Direction-adaptive discrete wavelet transform for image compression.

We propose a direction-adaptive DWT (DA-DWT) that locally adapts the filtering directions to image content based on directional lifting. With the adaptive transform, energy compaction is improved for sharp image features. A mathematical analysis based on an anisotropic statistical image model is presented to quantify the theoretical gain achieved by adapting the filtering directions. The analysis indicates that the proposed DA-DWT is more effective than other lifting-based approaches. Experimental results report a gain of up to 2.5 dB in PSNR over the conventional DWT for typical test images. Subjectively, the reconstruction from the DA-DWT better represents the structure in the image and is visually more pleasing.     

Color monogenic wavelet transform for multichannel image denoising

This paper proposes an effective color image denoising algorithm using the combination color monogenic wavelet transform (CMWT) with a trivariate shrinkage filter. The CMWT coefficients are one order of magnitude with three phases: two phases encode the local color information while the third contains geometric information relating to texture within the color image. In the CMWT domain, a trivariate Gaussian distribution is applied to capture statistical dependencies between the CMWT coefficients, and then a trivariate shrinkage filter is derived using a maximum a posteriori estimator. The performance of the proposed algorithm is experimentally verified using a variety of color test images with a range of noise levels in terms of PSNR and visual quality. The experimental results demonstrate that the proposed algorithm is equal to or better than current state-of-the-art algorithms in both visual and quantitative performance.     

用小波变换抑制SAR图像中的斑点噪声

抑制合成孔径雷达图像中的斑点噪声一直是处理图像并得到准确图像信息的难点，提出了一种基于小波变换抑制合成孔径雷达（SAR）图像中的斑点噪声的方法，对原有的小波变换方法作了改进，能更好地保留图像的边缘信息，并能简化计算量。在仿真实验中使用了合成的模拟图像和真实的合成孔径雷图像，并与以往的小波去噪滤波方法以及一些经典的斑点噪声滤波方法（包括中值滤波，Lee滤波，Frost滤波）进行比较，在综合考虑了滤波算法在均匀区域对斑点噪声的抑制能力以及保留边缘信息能力的情况下，提出的算法有更好的效果。     

基于小波变换的超声图像去噪算法研究

在超声无损检测中,图像在生成和传输过程中常常因受到各种噪声的干扰和影响而质量下降,这对缺陷的识别和定位将产生不利影响。在对超声检测信号和噪声的种类及特点进行深入分析的基础上,运用小波变换阈值去噪的理论,对四种不同的噪声(高斯噪声、泊松噪声、椒盐噪声和斑点噪声),分别运用软阈值去噪法、硬阈值去噪法及NeighShrink去噪法进行去噪,发现NeighShrink去噪法去噪后的图像性噪比提高最多,边缘模糊也最小。用这三种去噪法对超声B扫图像进行去噪,验证了NeighShrink去噪法对于超声B扫图像具有最出色的去噪效果。     

小波变换在图像压缩过程中的作用

介绍图像压缩原理,分析小波变换用于图像压缩的一般步骤,基于多分辨分析的理论基础,重点与详细的说明了小波变换在图像压缩中的数学计算过程所起到的作用,并用MATLAB给予模拟演示.     

基于小波变换的图像去噪方法研究

图像去噪问题是一个古老的难题,也是当前研究的热点问题,而图像小波去噪算法在图像去噪方面虽然已取得了一定进步,但在这一领域仍然有许多问题需要研究,为了进一步提高图像去噪质量,改善图像视觉效果。在此通过在小波阀值萎缩法、基于混合模型的小波去噪法、小波去噪与其他算法相结合的三类方法中分别选用了三种典型算法即VisuSh?rink法、基于高斯混合模型小波去噪法、中值滤波与小波去噪相结合的算法,对当前基于小波变换图像去噪这三类典型问题进行了研究。研究表明对于单一的噪声,用相应某种算法,就可能取得较理想效果。而对于混合噪声,单独的一种算法取得的效果是比较差的,只有采用几种算法相结合才能取得较好的效果,因而在此也为图像去噪指明了以后的研究方向。     

