L1 Fidelity Research Articles

Mixed Gaussian-impulse noise removal using non-convex high-order TV penalty

To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the ℓ2 plus ℓ0 data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the ℓ2 fidelity is adopted to suppress Gaussian noise, while the ℓ0-norm is more suitable for detecting and removing impulse noise. In addition, the non-convex regularization displays excellent performance in overcoming the staircase effect and preserving edge details. Computationally, by using the iteratively reweighted ℓ1 algorithm and variable splitting method, this work designs a modified alternating minimization method to solve the optimization problem we construct. In theory, the convergence proof of our resulting algorithm is also presented. Finally, in the experimental section, we conduct extensive numerical experiments on degraded images and compare with other existing techniques. From the intuitive effects and restoration accuracy, it follows that our newly proposed method is effective and competitive for image deblurring and mixed noise removal.

Nonconvex TVq model with l1 fidelity term in image restoration

Restoration of images based on a nonconvex �! variational model which contains the �" “norm,” q ∈ (0,1), is considered. The existence of a minimizer of the model is established in the discrete setting. To solve the minimization problem, Huber-type regularizations of the �" and the �!norms are performed on the model. A primal-dual semismooth Newton method with a trust region technique is adapted to solve the model and the convergence of the algorithm is presented. Applications are made on restoration of images corrupted with blur and impulse noise.

Local estimates for vectorial Rudin–Osher–Fatemi type problems in one dimension

We consider the Rudin–Osher–Fatemi variational denoising model with general regularizing term and L2 fidelity in one-dimensional, vector-valued setting. We obtain local estimates on the singular part of the variation measure of the minimizer in terms of the singular part of the variation measure of the datum. In the case of homogeneous regularizer, we prove local estimates on the whole variation measure of the minimizer and deduce an analogous result for the gradient flow of the regularizer. We also discuss the question of extending our results to other fidelities.

Color image restoration based on saturation-value total variation plus L1 fidelity* *Wang is supported by Natural Science Foundation of Shanghai (18ZR1441800, 22ZR1465300) and the Fundamental Research Funds for the Central Universities.

Color image restoration is one of the most important tasks in image processing. In this paper, we propose and develop a novel saturation-value total variation (SVTV) plus L1 fidelity (SVTV-L1) model for color image restoration. SVTV is incorporated in the proposed model for regularizing the objective color image, meanwhile, L1 norm is considered for data fitting term in the proposed energy functional. Theoretically, we investigate the properties of the objective functional and the objective model. Note that the proposed energy functional including L1 norm is nonsmooth. We develop a smooth approximation approach to study the existence and properties of the solution of the proposed optimization problem. Numerically, Poisson noise and mixed noise have been tested and studied in the experimental results. We formulate an effective and efficient algorithm to solve the proposed minimization problem based on the framework of alternating direction method of multipliers. Numerical examples are presented to demonstrate that the performance of the proposed SVTV-L1 model is better than that of other testing methods in terms of visual quality, peak signal-to-noise ratio, and structure similarity.

Fractional total variation denoising model with [formula omitted] fidelity

We study a nonlocal version of the total variation-based model with L1 fidelity for image denoising, where the regularizing term is replaced with the fractional s-total variation. We discuss regularity of the level sets and uniqueness of solutions, both for high and low values of the fidelity parameter. We analyse in detail the case of binary data given by the characteristic functions of convex sets.

Efficient Iterative Regularization Method for Total Variation-Based Image Restoration

Total variation (TV) regularization has received much attention in image restoration applications because of its advantages in denoising and preserving details. A common approach to address TV-based image restoration is to design a specific algorithm for solving typical cost function, which consists of conventional ℓ2 fidelity term and TV regularization. In this work, a novel objective function and an efficient algorithm are proposed. Firstly, a pseudoinverse transform-based fidelity term is imposed on TV regularization, and a closely-related optimization problem is established. Then, the split Bregman framework is used to decouple the complex inverse problem into subproblems to reduce computational complexity. Finally, numerical experiments show that the proposed method can obtain satisfactory restoration results with fewer iterations. Combined with the restoration effect and efficiency, this method is superior to the competitive algorithm. Significantly, the proposed method has the advantage of a simple solving structure, which can be easily extended to other image processing applications.

