Effective Alternating Direction Optimization Methods for Sparsity-Constrained Blind Image Deblurring

On the preconditioning of the primal form of TFOV-based image deblurring model

To address the staircasing problem in deblurred images generated by a simple total variation (TV) based model, one approach is to use the total fractional-order variation (TFOV) image deblurring model. However, the discretization of the Euler-Lagrange equations for the TFOV-based model results in a nonlinear ill-conditioned system, which adversely influences the performance of computational methods like Krylov subspace algorithms (e.g., Generalized Minimal Residual, Conjugate Gradient). To address this challenge, three novel preconditioned matrices are proposed to improve the conditioning of the primal model when using the conjugate gradient method. These matrices are designed based on circulant approximations of the matrix associated with blurring kernel. Experimental evaluations demonstrate the effectiveness of the proposed preconditioned matrices in enhancing the convergence and accuracy of the conjugate gradient method for solving the primal form of the TFOV-based image deblurring model. The results highlight the importance of appropriate preconditioning strategies in achieving robust and high-quality image deblurring using the TFOV approach.

Effective Blind Image Deblurring Using Matrix-Variable Optimization

Blind image deblurring has been a challenging issue due to the unknown blur and computation problem. Recently, the matrix-variable optimization method successfully demonstrates its potential advantages in computation. This paper proposes an effective matrix-variable optimization method for blind image deblurring. Blur kernel matrix is exactly decomposed by a direct SVD technique. The blur kernel and original image are well estimated by minimizing a matrix-variable optimization problem with blur kernel constraints. A matrix-type alternative iterative algorithm is proposed to solve the matrix-variable optimization problem. Finally, experimental results show that the proposed blind image deblurring method is much superior to the state-of-the-art blind image deblurring algorithms in terms of image quality and computation time.

Through-Wall UWB Radar Based on Sparse Deconvolution with Arctangent Regularization for Locating Human Subjects

A common problem in through-wall radar is reflected signals much attenuated by wall and environmental noise. The reflected signal is a convolution product of a wavelet and an unknown object time series. This paper aims to extract the object time series from a noisy receiving signal of through-wall ultrawideband (UWB) radar by sparse deconvolution based on arctangent regularization. Arctangent regularization is one of the suitably nonconvex regularizations that can provide a reliable solution and more accuracy, compared with convex regularizations. An iterative technique for this deconvolution problem is derived by the majorization–minimization (MM) approach so that the problem can be solved efficiently. In the various experiments, sparse deconvolution with the arctangent regularization can identify human positions from the noisy received signals of through- wall UWB radar. Although the proposed method is an odd concept, the interest of this paper is in applying sparse deconvolution, based on arctangent regularization with an S-band UWB radar, to provide a more accurate detection of a human position behind a concrete wall.

Gravitational-Wave Burst Signals Denoising Based on the Adaptive Modification of the Intersection of Confidence Intervals Rule

Gravitational-wave data (discovered first in 2015 by the Advanced LIGO interferometers and awarded by the Nobel Prize in 2017) are characterized by non-Gaussian and non-stationary noise. The ever-increasing amount of acquired data requires the development of efficient denoising algorithms that will enable the detection of gravitational-wave events embedded in low signal-to-noise-ratio (SNR) environments. In this paper, an algorithm based on the local polynomial approximation (LPA) combined with the relative intersection of confidence intervals (RICI) rule for the filter support selection is proposed to denoise the gravitational-wave burst signals from core collapse supernovae. The LPA-RICI denoising method's performance is tested on three different burst signals, numerically generated and injected into the real-life noise data collected by the Advanced LIGO detector. The analysis of the experimental results obtained by several case studies (conducted at different signal source distances corresponding to the different SNR values) indicates that the LPA-RICI method efficiently removes the noise and simultaneously preserves the morphology of the gravitational-wave burst signals. The technique offers reliable denoising performance even at the very low SNR values. Moreover, the analysis shows that the LPA-RICI method outperforms the approach combining LPA and the original intersection of confidence intervals (ICI) rule, total-variation (TV) based method, the method based on the neighboring thresholding in the short-time Fourier transform (STFT) domain, and three wavelet-based denoising techniques by increasing the improvement in the SNR by up to 118.94% and the peak SNR by up to 138.52%, as well as by reducing the root mean squared error by up to 64.59%, the mean absolute error by up to 55.60%, and the maximum absolute error by up to 84.79%.