基于KL与小波联合变换的多光谱图像压缩

鉴于卫星拍摄的遥感图像的空间分辨率和光谱分辨率越来越高,在一些应用中,常会对多光谱图像进行压缩。为了提高多光谱图像的压缩质量,提出了联合相位相关和仿射变换的图像配准方法,有效提高了图像谱段之间的相关性。针对多光谱图像压缩,提出了结合Karhunen-Love,KL变换去除谱间相关和嵌入式二维小波编码方法。相比JPEG2000谱段图像独立压缩方法,提出方法解压图像的Peak Signal to Noise Ratio,PSNR值平均提高2.1 dB。实验结果表明:所提出的方法能在相同的压缩率下获得比JPEG2000谱段图像独立压缩方法更好的图像质量。     

Edge-preserving image compression using adaptive lifting wavelet transform

In this paper, a novel 2-D adaptive lifting wavelet transform is presented. The proposed algorithm is designed to further reduce the high-frequency energy of wavelet transform, improve the image compression efficiency and preserve the edge or texture of original images more effectively. In this paper, a new optional direction set, covering the surrounding integer pixels and sub-pixels, is designed. Hence, our algorithm adapts far better to the image orientation features in local image blocks. To obtain the computationally efficient and coding performance, the complete processes of 2-D adaptive lifting wavelet transform is introduced and implemented. Compared with the traditional lifting-based wavelet transform, the adaptive directional lifting and the direction-adaptive discrete wavelet transform, the new structure reduces the high-frequency wavelet coefficients more effectively, and the texture structures of the reconstructed images are more refined and clear than that of the other methods. The peak signal-to-noise ratio and the subjective quality of the reconstructed images are significantly improved.     

基于小波变换图像压缩芯片的实现

简述了图像压缩中小波变换的几种方法,介绍了国内外小波芯片现状,提出了在设计小波算法和芯片时需要解决的问题,最后探讨了小波芯片未来的发展机遇。     

Feature-based wavelet shrinkage algorithm for image denoising.

A selective wavelet shrinkage algorithm for digital image denoising is presented. The performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings. The improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods. The denoising method incorporated in the proposed algorithm involves a two-threshold validation process for real-time selection of wavelet coefficients. The two-threshold criteria selects wavelet coefficients based on their absolute value, spatial regularity, and regularity across multiresolution scales. The proposed algorithm takes image features into consideration in the selection process. Statistically, most images have regular features resulting in connected subband coefficients. Therefore, the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients. In the proposed algorithm, coefficients are selected due to their magnitude, and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction. Therefore, two thresholds are used in the coefficient selection process. The first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity. The performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques, as well as being computationally efficient to facilitate real-time image-processing applications.     

基于离散正交小波变换的红外图像去噪方法

提出红外图像去噪方法，将小波变换与广义交叉确认原理相结合，在噪声方差未知的前提下，只利用红外图像的输入数据就可以确定所要求的渐近最优阈值。对红外图像进行离散正交小波变换后，分别对各个分解层的高频子带利用所提出的方法进行迭代去噪，使各个高频子带分别收敛于其最大信噪比。实验结果表明，该方法在有效地去除噪声的同时，能较好地保持红外图像的细节信息。算法在性能指标和视觉质量上均优于Donoho提出的小波阈值去噪方法、Johnstone提出经过调整的小波阈值法和传统的中值滤波法。     

基于能量的自适应小波变换图像压缩算法

针对现有压缩算法计算量大以及压缩质量差等问题,文章根据图像能量的分布特性,提出了一种基于能量的自适应小波变换图像压缩算法。通过优化扫描法以及小波的分解模式来提高算法的准确率,并根据低频子带的扰动性大小,来对低频子带进行量化处理,而高频子带则是利用边缘检测算法的高效性,来提取高频子带中的有效信号,进而保证图像压缩的高效性与准确性。实验结果表明,文章算法的仿真结果与预期目标相符,有效证明了算法的可行性。     

