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.     

Optimal filter-based detection of microcalcifications

This paper deals with the problem of texture feature extraction in digital mammograms. We use the extracted features to discriminate between texture representing clusters of microcalcifications and texture representing normal tissue. Having a two-class problem, we suggest a texture feature extraction method based on a single filter optimized with respect to the Fisher criterion. The advantage of this criterion is that it uses both the feature mean and the feature variance to achieve good feature separation. Image compression is desirable to facilitate electronic transmission and storage of digitized mammograms. In this paper, we also explore the effects of data compression on the performance of our proposed detection scheme. The mammograms in our test set were compressed at different ratios using the Joint Photographic Experts Group compression method. Results from an experimental study indicate that our scheme is very well suited for detecting clustered microcalcifications in both uncompressed and compressed mammograms. For the uncompressed mammograms, at a rate of 1.5 false positive clusters/image our method reaches a true positive rate of about 95%, which is comparable to the best results achieved so far. The detection performance for images compressed by a factor of about four is very similar to the performance for uncompressed images.     

航空图像压缩的双正交小波滤波器整数化设计

在航空图像压缩中,通常采用具有线性相位、正则性、消失矩和完全重构,及适于硬件实现、实时等特性的小波。根据小波滤波器设计,提出了一种基于图像压缩的构造整数双正交小波滤波器的设计方法。从选择小波基的原则为出发点,以CDF9-7小波基为参考,以压缩效果为准则来构造出更优的双正交整数小波基,并且采用航空图像为标准训练图像,以压缩比、峰值信噪比、压缩后保留能量百分比为参数,来寻找最优的小波基。试验结果证明,此方法可以实施非常简单的、无浮点乘法的运算,因而减少运算复杂性以及降低小波硬件实现的难度。     

一种基于提升小波的SAR图像有损压缩算法

该文根据合成孔径雷达(SAR)图像局部相关性较弱,存在相干斑噪声的特点,提出了一种基于提升小波的SAR图像有损压缩算法。它可有效去除相干斑噪声,提高计算精度和速度,改进SAR图像的压缩性能。该算法采用了嵌入式零树小波的编码方法,很好地利用小波系数的特性,使得输出的码流具有嵌入特性。利用大量的实际SAR图像对所提算法进行了仿真验证,并与其它图像压缩算法进行了对比分析,表明所提算法是有效的。     

Detection of microcalcifications in digital mammograms usingwavelets

This paper presents an approach for detecting micro-calcifications in digital mammograms employing wavelet-based subband image decomposition. The microcalcifications appear in small clusters of few pixels with relatively high intensity compared with their neighboring pixels. These image features can be preserved by a detection system that employs a suitable image transform which can localize the signal characteristics in the original and the transform domain. Given that the microcalcifications correspond to high-frequency components of the image spectrum, detection of microcalcifications is achieved by decomposing the mammograms into different frequency subbands, suppressing the low-frequency subband, and, finally, reconstructing the mammogram from the subbands containing only high frequencies. Preliminary experiments indicate that further studies are needed to investigate the potential of wavelet-based subband image decomposition as a tool for detecting microcalcifications in digital mammograms     

Detection of Clustered Microcalcifications on Mammograms Using Surrounding Region Dependence Method and Artificial Neural Network

Clustered microcalcifications on X-ray mammograms are an important sign in the detection of breast cancer. A statistical texture analysis method, called the surrounding region dependence method (SRDM), is proposed for the detection of clustered microcalcifications on digitized mammograms. The SRDM is based on the second-order histogram in two surrounding regions. This method defines four textural features to classify region of interests (ROIs) into positive ROIs containing clustered microcalcifications and negative ROIs of normal tissues. The database is composed of 64 positive and 76 negative ROI images, which are selected from digitized mammograms with a pixel size of 100 × 100 m² and 12 bits per pixel. An ROI is selected as an area of 128 × 128 pixels on the digitized mammograms. In order to classify ROIs into the two types, a three-layer backpropagation neural network is employed as a classifier. A segmentation of individual microcalcifications is also proposed to show their morphologies. The classification performance of the proposed method is evaluated by using the round-robin method and a free-response receiver operating-characteristics (FROC) analysis. A receiver operating-characteristics (ROC) analysis is employed to present the results of the round-robin testing for the case of several hidden neurons. The area under the ROC curve, A _z, is 0.997, which is achieved in the case of 4 hidden neurons. The FROC analysis is performed on 20 cropped images. A cropped image is selected as an area of 512 × 512 pixels on the digitized mammograms. In terms of the FROC, a sensitivity of more than 90% is obtained with a low false-positive (FP) detection rate of 0.67 per cropped image.     

