Licheng Liu

A new weighted mean filter with a two-phase detector for removing impulse noise

Abstract This paper proposes a new weighted mean filter with a two-phase noise detector for image denoising. Operations are carried out by the detection followed by filtering strategy. For detection, a two-phase noise detector is presented to detect impulse noise (IN). In the first phase, a rank-ordered difference of ROAD (ROD-ROAD) scheme is introduced for detecting noise candidates. Different from most of the existing IN detectors, the proposed detector identifies a pixel by a fuzzy rule that matches the stochastic nature of IN and greatly improves the denoising performance. In the second phase, a local image statistic minimum edge pixels difference (MEPD) is proposed to identify edge pixels from noise candidates. This preserves edges from being wrongly detected as noise; therefore, improves the detection accuracy. For filtering, we design a new weighted mean filter (WMF) that is more suitable for IN to suppress the detected noisy pixels. Finally, an iterative denoising algorithm is presented by combining the proposed two-phase noise detector and the new WMF. The proposed method is accessible and easy to implement. Experimental results show that the proposed method outperforms all the tested state-of-the-art denoising methods with respect to the visual effects and quantitative measure results.

Weighted Joint Sparse Representation for Removing Mixed Noise in Image

Joint sparse representation (JSR) has shown great potential in various image processing and computer vision tasks. Nevertheless, the conventional JSR is fragile to outliers. In this paper, we propose a weighted JSR (WJSR) model to simultaneously encode a set of data samples that are drawn from the same subspace but corrupted with noise and outliers. Our model is desirable to exploit the common information shared by these data samples while reducing the influence of outliers. To solve the WJSR model, we further introduce a greedy algorithm called weighted simultaneous orthogonal matching pursuit to efficiently approximate the global optimal solution. Then, we apply the WJSR for mixed noise removal by jointly coding the grouped nonlocal similar image patches. The denoising performance is further improved by incorporating it with the global prior and the sparse errors into a unified framework. Experimental results show that our denoising method is superior to several state-of-the-art mixed noise removal methods.

Weighted Couple Sparse Representation With Classified Regularization for Impulse Noise Removal

Many impulse noise (IN) reduction methods suffer from two obstacles, the improper noise detectors and imperfect filters they used. To address such issue, in this paper, a weighted couple sparse representation model is presented to remove IN. In the proposed model, the complicated relationships between the reconstructed and the noisy images are exploited to make the coding coefficients more appropriate to recover the noise-free image. Moreover, the image pixels are classified into clear, slightly corrupted, and heavily corrupted ones. Different data-fidelity regularizations are then accordingly applied to different pixels to further improve the denoising performance. In our proposed method, the dictionary is directly trained on the noisy raw data by addressing a weighted rank-one minimization problem, which can capture more features of the original data. Experimental results demonstrate that the proposed method is superior to several state-of-the-art denoising methods.

A robust bi-sparsity model with non-local regularization for mixed noise reduction

Sparse representation model (SRM) has been widely used in many image processing and computer vision tasks. However, the conventional SRM usually neglects the prior knowledge about similar signals. Considering the fact that similar signals also have subtle differences, in this paper we propose a robust bi-sparsity model (RBSM) to effectively exploit the prior knowledge about the similarities and the distinctions of signals. In RBSM, similar signals are encouraged to be coded on the same sub-dictionary. But the distinctiveness of similar signals is also addressed by imposing the l0-norm regularization on the difference between each coefficient and its non-local means. In addition, a weight vector is incorporated into the loss function to make the proposed model robust to outliers. We apply RBSM for mixed noise reduction and experimental results show that our proposed model is superior to several state-of-the-art mixed noise removal methods.

Impulse noise removal using sparse representation with fuzzy weights

Many impulse noise removal algorithms do not reach good denoising performance mainly due to the imperfect filters they adopted. In this paper, the popular used sparse representation model is extended for impulse noise removal by using a fuzzy weight matrix. This fuzzy weight is used to describe the noise-like level of the current pixel, and to determine how much information of this pixel should be used in the sparse land model. Besides, a regularization term which counts the proximity between the reconstructed image and the noisy image is also added into the sparse model. This makes the proposed model more robust to the noise detector which generates the fuzzy weight matrix. Moreover, unlike other sparse model, the dictionary used in our model is trained from some reference images that keep the similar structure information of the original image. Therefore, it is more suitable for reconstructing the original image. Simulation results show that our method is superior to all the tested state-of-the-art impulse noise removal methods.