基于图形小波变换的遥感图像表示与去噪

离散小波变换(Discrete Wavelet Transform,DWT)通常用于图像的表示。然而,对于具有不规则形状边缘的图像,尤其是对于纹理和细节信息较多的遥感图像,DWT却很难有效表示,进而影响后续去噪效果。针对该问题,提出了一种基于图形小波变换(Graphic Wavelet Transform,GWT)的图像去噪方法。首先,将图像表示为图形信号,并通过该图形信号的谱表示构造相应的变换矩阵;然后,设计了一种改进自适应阈值的图像去噪方法,在GWT变换域内对图像去噪。实验结果表明,与常用的图像去噪方法相比,所提算法能够提供更好的图像主观质量。采用均方根误差(Root Mean Square Error,RMSE)和峰值信噪比(Peak Signal-to-Noise Ratio,PSNR)作为客观指标,结果表明,采用所提方法得到的重建图像客观质量更优。     

Adaptive wavelet threshold for image denoising

Threshold selection is the critical issue in image denoising via wavelet shrinkage. Many powerful approaches have been investigated, but few have been to make the threshold values adaptive to the changing statistics of images and meanwhile maintain the efficiency of the algorithm. In this work an efficient adaptive algorithm to capture the dependency of inter-scale wavelet coefficients is proposed. Experiments show that higher peak signal-to-noise ratio can be obtained as compared to other threshold-denoising algorithms.     

Curved wavelet transform for image coding.

The conventional two-dimensional wavelet transform used in existing image coders is usually performed through one-dimensional (1-D) filtering in the vertical and horizontal directions, which cannot efficiently represent edges and lines in images. The curved wavelet transform presented in this paper is carried out by applying 1-D filters along curves, rather than being restricted to vertical and horizontal straight lines. The curves are determined based on image content and are usually parallel to edges and lines in the image to be coded. The pixels along these curves can be well represented by a small number of wavelet coefficients. The curved wavelet transform is used to construct a new image coder. The code-stream syntax of the new coder is the same as that of JPEG2000, except that a new marker segment is added to the tile headers. Results of image coding and subjective quality assessment show that the new image coder performs better than, or as well as, JPEG2000. It is particularly efficient for images that contain sharp edges and can provide a PSNR gain of up to 1.67 dB for natural images compared with JPEG2000.     

The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a; trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement.     

Two denoising methods by wavelet transform

To wavelet-based noise reduction methods are discussed. First, we improve the traditional spatially selective noise filtration technique proposed by Xu et al. (1994). Second, we introduce a new threshold-based denoising algorithm based on undecimated discrete wavelet transform. Simulations and comparisons are given     

一种新的小波图像去噪方法

小波图像去噪已经成为目前图像去噪的主要方法之一，目前的研究主要集中于如何选取阈值使去噪达到较好的效果。边缘信息是图像最为有用的高频信息，在图像去噪的同时，应尽量保留图像的边缘信息，基于这一思想，提出一种新的小波图像去噪方法。用数学形态学算子对图像小波变换后的小波系数进行处理，以去除具有较小支持域的噪声，保留具有连续支持域的边缘。实验结果表明，与普通的小波阈值去噪方法相比，该方法不但可以保留图像的边缘信息，而且能提高去噪后图像的峰值信噪比2～5dB，提高信噪比6～10dB。     

B-spline wavelets for signal denoising and image compression

In this paper we propose to develop novel techniques for signal/image decomposition, and reconstruction based on the B-spline mathematical functions. Our proposed B-spline based multiscale/resolution representation is based upon a perfect reconstruction analysis/synthesis point of view. Our proposed B-spline analysis can be utilized for different signal/imaging applications such as compression, prediction, and denoising. We also present a straightforward computationally efficient approach for B-spline basis calculations that is based upon matrix multiplication and avoids any extra generated basis. Then we propose a novel technique for enhanced B-spline based compression for different image coders by preprocessing the image prior to the decomposition stage in any image coder. This would reduce the amount of data correlation and would allow for more compression, as will be shown with our correlation metric. Extensive simulations that have been carried on the well-known SPIHT image coder with and without the proposed correlation removal methodology are presented. Finally, we utilized our proposed B-spline basis for denoising and estimation applications. Illustrative results that demonstrate the efficiency of the proposed approaches are presented.