Novel Bayesian multiscale method for speckle removal in medical ultrasound images

A novel speckle suppression method for medical ultrasound images is presented. First, the logarithmic transform of the original image is analyzed into the multiscale wavelet domain. We show that the subband decompositions of ultrasound images have significantly non-Gaussian statistics that are best described by families of heavy-tailed distributions such as the alpha-stable. Then, we design a Bayesian estimator that exploits these statistics. We use the alpha-stable model to develop a blind noise-removal processor that performs a nonlinear operation on the data. Finally, we compare our technique with current state-of-the-art soft and hard thresholding methods applied on actual ultrasound medical images and we quantify the achieved performance improvement.     

Image coding using wavelet transform and classified vectorquantisation

The wavelet transform, which provides a multiresolution representation of images, has been widely used in image compression. A new image coding scheme using the wavelet transform and classified vector quantisation is presented. The input image is first decomposed into a hierarchy of three layers containing ten subimages by the discrete wavelet transform. The lowest resolution low frequency subimage is scalar quantised with 8 bits/pixel. The high frequency subimages are compressed by classified vector quantisation to utilise the crosscorrelation among different resolutions while reducing the edge distortion and computational complexity. Vectors are constructed by combining the corresponding wavelet coefficients of different resolutions in the same orientation and classified according to the magnitude and the position of wavelet transform coefficients. Simulation results show that the proposed scheme has a better performance than those utilising current scalar or vector quantisation schemes     

Wavelet-based feature extraction from oceanographic images

Features in satellite images of the oceans often have weak edges. These images also have a significant amount of noise, which is either due to the clouds or atmospheric humidity. The presence of noise compounds the problems associated with the detection of features, as the use of any traditional noise removal technique will also result in the removal of weak edges. Recently, there have been rapid advances in image processing as a result of the development of the mathematical theory of wavelet transforms. This theory led to multifrequency channel decomposition of images, which further led to the evolution of important algorithms for the reconstruction of images at various resolutions from the decompositions. The possibility of analyzing images at various resolutions can be useful not only in the suppression of noise, but also in the detection of fine features and their classification. This paper presents a new computational scheme based on multiresolution decomposition for extracting the features of interest from the oceanographic images by suppressing the noise. The multiresolution analysis from the median presented by Starck-Murtagh-Bijaoui (1994) is used for the noise suppression     

Solution of inverse problems in image processing by waveletexpansion

We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results.     

SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling

Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. This paper proposes a novel Bayesian-based algorithm within the framework of wavelet analysis, which reduces speckle in SAR images while preserving the structural features and textural information of the scene. First, we show that the subband decompositions of logarithmically transformed SAR images are accurately modeled by alpha-stable distributions, a family of heavy-tailed densities. Consequently, we exploit this a priori information by designing a maximum a posteriori (MAP) estimator. We use the alpha-stable model to develop a blind speckle-suppression processor that performs a nonlinear operation on the data and we relate this nonlinearity to the degree of non-Gaussianity of the data. Finally, we compare our proposed method to current state-of-the-art soft thresholding techniques applied on real SAR imagery and we quantify the achieved performance improvement.     

一种基于小波多分辨率分解的图像融合新算法

提出了一种新的基于小波多分辨率分解的图像融合方法。该方法先利用小波变换将图像分解为不同分辨率、不同方向的分量,然后利用方向对比度和基于区域标准差最大化的融合规则得到融合图像的小波系数;最后通过逆小波变换得到融合图像。实验结果表明,本方法是十分有效的。     

Integrated wavelets for enhancement of microcalcifications in digital mammography

This paper presents a new algorithm for enhancement of microcalcifications in mammograms. The main novelty is the application of techniques we have developed for construction of filterbanks derived from the continuous wavelet transform. These discrete wavelet decompositions, called integrated wavelets, are optimally designed for enhancement of multiscale structures in images. Furthermore, we use a model based approach to refine existing methods for general enhancement of mammograms resulting in a more specific enhancement of microcalcifications. We present results of our method and compare them with known algorithms. Finally, we want to indicate how these techniques can also be applied to the detection of microcalcifications. Our algorithm was positively evaluated in a clinical study. It has been implemented in a mammography workstation designed for soft-copy reading of digital mammograms developed by IMAGETOOL, Germany.     

