Constrained low-rank quaternion approximation for color image denoising by bilateral random projections

In this letter, we propose a novel low-rank quaternion approximation (LRQA) model by directly constraining the quaternion rank prior for effectively removing the noise in color images. The LRQA model treats the color image holistically rather than independently for the color space components, thus it can fully utilize the high correlation among RGB channels. We design an iterative algorithm by using quaternion bilateral random projections (Q-BRP) to efficiently optimize the proposed model. The main advantage of Q-BRP is that the approximation of the low-rank quaternion matrix can be obtained quite accurately in an inexpensive way. Furthermore, color image denoising is further based on nonlocal self-similarity (NSS) prior. The experimental results on color image denoising illustrate the effectiveness and superiority of the proposed method

A hue-preserving tone mapping scheme based on constant-hue plane without gamut problem

We propose a novel hue-preserving tone mapping scheme. Various tone mapping operations have been studied so far, but there are very few works on color distortion caused in image tone mapping. First, LDR images produced from HDR ones by using conventional tone mapping operators (TMOs) are pointed out to have some distortion in hue values due to clipping and rounding quantization processing. Next,we propose a novel method which allows LDR images to have the same maximally saturated color values as those of HDR ones. Generated LDR images by the proposed method have smaller hue degradation than LDR ones generated by conventional TMOs. Moreover, the proposed method is applicable to any TMOs. In an experiment, the proposed method is demonstrated not only to produce images with small hue degradation but also to maintain well-mapped luminance, in terms of three objective metrics: TMQI, hue value in CIEDE2000, and the maximally saturated color on the constant-hue plane in the RGB color space

Hue-Correction Scheme Considering Non-Linear Camera Response for Multi-Exposure Image Fusion

We propose a novel hue-correction scheme for multi-exposure image fusion (MEF). Various MEF methods have so far been studied to generate higher-quality images. However, there are few MEF methods considering hue distortion unlike other fields of image processing, due to a lack of a reference image that has correct hue. In the proposed scheme, we generate an HDR image as a reference for hue correction, from input multi-exposure images. After that, hue distortion in images fused by an MEF method is removed by using hue information of the HDR one, on the basis of the constant-hue plane in the RGB color space. In simulations, the proposed scheme is demonstrated to be effective to correct hue-distortion caused by conventional MEF methods. Experimental results also show that the proposed scheme can generate high-quality images, regardless of exposure conditions of input multi-exposure images

Low Rank Quaternion Matrix Recovery via Logarithmic Approximation

In color image processing, image completion aims to restore missing entries from the incomplete observation image. Recently, great progress has been made in achieving completion by approximately solving the rank minimization problem. In this paper, we utilize a novel quaternion matrix logarithmic norm to approximate rank under the quaternion matrix framework. From one side, unlike the traditional matrix completion method that handles RGB channels separately, the quaternion-based method is able to avoid destroying the structure of images via putting the color image in a pure quaternion matrix. From the other side, the logarithmic norm induces a more accurate rank surrogate. Based on the logarithmic norm, we take advantage of not only truncated technique but also factorization strategy to achieve image restoration. Both strategies are optimized based on the alternating minimization framework. The experimental results demonstrate that the use of logarithmic surrogates in the quaternion domain is more superior in solving the problem of color images completion.Comment: 35 pages, 7 figure

Quaternion-based bilinear factor matrix norm minimization for color image inpainting

As a new color image representation tool, quaternion has achieved excellent results in the color image processing, because it treats the color image as a whole rather than as a separate color space component, thus it can make full use of the high correlation among RGB channels. Recently, low-rank quaternion matrix completion (LRQMC) methods have proven very useful for color image inpainting. In this paper, we propose three novel LRQMC methods based on three quaternion-based bilinear factor (QBF) matrix norm minimization models. Specifically, we define quaternion double Frobenius norm (Q-DFN), quaternion double nuclear norm (Q-DNN) and quaternion Frobenius/nuclear norm (Q-FNN), and then show their relationship with quaternion-based matrix Schatten-p (Q- Schatten-p ) norm for certain p values. The proposed methods can avoid computing quaternion singular value decompositions (QSVD) for large quaternion matrices, and thus can effectively reduce the calculation time compared with existing (LRQMC) methods. The experimental results demonstrate the superior performance of the proposed methods over some state-of-the-art low-rank (quaternion) matrix completion methods