利用子波变换的图象压缩编码技术

从1988年Malial将子波交换用于信号处理提出多分辨率分析概念，给出了信号或图象分解为不同频率通道的算法和重构算法，开创了子波变换在图象处理中的应用．于波变换在时域和频域同时具有良好的局部化性能，使子波变换成为视频图象压缩编码的主要技术，专家预计在1996年将会高清晰度电视标准的子波变换视频图象压缩技术将推出问世．本文将综述子波变换图象压缩编码技术当前的进展。     

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.     

Wavelet-domain approximation and compression of piecewise smooth images.

The wavelet transform provides a sparse representation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to piecewise smooth images, where edge discontinuities separating smooth regions persist along smooth contours. This lack of sparsity hampers the efficiency of wavelet-based approximation and compression. On the class of images containing smooth C2 regions separated by edges along smooth C2 contours, for example, the asymptotic rate-distortion (R-D) performance of zerotree-based wavelet coding is limited to D(R) (< or = 1/R, well below the optimal rate of 1/R2. In this paper, we develop a geometric modeling framework for wavelets that addresses this shortcoming. The framework can be interpreted either as 1) an extension to the "zerotree model" for wavelet coefficients that explicitly accounts for edge structure at fine scales, or as 2) a new atomic representation that synthesizes images using a sparse combination of wavelets and wedgeprints--anisotropic atoms that are adapted to edge singularities. Our approach enables a new type of quadtree pruning for piecewise smooth images, using zerotrees in uniformly smooth regions and wedgeprints in regions containing geometry. Using this framework, we develop a prototype image coder that has near-optimal asymptotic R-D performance D(R) < or = (log R)2 /R2 for piecewise smooth C2/C2 images. In addition, we extend the algorithm to compress natural images, exploring the practical problems that arise and attaining promising results in terms of mean-square error and visual quality.     

Subband image coding using watershed and watercourse lines of thewavelet transform

Reports progress in primitive-based image coding using nonorthogonal dyadic wavelets. A 3D isotropic wavelet is used to approximate the difference-of-Gaussians (D-o-G) operator. Convolution of the image with dilated versions of the wavelet produces three band-pass signals that approximate multiscale smoothed second derivatives. An additional convolution of the image with a Gaussian-shaped low-pass wavelet creates a fourth subband signal that preserves low-frequency information not described by the three band-pass signals. The authors show that the original image can be recovered from the watershed and watercourse lines of the three band-pass signals plus the lowpass subband signal. By thresholding the watershed/watercourse representation, subsampling the low-pass subband, and using edge post emphasis, the authors achieve data reduction with little loss of fidelity. Further compression of the watersheds and watercourses is achieved by chain coding their shapes and predictive coding their amplitudes prior to lossless arithmetic coding. Results are presented for grey-level test images at data rates between 0.1 and 0.3 b/pixel.     