基于提升格式的自适应预测小波变换算法

基于提升格式的小波变换被称为第二代小波变换,该种结构提供了一种灵活构造非线性小波分解和精确重构的方法。本文根据提升格式的小波变换结构,针对具有突变点的光滑信号,以LeGall5/3小波为例,提出了一种不需要额外附加信息和存储空间就可完成精确重构的自适应预测算法。实验结果表明,该算法应用于分段连续信的一维信号,可较大概率取得零高频系数,获得较好的线性近似结果。     

Image compression using wavelet transform and multiresolutiondecomposition

Schemes for image compression of black-and-white images based on the wavelet transform are presented. The multiresolution nature of the discrete wavelet transform is proven as a powerful tool to represent images decomposed along the vertical and horizontal directions using the pyramidal multiresolution scheme. The wavelet transform decomposes the image into a set of subimages called shapes with different resolutions corresponding to different frequency bands. Hence, different allocations are tested, assuming that details at high resolution and diagonal directions are less visible to the human eye. The resultant coefficients are vector quantized (VQ) using the LGB algorithm. By using an error correction method that approximates the reconstructed coefficients quantization error, we minimize distortion for a given compression rate at low computational cost. Several compression techniques are tested. In the first experiment, several 512x512 images are trained together and common table codes created. Using these tables, the training sequence black-and-white images achieve a compression ratio of 60-65 and a PSNR of 30-33. To investigate the compression on images not part of the training set, many 480x480 images of uncalibrated faces are trained together and yield global tables code. Images of faces outside the training set are compressed and reconstructed using the resulting tables. The compression ratio is 40; PSNRs are 30-36. Images from the training set have similar compression values and quality. Finally, another compression method based on the end vector bit allocation is examined.     

Non-Iterative Hierarchical Registration for Medical Images

Digital images from diverse medical imaging modalities and from different imaging times are becoming an indispensable information resource for making clinical decisions. Image registration is an enabling technique for more fully utilizing the embedded heterogeneous image information. However, in addition to the complex differences and deformations inherent in the medical images, the increasing scope, resolution, and dimensionality of imaging pose significant challenges in this medical arena. Wavelets have shown great potential in multi-scale registration due to their superior capacity for representing image information at different resolutions and spatial frequencies. However, the application of wavelets in registration is hindered by their lack of rotation- and translation-invariance. To overcome this obstacle, this paper proposes a non-iterative hierarchical registration method based on points of interest which are extracted automatically from wavelet decompositions. The proposed algorithm for two-dimensional monomodal medical images has been validated by experiments on phantom data and clinical imaging data. This proposed non-iterative method provides a computationally efficient registration, as well as assists in avoiding the non-convergence problem.     

Region adaptive subband image coding

We present a region adaptive subband image coding scheme using the statistical properties of image subbands for various subband decompositions. Motivated by analytical results obtained when the input signal to the subband decomposition is a unit step function, we analyze the energy packing properties toward the lower frequency subbands, edges, and the dependency of energy distribution on the orientation of the edges, in subband decomposed images. Based on these investigations and ideal analysis/synthesis filtering done in the frequency domain, the region adaptive subband image coding scheme extracts suitably shaped regions in each subband and then uses adaptive entropy-constrained quantizers for different regions under the assumption of a generalized Gaussian distribution for the image subbands. We also address the problem of determining an optimal subband decomposition among all possible decompositions. Experimental results show that visual degradations in the reconstructed image are negligible at a bit rate of 1.0 b/pel and reasonable quality images are obtainable at rates as low as 0.25 b/pel.     