Robust Face Hallucination via Locality-Constrained Bi-Layer Representation

Recently, locality-constrained linear coding (LLC) has been drawn great attentions and been widely used in image processing and computer vision tasks. However, the conventional LLC model is always fragile to outliers. In this paper, we present a robust locality-constrained bi-layer representation model to simultaneously hallucinate the face images and suppress noise and outliers with the assistant of a group of training samples. The proposed scheme is not only able to capture the nonlinear manifold structure but also robust to outliers by incorporating a weight vector into the objective function to subtly tune the contribution of each pixel offered in the objective. Furthermore, a high-resolution (HR) layer is employed to compensate the missed information in the low-resolution (LR) space for coding. The use of two layers (the LR layer and the HR layer) is expected to expose the complicated correlation between the LR and HR patch spaces, which helps to obtain the desirable coefficients to reconstruct the final HR face. The experimental results demonstrate that the proposed method outperforms the state-of-the-art image super-resolution methods in terms of both quantitative measurements and visual effects.

Fast Fourier transform using matrix decomposition

To reduce both the multiplicative complexity and total number of operations, this paper introduces a modeling scheme of the fast Fourier transform (FFT) to decompose the discrete Fourier transform (DFT) matrix recursively into a set of sparse matrices. Integrating three orthogonal transforms, the Hadamard, Modified Haar and Hybrid transforms, the proposed scheme is able to obtain different FFT representations with less computation operations than state of the arts. To investigate the applications of the proposed FFT scheme, a multi-stage image encryption algorithm is also introduced. Experimental results and security analysis are provided to show its encryption performance.

Quaternion Locality-Constrained Coding for Color Face Hallucination

Recently, the locality linear coding (LLC) has attracted more and more attentions in the areas of image processing and computer vision. However, the conventional LLC with real setting is just designed for the grayscale image. For the color image, it usually treats each color channel individually or encodes the monochrome image by concatenating all the color channels, which ignores the correlations among different channels. In this paper, we propose a quaternion-based locality-constrained coding (QLC) model for color face hallucination in the quaternion space. In QLC, the face images are represented as quaternion matrices. By transforming the channel images into an orthogonal feature space and encoding the coefficients in the quaternion domain, the proposed QLC is expected to learn the advantages of both quaternion algebra and locality coding scheme. Hence, the QLC cannot only expose the true topology of image patch manifold but also preserve the inherent correlations among different color channels. Experimental results demonstrated that our proposed QLC method achieved superior performance in color face hallucination compared with other state-of-the-art methods.

A new selective filtering algorithm for image denoising

This paper proposes a simple but efficient selective filtering algorithm (SFA) for removing the impulse noise in images. Integrating the noise detector with the relationship between a pixel and its neighbors, the SFA is able to efficiently detect and remove noise pixels while well preserving information pixels. Experimental results and comparisons demonstrate that the proposed SFA outperforms several existing denoising methods with respect to the visual effects and quantitative measure results.

Mixed Noise Removal via Robust Constrained Sparse Representation

In recent years, the sparse coding-based techniques have been widely used for image denoising. However, most of the sparse coding-based mixed noise reduction methods fail to take full advantage of the geometric structure of data samples. In other words, they neglect the common information shared by the similar patches in sparse coding. To address this concern, in this paper, we propose a robust constrained sparse representation (RCSR) method to remove mixed noise. By using the center coefficient of similar patches as the guider which is approximated by the coefficient of query patch in sparse coding, the geometric structure of data can be well preserved. Moreover, different from most existing two-stage mixed noise reduction methods that use explicit detectors to restrain impulse noise, the proposed RCSR adaptively adjusts the contribution of each pixel in the loss function to eliminate the influences of outliers. Experiments on the reconstruction of synthetic data and the removal of mixed noise in real images demonstrate the effectiveness of our proposed method.