An efficient primal-dual method for solving non-smooth machine learning problem

This paper deals with the machine learning model as a framework of regularized loss minimization problem in order to obtain a generalized model. Recently, some studies have proved the success and the efficiency of nonsmooth loss function for supervised learning problems Lyaqini et al. [1]. Motivated by the success of this choice, in this paper we formulate the supervised learning problem based on L1 fidelity term. To solve this nonsmooth optimization problem we transform it into a mini-max one. Then we propose a Primal-Dual method that handles the mini-max problem. This method leads to an efficient and significantly faster numerical algorithm to solve supervised learning problems in the most general case. To illustrate the effectiveness of the proposed approach we present some experimental-numerical validation examples, which are made through synthetic and real-life data. Thus, we show that our approach is outclassing existing methods in terms of convergence speed, quality, and stability of the predicted models.

A multi-frame super-resolution based on new variational data fidelity term

The main idea of multi-frame super-resolution (SR) algorithm is to recover a single high-resolution (HR) image from a sequence of low resolution ones of the same scene. Since the restoration step of super-resolution algorithms is always an ill-posed problem, the choice of the fidelity term and the regularization are always crucial. In this paper, we propose a new variational SR framework based on an automatic selection of the weighting parameter that control the balance between the L1 and L2 fidelity terms, which handle different type of noise distributions. Concerning the regularization, we use the combined total variation (TV) and the total variation of the first derivatives (TV2) model with a new implementation of the Primal-dual algorithm to solve the corresponding discretized problem. The obtained results are compared with some competitive algorithms and confirm that the proposed method has much benefices over the others in avoiding some undesirable artifacts.

ℓ1 − αℓ2 minimization methods for signal and image reconstruction with impulsive noise removal

In this paper, we study ℓ1 − αℓ2 (0 < α ⩽ 1) minimization methods for signal and image reconstruction with impulsive noise removal. The data fitting term is based on ℓ1 fidelity between the reconstruction output and the observational data, and the regularization term is based on ℓ1 − αℓ2 nonconvex minimization of the reconstruction output or its total variation. Theoretically, we show that under the generalized restricted isometry property that the underlying signal or image can be recovered exactly. Numerical algorithms are also developed to solve the resulting optimization problems. Experimental results have shown that the proposed models and algorithms can recover signal or images under impulsive noise degradation, and their performance is better than that of the existing methods.

Adaptive total variation L1 regularization for salt and pepper image denoising

In this article, we propose an adaptive total variation (TV) regularization model for salt and pepper denoising in digital images. The adaptive TV denoising method is developed based on the general regularized image restoration model with L1 fidelity for handling salt and pepper noise model. An estimation for regularization parameter is also proposed based on the characteristics of the salt and pepper noise. We implement the proposed adaptive TV-L1 regularization model efficiently for image denoising using the primal dual gradient method. In the experiments, the full-reference image quality assessment metrics are used for evaluating denoising quality across various noise levels in different synthetic and real images. The denoising results are compared to other similar salt and pepper image denoising methods and our results indicate we obtain artifact free edge preserving restorations.

Variational Destriping in Remote Sensing Imagery: Total Variation with L1 Fidelity

This paper introduces a variational method for destriping data acquired by pushbroom-type satellite imaging systems. The model leverages sparsity in signals and is based on current research in sparse optimization and compressed sensing. It is based on the basic principles of regularization and data fidelity with certain constraints using modern methods in variational optimization, namely, total variation (TV), L 1 fidelity, and the alternating direction method of multipliers (ADMM). The proposed algorithm, TV– L 1 , uses sparsity-promoting energy functionals to achieve two important imaging effects. The TV term maintains boundary sharpness of the content in the underlying clean image, while the L 1 fidelity allows for the equitable removal of stripes without over- or under-penalization, providing a more accurate model of presumably independent sensors with an unspecified and unrestricted bias distribution. A comparison is made between the TV– L 2 model and the proposed TV– L 1 model to exemplify the qualitative efficacy of an L 1 striping penalty. The model makes use of novel minimization splittings and proximal mapping operators, successfully yielding more realistic destriped images in very few iterations.