Wavelet transforms for detecting microcalcifications in mammograms

Clusters of fine, granular microcalcifications in mammograms may be an early sign of disease. Individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous. The authors develop a 2-stage method based on wavelet transforms for detecting and segmenting calcifications. The first stage is based on an undecimated wavelet transform, which is simply the conventional filter bank implementation without downsampling, so that the low-low (LL), low-high (LH), high-low (HL), and high-high (HH) sub-bands remain at full size. Detection takes place in HH and the combination LH+HL. Four octaves are computed with 2 inter-octave voices for finer scale resolution. By appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized. In fact, the filters which transform the input image into HH and LH+HL are closely related to prewhitening matched filters for detecting Gaussian objects (idealized microcalcifications) in 2 common forms of Markov (background) noise. The second stage is designed to overcome the limitations of the simplistic Gaussian assumption and provides an accurate segmentation of calcification boundaries. Detected pixel sites in HH and LH+HL are dilated then weighted before computing the inverse wavelet transform. Individual microcalcifications are greatly enhanced in the output image, to the point where straightforward thresholding can be applied to segment them. FROG curves are computed from tests using a freely distributed database of digitized mammograms.     

A review of wavelets in biomedical applications

We present an overview of the various uses of the wavelet transform (WT) in medicine and biology. We start by describing the wavelet properties that are the most important for biomedical applications. In particular we provide an interpretation of the the continuous wavelet transform (CWT) as a prewhitening multiscale matched filter. We also briefly indicate the analogy between the WT and some of the the biological processing that occurs in the early components of the auditory and visual system. We then review the uses of the WT for the analysis of 1-D physiological signals obtained by phonocardiography, electrocardiography (ECG), mid electroencephalography (EEG), including evoked response potentials. Next, we provide a survey of wavelet developments in medical imaging. These include biomedical image processing algorithms (e.g., noise reduction, image enhancement, and detection of microcalcifications in mammograms), image reconstruction and acquisition schemes (tomography, and magnetic resonance imaging (MRI)), and multiresolution methods for the registration and statistical analysis of functional images of the brain (positron emission tomography (PET) and functional MRI (fMRI)). In each case, we provide the reader with same general background information and a brief explanation of how the methods work     

New image compression techniques using multiwavelets andmultiwavelet packets

Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. For best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogonality and symmetry. However, the design possibilities for wavelets are limited because they cannot simultaneously possess all of the desirable properties. The relatively new field of multiwavelets shows promise in obviating some of the limitations of wavelets. Multiwavelets offer more design options and are able to combine several desirable transform features. The few previously published results of multiwavelet-based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms. This paper presents new multiwavelet transform and quantization methods and introduces multiwavelet packets. Extensive experimental results demonstrate that our techniques exhibit performance equal to, or in several cases superior to, the current wavelet filters.     

Performance analysis of image compression using wavelets

The aim of this paper is to examine a set of wavelet functions (wavelets) for implementation in a still image compression system and to highlight the benefit of this transform relating to today's methods. The paper discusses important features of wavelet transform in compression of still images, including the extent to which the quality of image is degraded by the process of wavelet compression and decompression. Image quality is measured objectively, using peak signal-to-noise ratio or picture quality scale, and subjectively, using perceived image quality. The effects of different wavelet functions, image contents and compression ratios are assessed. A comparison with a discrete-cosine-transform-based compression system is given. Our results provide a good reference for application developers to choose a good wavelet compression system for their application     

A novel approach to microcalcification detection using fuzzy logictechnique

Breast cancer continues to be a significant public health problem in the United States. Approximately, 182,000 new cases of breast cancer are diagnosed and 46,000 women die of breast cancer each year. Even more disturbing is the fact that one out of eight women in the United States will develop breast cancer at some point during her lifetime. Since the cause of breast cancer remains unknown, primary prevention becomes impossible. Computer-aided mammography is an important and challenging task in automated diagnosis. It has great potential over traditional interpretation of film-screen mammography in terms of efficiency and accuracy. Microcalcifications are the earliest sign of breast carcinomas and their detection is one of the key issues for breast cancer control. In this study, a novel approach to microcalcification detection based on fuzzy logic technique is presented. Microcalcifications are first enhanced based on their brightness and nonuniformity. Then, the irrelevant breast structures are excluded by a curve detector. Finally, microcalcifications are located using an iterative threshold selection method. The shapes of microcalcifications are reconstructed and the isolated pixels are removed by employing the mathematical morphology technique. The essential idea of the proposed approach is to apply a fuzzified image of a mammogram to locate the suspicious regions and to interact the fuzzified image with the original image to preserve fidelity. The major advantage of the proposed method is its ability to detect microcalcifications even in very dense breast mammograms. A series of clinical mammograms are employed to test the proposed algorithm and the performance is evaluated by the free-response receiver operating characteristic curve. The experiments aptly show that the microcalcifications can be accurately detected even in very dense mammograms using the proposed approach     