Image deconvolution for confocal laser scanning microscopy using constrained total variation with a gradient field

As for the confocal laser scanning microscope (CLSM) imaging system, the collected weak fluorescence signals are always distorted by optic blur and severe photon-counting noise, and the deconvolution for CLSM images is a typical ill-posed inverse problem, which is highly sensitive to the measurement noise. To promote the reconstruction quality for characteristics of low intensity and strong noise, we employed the prominent total variation regularization (TV) to enforce the sparsity of a fluorescent image gradient with rich details. However, the well-known reconstruction artifacts (e.g., artificial staircase) emerge with TV prior. To settle this issue, we utilized a robust first-order discretization yielding near-isotropy with a gradient field to depress the reconstruction artifacts. Furthermore, the bound constraint was suited to restrain final reconstruction results from appearing unreasonably explosive. For the proposed optimization minimizer with linear constraint, we take one proximal gradient for approximate estimation of each subproblem under the framework of the inexact alternating direction method of multipliers. Moreover, we incorporated a Nesterov's scheme into the numerical method for acceleration of iteration updating. Compared with other competing methods, both the simulation and practical results demonstrate the effectiveness of our proposed model for CLSM image deconvolution.

Combining Motion Compensation with Spatiotemporal Constraint for Video Deblurring

We propose a video deblurring method by combining motion compensation with spatiotemporal constraint for restoring blurry video caused by camera shake. The proposed method makes effective full use of the spatiotemporal information not only in the blur kernel estimation, but also in the latent sharp frame restoration. Firstly, we estimate a motion vector between the current and the previous blurred frames, and introduce the estimated motion vector for deriving the motion-compensated frame with the previous restored frame. Secondly, we proposed a blur kernel estimation strategy by applying the derived motion-compensated frame to an improved regularization model for improving the quality of the estimated blur kernel and reducing the processing time. Thirdly, we propose a spatiotemporal constraint algorithm that can not only enhance temporal consistency, but also suppress noise and ringing artifacts of the deblurred video through introducing a temporal regularization term. Finally, we extend Fast Total Variation de-convolution (FTVd) for solving the minimization problem of the proposed spatiotemporal constraint energy function. Extensive experiments demonstrate that the proposed method achieve the state-of-the-art results either in subjective vision or objective evaluation.

Motion-Blur-Free High-Speed Video Shooting Using a Resonant Mirror

This study proposes a novel concept of actuator-driven frame-by-frame intermittent tracking for motion-blur-free video shooting of fast-moving objects. The camera frame and shutter timings are controlled for motion blur reduction in synchronization with a free-vibration-type actuator vibrating with a large amplitude at hundreds of hertz so that motion blur can be significantly reduced in free-viewpoint high-frame-rate video shooting for fast-moving objects by deriving the maximum performance of the actuator. We develop a prototype of a motion-blur-free video shooting system by implementing our frame-by-frame intermittent tracking algorithm on a high-speed video camera system with a resonant mirror vibrating at 750 Hz. It can capture 1024 × 1024 images of fast-moving objects at 750 fps with an exposure time of 0.33 ms without motion blur. Several experimental results for fast-moving objects verify that our proposed method can reduce image degradation from motion blur without decreasing the camera exposure time.

Node Scheduling Strategies for Achieving Full-View Area Coverage in Camera Sensor Networks

Unlike conventional scalar sensors, camera sensors at different positions can capture a variety of views of an object. Based on this intrinsic property, a novel model called full-view coverage was proposed. We study the problem that how to select the minimum number of sensors to guarantee the full-view coverage for the given region of interest (ROI). To tackle this issue, we derive the constraint condition of the sensor positions for full-view neighborhood coverage with the minimum number of nodes around the point. Next, we prove that the full-view area coverage can be approximately guaranteed, as long as the regular hexagons decided by the virtual grid are seamlessly stitched. Then we present two solutions for camera sensor networks in two different deployment strategies. By computing the theoretically optimal length of the virtual grids, we put forward the deployment pattern algorithm (DPA) in the deterministic implementation. To reduce the redundancy in random deployment, we come up with a local neighboring-optimal selection algorithm (LNSA) for achieving the full-view coverage. Finally, extensive simulation results show the feasibility of our proposed solutions.