The vertical resolution of ground-based microwave radiometersanalyzed through a multiresolution wavelet technique

The spatial resolution of a ground-based microwave radiometer is analyzed through a multiresolution wavelet transform. This technique allows us to compare the ability of the instrument to detect perturbations in a profile under different observing configurations and different noise levels. The use of a wavelet transform applied to performance indicators enables us to isolate the altitude and scale of the perturbation providing an unambiguous definition of resolution. A suitable ensemble of channels and view angles can then be selected to optimize the performance at different altitudes and different resolutions. Several angle/channel configurations are simulated. Among the configurations examined, a scanning system with only one channel offered a resolution comparable to a multichannel system for boundary layer sensing. The simulation suggests that increasing the bandwidth in the multichannel system improves the performance of the fixed view configuration. For investigation above 1 km, a multichannel system with fixed angle seems to offer a better performance at a coarser resolution     

Multiple exemplar-based facial image retrieval using independent component analysis.

In this paper, we design a content-based image retrieval system where multiple query examples can be used to indicate the need to retrieve not only images similar to the individual examples, but also those images which actually represent a combination of the content of query images. We propose a scheme for representing content of an image as a combination of features from multiple examples. This scheme is exploited for developing a multiple example-based retrieval engine. We have explored the use of machine learning techniques for generating the most appropriate feature combination scheme for a given class of images. The combination scheme can be used for developing purposive query engines for specialized image databases. Here, we have considered facial image databases. The effectiveness of the image retrieval system is experimentally demonstrated on different databases.     

A wavelet-based analysis of fractal image compression

Why does fractal image compression work? What is the implicit image model underlying fractal block coding? How can we characterize the types of images for which fractal block coders will work well? These are the central issues we address. We introduce a new wavelet-based framework for analyzing block-based fractal compression schemes. Within this framework we are able to draw upon insights from the well-established transform coder paradigm in order to address the issue of why fractal block coders work. We show that fractal block coders of the form introduced by Jacquin (1992) are Haar wavelet subtree quantization schemes. We examine a generalization of the schemes to smooth wavelets with additional vanishing moments. The performance of our generalized coder is comparable to the best results in the literature for a Jacquin-style coding scheme. Our wavelet framework gives new insight into the convergence properties of fractal block coders, and it leads us to develop an unconditionally convergent scheme with a fast decoding algorithm. Our experiments with this new algorithm indicate that fractal coders derive much of their effectiveness from their ability to efficiently represent wavelet zero trees. Finally, our framework reveals some of the fundamental limitations of current fractal compression schemes.     

Capacity estimates for data hiding in compressed images

We present an information-theoretic approach to obtain an estimate of the number of bits that can be hidden in still images, or, the capacity of the data-hiding channel. We show how the addition of the message signal or signature in a suitable transform domain rather than the spatial domain can significantly increase the channel capacity. Most of the state-of-the-art schemes developed thus far for data-hiding have embedded bits in some transform domain, as it has always been implicitly understood that a decomposition would help. Though most methods reported in the literature use DCT or wavelet decomposition for data embedding, the choice of the transform is not obvious. We compare the achievable data hiding capacities for different decompositions like DCT, DFT, Hadamard, and subband transforms and show that the magnitude DFT decomposition performs best among the ones compared.     