Lossless image compression based on optimal prediction, adaptivelifting, and conditional arithmetic coding

The optimal predictors of a lifting scheme in the general n-dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row-column sampling. In each case, the efficiency of the linear predictors is enhanced nonlinearly. Directional postprocessing is used in the quincunx case, and adaptive-length postprocessing in the row-column case. Both methods are seen to perform well. The resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation. We further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework. Special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data. Experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution-based lossless image coding.     

A wavelet domain diversity method for transmission of images overwireless channels

We propose a wavelet domain diversity combining method to combat errors during image transmission on wireless channels. For images represented in the wavelet domain, diversity is used to obtain multiple data streams corresponding to the transmitted image at the receiver. These individual image data streams are combined to form a composite image with higher perceptual quality. Both uncompressed and compressed images are considered. The SPIHT algorithm is used for image compression. Diversity combining methods for both uncompressed and compressed images exploit the characteristics of the wavelet transform. For compressed images, unequal error protection is employed in conjunction with diversity combining. Simulation results demonstrate that the quality of the received image can be significantly improved     

A new multi-resolution hybrid wavelet for analysis and image compression

Most of the current image- and video-related applications require higher resolution of images and higher data rates during transmission, better compression techniques are constantly being sought after. This paper proposes a new and unique hybrid wavelet technique which has been used for image analysis and compression. The proposed hybrid wavelet combines the properties of existing orthogonal transforms in the most desirable way and also provides for multi-resolution analysis. These wavelets have unique properties that they can be generated for various sizes and types by using different component transforms and varying the number of components at each level of resolution. These hybrid wavelets have been applied to various standard images like Lena (512 × 512), Cameraman (256 × 256) and the values of peak signal to noise ratio (PSNR) obtained are compared with those obtained using some standard existing compression techniques. Considerable improvement in the values of PSNR, as much as 5.95 dB higher than the standard methods, has been observed, which shows that hybrid wavelet gives better compression. Images of various sizes like Scenery (200 × 200), Fruit (375 × 375) and Barbara (112 × 224) have also been compressed using these wavelets to demonstrate their use for different sizes and shapes.     

基于自适应小波变换的嵌入图像压缩算法

针对遥感、指纹、地震资料等图像纹理复杂丰富、局部相关性较弱等特点,文章通过实施自适应小波变换、合理确定系数扫描次序、分类量化小波系数等措施,提出了一种高效的图像压缩编码算法.仿真结果表明,相同压缩比下,本文算法的图像复原质量明显优于SPIHT算法(特别是对于纹理图像,如标准图像Barbara).     

Q-shift复小波的一种新型构造方法及其在图像去噪中的应用

为了提高复小波变换的效率,本文提出了一种设计Q-shift复小波滤波器的新方法。与目前采用多相位矩阵的晶格分解结构得到正交小波的方法不同的是,这里从更为一般的完全重构滤波器组出发寻求满足特定要求的正交小波。不但可以构造出系数更为简单、运算更加方便的小波,而且可以实现任意精度的复小波变换。该方法的可拓展性好,可以很方便的添加如高阶消失矩等限制并简化设计过程。以普遍采用的Q-shift10/10小波为例,利用本文构造的正交小波可将复小波变换中的乘法运算降低到原来的1/3,而加法基本相当,且小波的频率选择性质更好。将其用于图像去噪的实验表明,采用本文构造的小波可以显著提高处理速度并得到更高的峰值信噪比(PSNR)。