Fast algorithm for image denoising with different boundary conditions

In recent works several authors have considered the L1 fidelity term, the L2 fidelity term and the combined L1 and L2 fidelity term for denoising models, and they used the fast Fourier transform (FFT) algorithm which can only use periodic boundary conditions (BCs). In this paper, we combine the augmented Lagrangian method (ALM) and the symmetric Red–Black Gauss–Seidel (SRBGS) method to propose three algorithms that are suitable for different BCs. Experimental results show that the proposed algorithms are effective and the model with the combined L1 and L2 fidelity term demonstrates more advantages in efficiency and accuracy than other models with the L1 fidelity term or the L2 fidelity term.

VEHICLE DETECTION OF AERIAL IMAGE USING TV-L1 TEXTURE DECOMPOSITION

Abstract. Vehicle detection from high-resolution aerial image facilitates the study of the public traveling behavior on a large scale. In the context of road, a simple and effective algorithm is proposed to extract the texture-salient vehicle among the pavement surface. Texturally speaking, the majority of pavement surface changes a little except for the neighborhood of vehicles and edges. Within a certain distance away from the given vector of the road network, the aerial image is decomposed into a smoothly-varying cartoon part and an oscillatory details of textural part. The variational model of Total Variation regularization term and L1 fidelity term (TV-L1) is adopted to obtain the salient texture of vehicles and the cartoon surface of pavement. To eliminate the noise of texture decomposition, regions of pavement surface are refined by seed growing and morphological operation. Based on the shape saliency analysis of the central objects in those regions, vehicles are detected as the objects of rectangular shape saliency. The proposed algorithm is tested with a diverse set of aerial images that are acquired at various resolution and scenarios around China. Experimental results demonstrate that the proposed algorithm can detect vehicles at the rate of 71.5% and the false alarm rate of 21.5%, and that the speed is 39.13 seconds for a 4656 x 3496 aerial image. It is promising for large-scale transportation management and planning.

VEHICLE DETECTION OF AERIAL IMAGE USING TV-L1 TEXTURE DECOMPOSITION

Vehicle detection from high-resolution aerial image facilitates the study of the public traveling behavior on a large scale. In the context of road, a simple and effective algorithm is proposed to extract the texture-salient vehicle among the pavement surface. Texturally speaking, the majority of pavement surface changes a little except for the neighborhood of vehicles and edges. Within a certain distance away from the given vector of the road network, the aerial image is decomposed into a smoothly-varying cartoon part and an oscillatory details of textural part. The variational model of Total Variation regularization term and L1 fidelity term (TV-L1) is adopted to obtain the salient texture of vehicles and the cartoon surface of pavement. To eliminate the noise of texture decomposition, regions of pavement surface are refined by seed growing and morphological operation. Based on the shape saliency analysis of the central objects in those regions, vehicles are detected as the objects of rectangular shape saliency. The proposed algorithm is tested with a diverse set of aerial images that are acquired at various resolution and scenarios around China. Experimental results demonstrate that the proposed algorithm can detect vehicles at the rate of 71.5% and the false alarm rate of 21.5%, and that the speed is 39.13 seconds for a 4656 x 3496 aerial image. It is promising for large-scale transportation management and planning.

An image restoration model combining mixed [formula omitted]/[formula omitted] fidelity terms

Image restoration is a common problem in visual process. In this paper, a modified minimization model is presented, which combines the L1 and L2 fidelity terms with a combined quadratic L2 and TV regularizer just as the regularizer of Cai et al. (2013). The combined regularizer has the priorities of preserving desirable edges and ensuring several kinds of noises can be removed clearly. Split-Bregman algorithm is efficiently employed to solve this model and convergence analysis is also discussed. Moreover, we extend the proposed model and algorithm for image restoration involving blurry images and color images. Experimental results show that our proposed model and algorithm have good performance both in visual and ISNR values for different kinds of blurs and noises including mixed noise.