Hiding digital watermarks using multiresolution wavelet transform

In this paper, an image accreditation technique by embedding digital watermarks in images is proposed. The proposed method for the digital watermarking is based on the wavelet transform. This is unlike most previous work, which used a random number of a sequence of bits as a watermark and where the watermark can only be detected by comparing an experimental threshold value to determine whether a sequence of random signals is the watermark. The proposed approach embeds a watermark with visual recognizable patterns, such as binary, gray, or color image in images by modifying the frequency part of the images. In the proposed approach, an original image is decomposed into wavelet coefficients. Then, multi-energy watermarking scheme based on the qualified significant wavelet tree (QSWT) is used to achieve the robustness of the watermarking. Unlike other watermarking techniques that use a single casting energy, QSWT adopts adaptive casting energy in different resolutions. The performance of the proposed watermarking is robust to a variety of signal distortions, such as JPEG, image cropping, sharpening, median filtering, and incorporating attacks     

小波变换在三维面形测量中的最佳小波的选择

在几种不同的复小波函数内优选出表现最佳的小波进行小波间比较,利用连续小波变换(CWT)对同一图像进行恢复处理。通过比较不同小波的频域分布、恢复图像的效果和在恢复不同图像所得到的数据表明,复Morlet小波中的cmor1-1小波相对于其它小波在恢复图像中更具有优势。计算机模拟和实验验证了该结论的正确性和可行性。     

On the number of rectangular tilings.

Adaptive multiscale representations via quadtree splitting and two-dimensional (2-D) wavelet packets, which amount to space and frequency decompositions, respectively, are powerful concepts that have been widely used in applications. These schemes are direct extensions of their one-dimensional counterparts, in particular, by coupling of the two dimensions and restricting to only one possible further partition of each block into four subblocks. In this paper, we consider more flexible schemes that exploit more variations of multidimensional data structure. In the meantime, we restrict to tree-based decompositions that are amenable to fast algorithms and have low indexing cost. Examples of these decomposition schemes are anisotropic wavelet packets, dyadic rectangular tilings, separate dimension decompositions, and general rectangular tilings. We compute the numbers of possible decompositions for each of these schemes. We also give bounds for some of these numbers. These results show that the new rectangular tiling schemes lead to much larger sets of 2-D space and frequency decompositions than the commonly-used quadtree-based schemes, therefore bearing the potential to obtain better representation for a given image.     

Curvelet based face recognition via dimension reduction

Multiresolution ideas, notably the wavelet transform, have been proved quite useful for analyzing the information content of facial images. Numerous papers and research articles have discussed the application of wavelet transform in face recognition. However, little attention has been paid to the newly developed multiresolution tools (contourlet, curvelet, etc.) despite their improved directional elements and other promising abilities compared to traditional wavelet transform. In this article we introduce the application of digital curvelet transform in conjunction with different dimensionality reduction tools, looking particularly at the problem of facial feature extraction from 2D images. The purpose of this paper is exploratory. We do not claim that the results achieved here are the best possible. Rather, we aim at showing that curvelets can serve as an effective alternative to wavelets as a feature extraction tool. This work can be seen as a stepping stone for further research in this direction. Our methods have been evaluated on well-known databases like ORL, Essex Grimace and Yale face. Curvelet based results have been compared with that achieved using wavelets and other existing techniques to show that curvelets indeed has the potential to supersede wavelet based results.     

Spherical Coding Algorithm for Wavelet Image Compression

In recent literature, there exist many high-performance wavelet coders that use different spatially adaptive coding techniques in order to exploit the spatial energy compaction property of the wavelet transform. Two crucial issues in adaptive methods are the level of flexibility and the coding efficiency achieved while modeling different image regions and allocating bitrate within the wavelet subbands. In this paper, we introduce the ldquospherical coder,rdquo which provides a new adaptive framework for handling these issues in a simple and effective manner. The coder uses local energy as a direct measure to differentiate between parts of the wavelet subband and to decide how to allocate the available bitrate. As local energy becomes available at finer resolutions, i.e., in smaller size windows, the coder automatically updates its decisions about how to spend the bitrate. We use a hierarchical set of variables to specify and code the local energy up to the highest resolution, i.e., the energy of individual wavelet coefficients. The overall scheme is nonredundant, meaning that the subband information is conveyed using this equivalent set of variables without the need for any side parameters. Despite its simplicity, the algorithm produces PSNR results that are competitive with the state-of-art coders in literature.