Bilateral Total Variation Regularization Research Articles

Full-Waveform Inversion for Subsurface Penetrating Radar based on Adaptive Bilateral Total Variation Regularization

Full-waveform inversion (FWI) of subsurface penetrating radar (SPR) is one of the most promising techniques for quantitative reconstruction of high-resolution dielectric properties distribution. However, due to the incomplete observation data of surface detection, there is significant ill-posedness in inversion and the inversion accuracy is lower than expected. In this paper, an FWI method for SPR data with adaptive bilateral total variation (ABTV) regularization is proposed. The method utilizes ABTV regularization to supplement the data constraints and retains the anomaly body boundary information. In addition, the regularization function of adaptive weight factor matrix is designed for the limitation of the standard bilateral total variation (BTV) regularization, which considers both the smoothing effect and the edge preservation effect. Synthetic experiment shows that the proposed method can reconstruct the permittivity distribution more accurately from 2-D SPR data.

Blind deconvolution using bilateral total variation regularization: a theoretical study and application

ABSTRACT Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chan's approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations.

Spatiotemporal Adaptive Nonuniformity Correction Based on BTV Regularization

The residual nonuniformity response, ghosting artifacts, and over-smooth effects are the main defects of the existing nonuniformity correction (NUC) methods. In this paper, a spatiotemporal feature-based adaptive NUC algorithm with bilateral total variation (BTV) regularization is presented. The primary contributions of the innovative method are embodied in the following aspects: BTV regularizer is introduced to eliminate the nonuniformity response and suppress the ghosting effects. The spatiotemporal adaptive learning rate is presented to further accelerate convergence, remove ghosting artifacts, and avoid over-smooth. Moreover, the random projection-based bilateral filter is proposed to estimate the desired target image more accurately which yields more details in the actual scene. The experimental results validated that the proposed algorithm achieves outstanding performance upon both simulated data and real-world sequence.

Full 3D Reconstruction of Non-Rigidly Deforming Objects

In this article, we discuss enhanced full 360° 3D reconstruction of dynamic scenes containing non-rigidly deforming objects using data acquired from commodity depth or 3D cameras. Several approaches for enhanced and full 3D reconstruction of non-rigid objects have been proposed in the literature. These approaches suffer from several limitations due to requirement of a template, inability to tackle large local deformations and topology changes, inability to tackle highly noisy and low-resolution data, and inability to produce online results. We target online and template-free enhancement of the quality of noisy and low-resolution full 3D reconstructions of dynamic non-rigid objects. For this purpose, we propose a view-independent recursive and dynamic multi-frame 3D super-resolution scheme for noise removal and resolution enhancement of 3D measurements. The proposed scheme tracks the position and motion of each 3D point at every timestep by making use of the current acquisition and the result of the previous iteration. The effects of system blur due to per-point tracking are subsequently tackled by introducing a novel and efficient multi-level 3D bilateral total variation regularization. These characteristics enable the proposed scheme to handle large deformations and topology changes accurately. A thorough evaluation of the proposed scheme on both real and simulated data is carried out. The results show that the proposed scheme improves upon the performance of the state-of-the-art methods and is able to accurately enhance the quality of low-resolution and highly noisy 3D reconstructions while being robust to large local deformations.

Building block extraction and classification by means of aerial images fused with super-resolution reconstructed elevation data

The detailed three-dimensional modeling of buildings utilizing elevation data, such as those provided by light detection and ranging (LiDAR) airborne scanners, is increasingly demanded today. There are certain application requirements and available datasets to which any research effort has to be adapted. Our dataset includes aerial orthophotos, with a spatial resolution 20 cm, and a digital surface model generated from LiDAR, with a spatial resolution 1 m and an elevation resolution 20 cm, from an area of Athens, Greece. The aerial images are fused with LiDAR, and we classify these data with a multilayer feedforward neural network for building block extraction. The innovation of our approach lies in the preprocessing step in which the original LiDAR data are super-resolution (SR) reconstructed by means of a stochastic regularized technique before their fusion with the aerial images takes place. The Lorentzian estimator combined with the bilateral total variation regularization performs the SR reconstruction. We evaluate the performance of our approach against that of fusing unprocessed LiDAR data with aerial images. We present the classified images and the statistical measures confusion matrix, kappa coefficient, and overall accuracy. The results demonstrate that our approach predominates over that of fusing unprocessed LiDAR data with aerial images.

Iteratively reweighted blind deconvolution for passive millimeter-wave images

Passive millimeter-wave (PMMW) imaging frequently suffers from blurring and low resolution due to the diffraction limits and the long wavelengths compared with visual and infrared radiation. Moreover, the observed image is inevitably degraded by the system noise and natural clutter noise. The blur and noise limit the capability of PMMW images in practical applications. In this study, we propose an iteratively reweighted blind deconvolution method for obtaining high quality PMMW images. A weighted least-squares data-fidelity term that is robust to modeling error and a weighted bilateral total variation regularization term are incorporated into the variational blind deconvolution framework. Furthermore, we impose an appropriate smooth constraint for the point spread function of the imaging system. In addition, to improve the practicality of the method, we derive a formula to automatically update the regularization parameter from the data. Comparative experimental results on simulated and real images show that the proposed method is superior to the state-of-the-art methods in terms of both subjective measure and visual quality.