Improved L0 Gradient Minimization with L1 Fidelity for Image Smoothing.

Edge-preserving image smoothing is one of the fundamental tasks in the field of computer graphics and computer vision. Recently, L0 gradient minimization (LGM) has been proposed for this purpose. In contrast to the total variation (TV) model which employs the L1 norm of the image gradient, the LGM model adopts the L0 norm and yields much better results for the piecewise constant image. However, as an improvement of the total variation (TV) model, the LGM model also suffers, even more seriously, from the staircasing effect and is not robust to noise. In order to overcome these drawbacks, in this paper, we propose an improvement of the LGM model by prefiltering the image gradient and employing the L1 fidelity. The proposed improved LGM (ILGM) behaves robustly to noise and overcomes the staircasing artifact effectively. Experimental results show that the ILGM is promising as compared with the existing methods.

Detail preserved fusion of visible and infrared images using regional saliency extraction and multi-scale image decomposition

Fusion method of infrared and visible images to a synthetic image is a significant research topic in image process. It is an effective way to extract the detail information of the visible image and target regions of the infrared image in the final fused result. In this paper, a detail preserved fusion algorithm of visible and infrared images is proposed based on the regional saliency extraction technique and multi scale image decomposition. The multi-scale image decomposition is firstly applied to the infrared and visible images under the image smoothing framework using L1 fidelity with L0 gradient. Then for each decomposition layer the saliency map is extracted by the frequency-tuned saliency map extraction algorithm. The final fused result is reconstructed by synthesizing different levels with proper weight values. Experiments are implemented to test the performance of the proposed fusion approach compared with other excellent fusion methods. Both the subjective perception and quantitative index results demonstrate that the proposed approach obtains better performance in preserving the edge detail information as well as enhancing the infrared targert signals.

Segmentation and Enhancement of Latent Fingerprints: A Coarse to Fine Ridge Structure Dictionary.

Latent fingerprint matching has played a critical role in identifying suspects and criminals. However, compared to rolled and plain fingerprint matching, latent identification accuracy is significantly lower due to complex background noise, poor ridge quality and overlapping structured noise in latent images. Accordingly, manual markup of various features (e.g., region of interest, singular points and minutiae) is typically necessary to extract reliable features from latents. To reduce this markup cost and to improve the consistency in feature markup, fully automatic and highly accurate ("lights-out" capability) latent matching algorithms are needed. In this paper, a dictionary-based approach is proposed for automatic latent segmentation and enhancement towards the goal of achieving "lights-out" latent identification systems. Given a latent fingerprint image, a total variation (TV) decomposition model with L1 fidelity regularization is used to remove piecewise-smooth background noise. The texture component image obtained from the decomposition of latent image is divided into overlapping patches. Ridge structure dictionary, which is learnt from a set of high quality ridge patches, is then used to restore ridge structure in these latent patches. The ridge quality of a patch, which is used for latent segmentation, is defined as the structural similarity between the patch and its reconstruction. Orientation and frequency fields, which are used for latent enhancement, are then extracted from the reconstructed patch. To balance robustness and accuracy, a coarse to fine strategy is proposed. Experimental results on two latent fingerprint databases (i.e., NIST SD27 and WVU DB) show that the proposed algorithm outperforms the state-of-the-art segmentation and enhancement algorithms and boosts the performance of a state-of-the-art commercial latent matcher.

Image denoising algorithm with variable exponent regularization and L1 fidelity

Image denoising algorithm with variable exponent regularization and L1 fidelity

Deblurring of Color Images Corrupted by Impulsive Noise

We consider the problem of restoring a multichannel image corrupted by blur and impulsive noise (e.g., salt-and-pepper noise). Using the variational framework, we consider the L1 fidelity term and several possible regularizers. In particular, we use generalizations of the Mumford-Shah (MS) functional to color images and gamma-convergence approximations to unify deblurring and denoising. Experimental comparisons show that the MS stabilizer yields better results with respect to Beltrami and total variation regularizers. Color edge detection is a beneficial by-product of our methods.