitBerg approach can further reduce the necessary number of MR imaging (MRI) measurements for the recovery and better differentiate true MRI images from noisy data.

A compressive hybrid conjugate gradient image recovery approach for radial MRI

ABSTRACT This paper investigates an efficient compressed sensing (CS) approach that can be used to reconstruct radial magnetic resonance (MR) images from under-sampled measurements. In this approach, we propose a hybrid conjugate gradient (CG) method with a hybrid update parameter to optimize the CS cost function. With detailed mathematical proofs, the proposed CG method has proved to have sufficient descent and global convergence properties. In order to show efficiency of the proposed approach, experiments using a phantom and a living mouse cardiac example are carried out. Compared with two other widely used compressive CG approaches with undersampling rates from 5% to 20%, the proposed approach achieves better image quality and requires less running time. Meanwhile, the proposed H-CG approach can improve the robustness of magnetic resonance imaging image recovery above existing compressive CG approaches.

MRI Reconstruction Algorithm Using Conjugate Gradient Method with Improved Line Search

The critical problem in MRI is that the scanning speed is too slow. In order to reduce the scanning time of magnetic resonance imaging (MRI), a MRI reconstruction algorithm is proposed in this paper. This algorithm is under the framework of compressed sensing. It combines sub-nyquist sampling data and nonlinear reconstruction algorithms to realize the real-time or quasi real-time imaging requirement. The sparseness of MRI images in the transform domain and the gradient domain are included in the compressed sensing model. A conjugate gradient method is used to reconstruct the magnetic resonance image, in which an improved line search method is proposed to reduce the CPU running time. The proposed line search method optimizes the searching step size with a prediction approach, which significantly reduces the line search cost. A living mouse cardiac experiment results, with under-sampling rate at 10%, 20% and 30%, show that the proposed line search method achieves the better image reconstruction and the shorter running time in comparison to the backtracking line search, which is widely used in conjugate gradient method.

Measurement Uncertainty Estimation for Electromagnetism Devices and Equipment Using Extreme Fisher Information

In electromagnetism devices and equipment measurement activities, it is hard to identify and compensate every effect in measurement and evaluate the incompleteness of the measurement results accurately and efficiently. In this paper, we employ the probability density functions (PDFs) derived from the extreme Fisher information (EFI) method in the view of information theory for estimating the measurement uncertainty of the measurement result. By considering the physical essence of EFI, a differential equation model is established for the measurement practice and the explicit form of the solution PDF corresponding to EFI is given, which guarantees the dynamics and the practicability of the estimation of the measurement uncertainty (MU). The obtained the PDF can describe the combined performance of the system and all the measurement effects, then, with the PDF and the confidence, MU can be estimated more dynamically and efficiently. The effectiveness of the proposed EFI method is demonstrated by the numerical results of two practical instances.

Rényi's Entropy Based Method for Analog Circuits Soft Fault Detection

We propose a Rényis entropy based analog circuit soft fault detection method. This method extracts the entropy information from the probability density function (PDF) of the output of the circuit under test (CUT), which is sensitive to the parameters of circuits. In this method, firstly, the Lagrange multiplier method with Rényis entropy is used to deduce PDF of the output signal. Then through the maximum likelihood estimation method, we estimate the parameter α of Rényis entropy adaptively according to the output of CUT. Finally, the value of Rényis entropy can be calculated using the PDF and α parameter. The divergence between the Rényis entropy corresponding to the fault and fault free circuits is adopted to detect the fault. This method can 100% detect soft faults, including the single fault and multiple faults, without complicate models and mass of data, and also with no need of interrupting the inherent contentions of CUT. Experiments are conducted respectively on two circuits that are implemented on an actual circuit board. The effectiveness of the proposed method is demonstrated by the result of the experiment.