Peak transform for efficient image representation and coding.

In this work, we introduce a nonlinear geometric transform, called peak transform (PT), for efficient image representation and coding. The proposed PT is able to convert high-frequency signals into low-frequency ones, making them much easier to be compressed. Coupled with wavelet transform and subband decomposition, the PT is able to significantly reduce signal energy in high-frequency subbands and achieve a significant transform coding gain. This has important applications in efficient data representation and compression. To maximize the transform coding gain, we develop a dynamic programming solution for optimum PT design. Based on PT, we design an image encoder, called the PT encoder, for efficient image compression. Our extensive experimental results demonstrate that, in wavelet-based subband decomposition, the signal energy in high-frequency subbands can be reduced by up to 60% if a PT is applied. The PT image encoder outperforms state-of-the-art JPEG2000 and H.264 (INTRA) encoders by up to 2-3 dB in peak signal-to-noise ratio (PSNR), especially for images with a significant amount of high-frequency components. Our experimental results also show that the proposed PT is able to efficiently capture and preserve high-frequency image features (e.g., edges) and yields significantly improved visual quality. We believe that the concept explored in this work, designing a nonlinear transform to convert hard-to-compress signals into easy ones, is very useful. We hope this work would motivate more research work along this direction.     

Translation-invariant contourlet transform and its application to image denoising.

Most subsampled filter banks lack the feature of translation invariance, which is an important characteristic in denoising applications. In this paper, we study and develop new methods to convert a general multichannel, multidimensional filter bank to a corresponding translation-invariant (TI) framework. In particular, we propose a generalized algorithme à trous, which is an extension of the algorithme à trous introduced for 1-D wavelet transforms. Using the proposed algorithm, as well as incorporating modified versions of directional filter banks, we construct the TI contourlet transform (TICT). To reduce the high redundancy and complexity of the TICT, we also introduce semi-translation-invariant contourlet transform (STICT). Then, we employ an adapted bivariate shrinkage scheme to the STICT to achieve an efficient image denoising approach. Our experimental results demonstrate the benefits and potential of the proposed denoising approach. Complexity analysis and efficient realization of the proposed TI schemes are also presented.     

基于方向区域的NSCT图像融合算法

提出一种新的基于方向区域的NSCT图像融合算法。算法首先对源图像进行NSCT分解,获得不同方向的高低频子带。其次对高低频系数,根据不同分解层的方向特性,按方向区域能量的规则进行融合。最后,通过反变换获得融合图像。该方法既保留了Contourlet变换方法的多尺度多方向特性,又具有移不变性。实验结果表明,提出的算法有效可行,对比常用的区域融合算法,获得了更好的融合效果。     

基于Contourlet变换的稳健性图像水印算法

提出了基于Contourlet变换的数字图像水印算法。与小波变换不同的是,Contourlet变换采用类似于线段(contoursegment)的基得到一种多分辨、局部化、方向性的图像表示。水印信号通过基于内容的乘性方案加载到Contourlet变换系数。在采用零均值广义高斯分布拟合Contourlet变换系数的基础上,提出采用极大似然估计实现水印的盲检测。依据Neyman-Pearson准则,在给定虚警率的情况下对判决准则进行了优化。实验结果表明在保证水印隐蔽性的前提下,水印对常见的信号处理手段以及几何变换具有很好的稳健性。     

An image multiresolution representation for lossless and lossycompression

We propose a new image multiresolution transform that is suited for both lossless (reversible) and lossy compression. The new transformation is similar to the subband decomposition, but can be computed with only integer addition and bit-shift operations. During its calculation, the number of bits required to represent the transformed image is kept small through careful scaling and truncations. Numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity. In addition, we propose entropy-coding methods that exploit the multiresolution structure, and can efficiently compress the transformed image for progressive transmission (up to exact recovery). The lossless compression ratios are among the best in the literature, and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods.     

The finite ridgelet transform for image representation

The ridgelet transform was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. We propose an orthonormal version of the ridgelet transform for discrete and finite-size images. Our construction uses the finite Radon transform (FRAT) as a building block. To overcome the periodization effect of a finite transform, we introduce a novel ordering of the FRAT coefficients. We also analyze the FRAT as a frame operator and derive the exact frame bounds. The resulting finite ridgelet transform (FRIT) is invertible, nonredundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional and orthonormal bases for images. Numerical results show that the FRIT is more effective than the wavelet transform in approximating and denoising images with straight edges.     

结合Contourlet变换的Bayes自适应图像去噪算法

提出了结合Contourlet变换的Bayes自适应图像去噪算法。充分利用Contourlet变换的局部性、多分辨率、各向异性等优点。通过Contourlet变换得到图像不同尺度不同方向上Contourlet系数矩阵,实现了建立在对图像多尺度几何分析基础上Bayes估计自适应图像去噪算法。实验表明,新算法能够获得良好的视觉效果并且有效地提高了去噪图像的PSNR值,同时有效的避免了“过扼杀”系数现象,更好地保留了图像的纹理和细节。     

Adaptive directional lifting-based wavelet transform for image coding.

We present a novel 2-D wavelet transform scheme of adaptive directional lifting (ADL) in image coding. Instead of alternately applying horizontal and vertical lifting, as in present practice, ADL performs lifting-based prediction in local windows in the direction of high pixel correlation. Hence, it adapts far better to the image orientation features in local windows. The ADL transform is achieved by existing 1-D wavelets and is seamlessly integrated into the global wavelet transform. The predicting and updating signals of ADL can be derived even at the fractional pixel precision level to achieve high directional resolution, while still maintaining perfect reconstruction. To enhance the ADL performance, a rate-distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features. Experimental results show that the proposed ADL-based image coding technique outperforms JPEG 2000 in both PSNR and visual quality, with the improvement up to 2.0 dB on images with rich orientation features.     

基于小波多尺度表示的图像匹配研究

根据小波变换系数对信号平移步长的变化规律,提出一种基于小波金字塔结构的、遍历式的图像匹配方法,这种方法消除了由于小波变换对平移的敏感性所引起的误匹配,在匹配策略上,以小波分解高频分量的匹配为主。实验证实,本匹配方法对实时图和参考图的局部灰度反转不敏感,具有一定抗几何失真的能力,优于经典的灰度相关匹配。     

基于非抽样复轮廓波变换的图像去噪算法研究

将二维双树复小波变换(DT-CWT)与非抽样方向滤波器组(NSDFB)相结合,构造一种新的非抽样复轮廓波变换(NSCCT),并对其平移不变性作了相应证明。同时利用对称的正态逆高斯(NIG)分布先验概率模型和贝叶斯最小均方算法,提出一种基于NSCCT的图像去噪算法。实验结果表明,本文构造的NSCCT能够有效地抑制伪Gibbs现象,并且具有更丰富的方向分量,因而在图像的细节和纹理表现方面有一定的优势。