Real-Time Enhancement of Dynamic Depth Videos with Non-Rigid Deformations.

We propose a novel approach for enhancing depth videos containing non-rigidly deforming objects. Depth sensors are capable of capturing depth maps in real-time but suffer from high noise levels and low spatial resolutions. While solutions for reconstructing 3D details in static scenes, or scenes with rigid global motions have been recently proposed, handling unconstrained non-rigid deformations in relative complex scenes remains a challenge. Our solution consists in a recursive dynamic multi-frame super-resolution algorithm where the relative local 3D motions between consecutive frames are directly accounted for. We rely on the assumption that these 3D motions can be decoupled into lateral motions and radial displacements. This allows to perform a simple local per-pixel tracking where both depth measurements and deformations are dynamically optimized. The geometric smoothness is subsequently added using a multi-level L1 minimization with a bilateral total variation regularization. The performance of this method is thoroughly evaluated on both real and synthetic data. As compared to alternative approaches, the results show a clear improvement in reconstruction accuracy and in robustness to noise, to relative large non-rigid deformations, and to topological changes. Moreover, the proposed approach, implemented on a CPU, is shown to be computationally efficient and working in real-time.

Robust Multiple Reblurred-Based CT Image Enhancement

In this paper, we present a new algorithm for solving the blind deconvolution problem. In our method, we reblur a given degraded CT image with R different, but known PSFs, and get R different degraded CT images. Then we blindly deblur using the R new degraded CT images. Also, we introduce Bilateral Total Variation regularization term. In computer simulations in Matlab, it is the most advantages of our proposed algorithm that it performs more effectively than M. Jiang’s ENR method.

Image Restoration Based on L1 + L1 Model

In this paper, we firstly propose a new image restoration model including non-smooth -norm regularization term based on the bilateral total variation regularization. Secondly, we prove the existence of minimal solutions of our proposed energy functional model. Thirdly, we consider the convergence of the discrete numerical algorithm, and obtain that the limit point of the solution sequence is the minimal point of our proposed energy functional. Finally, we give some experimental simulation results in the case of the single noisy image without blurring, multiple different noisy images without blurring, single noisy image with blurring, and multiple different noisy images with different blurring, respectively. The restoration results show our model works effectively.

Super-resolution image reconstruction based on Tukey data fusion and bilateral-total-variation regularization

Images of high-resolution are desired and often required in most photoelectronic imaging applications, and corresponding image reconstruction algorithm has became the frontier topics. On the basis of stochastic theory, a novel super-resolution image reconstruction algorithm based on Tukey norm data fusion and bilateral total variation regularization is proposed in this paper. The Tukey norm is employed for fusing the data of low-resolution frames and removing outliers in the data, and then aiming at the sickness of super-resolution reconstruction, the bilateral total variation regularization as a priori knowledge about the solution is incorporated to remove the artifacts from the final answer and improve the convergence rate. Simulated and real experiment results show that the proposed algorithm can improve the image resolution greatly and it is immune to noise and errors in motion and blur estimation.

Super-Resolution Reconstruction based on Tukey Norm and Adaptive Bilateral Total Variation

In Bilateral Total Variation (BTV) regularized super-resolution reconstruction (SRR), the fidelity item is only applicable to a specific noise model, and the fixed weight of BTV regularization term cannot adapt to the changes in an image. Thus, this paper proposes a SRR algorithm based on the Tukey fidelity term and adaptive BTV regularization term. The Tukey fidelity term has a more effective outliers suppression feature to deal with complex noises, and the weight of adaptive BTV regularization term can resize itself according to the changes of image textures, which can achieve the purposes of suppressing noises and preserving edges. Experimental results show that, compared with other algorithms, the proposed algorithm has better vision effects and higher Peak Signal-to-noise Ratio (PSNR) values.

A local structure adaptive super-resolution reconstruction method based on BTV regularization

Super-resolution (SR) image reconstruction has been one of the hottest research fields in recent years. The main idea of SR is to utilize complementary information from a set of low resolution (LR) images of the same scene to reconstruct a high-resolution image with more details. Under the framework of the regularization based SR, this paper presents a local structure adaptive BTV regularization based super-resolution reconstruction method to overcome the shortcoming of the Bilateral Total Variation (BTV) super resolution reconstruction model. The proposed method adaptively chooses prior model and regularization parameter according to the local structures. Experimental results show that the proposed method can get better reconstruction results and significantly reduces the manual workload of the regularization parameter selection.

Image Restoration Based on Adaptive Directional Regularization

This paper addresses problems appearing in restoration algorithms based on utilizing both Tikhonov and bilateral total variation (BTV) regularization. The former regularization assumes that prior information has Gaussian distribution which indeed fails at edges, while the later regularization highly depends on the selected bilateral filter's parameters. To overcome these problems, we propose a locally adaptive regularization. In the proposed algorithm, we use general directional regularization functions with adaptive weights. The adaptive weights are estimated from local patches based on the property of the partially restored image. Unlike Tikhonov regularization, it can avoid smoothness across edges by using adaptive weights. In addition, unlike BTV regularization, the proposed regularization function doesn't depend on parameters' selection. The convexity conditions as well as the convergence conditions are derived for the proposed algorithm.