Shearlet-Based Deconvolution

In this paper, a new type of deconvolution algorithm is proposed that is based on estimating the image from a shearlet decomposition. Shearlets provide a multidirectional and multiscale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. Constructions such as curvelets and contourlets share similar properties, yet their implementations are significantly different from that of shearlets. Taking advantage of unique properties of a new M-channel implementation of the shearlet transform, we develop an algorithm that allows for the approximation inversion operator to be controlled on a multiscale and multidirectional basis. A key improvement over closely related approaches such as ForWaRD is the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation (GCV). Various tests show that this method can perform significantly better than many competitive deconvolution algorithms.      

Moving window-based double Haar wavelet transform for image processing.

Image denoising is a lively research field. The classical nonlinear filters used for image denoising, such as median filter, are based on a local analysis of the pixels within a moving window. Recently, the research of image denoising has been focused on the wavelet domain. Compared to the classical nonlinear filters, it is based on a global multiscale analysis of images. Apparently, the wavelet transform can be embedded in a moving window. Thus, a moving window-based local multiscale analysis is obtained. In this paper, based on the Haar wavelet, a class of nonorthogonal multi-channel filter bank with its corresponding wavelet shrinkage called Lee shrinkage is derived. As a special case of this filter bank, the double Haar wavelet transform is introduced. Examples show that it is suitable for a moving window-based local multiscale analysis used for image denoising, edge detection, and edge enhancement.     

Shearlet-Based Total Variation Diffusion for Denoising

We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors.     

Shearlet变换域自适应图像去噪算法

首先采用Haar小波滤波器,设计出一种数字Shearlet变换算法。然后对Shearlet系数间的相关性进行统计分析,提出了一种尺度相关的自适应阈值收缩图像去噪算法。最后选用峰值信噪比和视觉质量为评价标准,实验验证算法的去噪性能。结果表明,本文算法获得更高的峰值信噪比,更好地保留了图像的细节信息。     

一种基于数学形态学与小波域增强的滤波算法

为了有效滤除图像高斯噪声,将数学形态学与小波域增强相结合,提出了一种高斯噪声新型滤波算法.该算法首先将噪声图像进行二维小波分解,得到低频和高频子图像;然后保留低频子图像不变,对各高频子图像根据其噪声分布特点分别设计出多角度、多结构逐级形态学滤波器进行滤波处理,并进行小波分解系数重构;最后对经过形态学滤波后的图像进行2层小波分解,通过设计出一种新型小波增强函数对不同幅值的小波系数进行不同程度的收缩处理,在此基础上进行分解系数重构.将自适应中值滤波与数学形态学滤波与本文算法进行比较,实验证明本文滤波算法其去噪效果优于前两种算法.     

Three-dimensional video compression using subband/wavelet transformwith lower buffering requirements

Three-dimensional (3-D) video compression using wavelets decomposition along the temporal axis dictates that a number of video frames must be buffered to allow for the temporal decomposition. Buffering of frames allows for the temporal correlation to be made use of, and the larger the buffer the more effective the decomposition. One problem inherent in such a set up in interactive applications such as video conferencing, is that buffering translates into a corresponding time delay. We show that 3-D coding of such image sequences can be achieved in the true sense of temporal direction decomposition but with much less buffering requirements. For a practical coder, this can be achieved by introducing an approximation to the way the transform coefficients are encoded. Applying wavelet decomposition using some types of filters may introduce edge errors, which become more prominent in short signal segments. We also present a solution to this problem for the Daubechies (1988) family of filters.     

基于二进小波变换的实信号的多尺度Hilbert变换和瞬时频率提取

该文着重讨论了使用二进小波变换方法实现数字Hilbert滤波,特别是使用滤波器组实现多尺度Hilbert滤波所要考虑的各尺度滤波器的设计问题。将多尺度Hilbert方法应用到求信号的瞬时参数中,并利用小波变换的去噪思想,取得了比使用DWT方法去噪更好的去噪效果。     

Block-median pyramidal transform: analysis and denoisingapplications

A nonlinear multiscale pyramidal transform based on nonoverlapping block decompositions using the median operation and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of oneand two-dimensional (1-D and 2-D) signals. Various denoising techniques are analyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresholds for denoising applications     

利用HSSIM和残差比阈值的3维激光扫描图像去噪

为了更好地实现3维激光扫描图像的去噪,提出一种融合直方图结构相似度(HSSIM)和残差比阈值的改进稀疏去噪算法。利用初始化过完备字典进行稀疏分解,以相似因子代替重构误差作为保真项,利用残差比阈值作为正交匹配追踪算法的迭代终止条件对图像进行去噪,获得了去噪后图像的峰值信噪比及HSSIM指标。结果表明,与基于db2小波变换、多尺度曲波变换和离散余弦变换的去噪方法相比,该算法能获得更好的峰值信噪比和HSSIM数据。在有效去除图像噪声的同时还能更有效地保留图像的细节特征。     

基于双域分解的图像增强算法

为解决图像增强中对比度提高与噪声抑制的矛盾,本文提出了一种基于双域分解的图像增强算法,同步实现图像对比度提高与噪声抑制.文中详述了空域分解、分层图像空域增强与变换域降噪、分层图像合成三个主要环节的原理、方法.首先,高斯滤波器将图像分解为基础层和细节层,实现对比度提高与噪声抑制的解耦合;其次,带校正功能的单尺度Retinex和硬阈值收缩的非下采样剪切波降噪算法同步实现基础层的增强和细节层的降噪;最后,分层图像合成、灰度数值延展和微分算子强化,实现合成图像的灰度延展与细节加强,确保增强图像的颜色均匀、细节突出.实验表明,本文算法提高图像对比度和抑制噪声的性能优于其他九种算法.     

Parallel image processing with the block data parallel architecture

Many digital signal and image processing algorithms can be speeded up by executing them in parallel on multiple processors. The speed of parallel execution is limited by the need for communication and synchronization between processors. In this paper, we present a paradigm for parallel processing that we call the block data flow paradigm (BDFP). The goal of this paradigm is to reduce interprocessor communication and relax the synchronization requirements for such applications. We present the block data parallel architecture which implements this paradigm, and we present methods for mapping algorithms onto this architecture. We illustrate this methodology for several applications including two-dimensional (2-D) digital filters, the 2-D discrete cosine transform, QR decomposition of a matrix and Cholesky factorization of a matrix. We analyze the resulting system performance for these applications with regard to speedup and efficiency as the number of processors increases. Our results demonstrate that the block data parallel architecture is a flexible, high-performance solution for numerous digital signal and image processing algorithms     

A Shearlet Approach to Edge Analysis and Detection

It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions.     

A novel nonnegative decomposition method and its application to 2-D digital filter design

In designing two-dimensional (2-D) digital filters in the frequency domain, an efficient technique is to first decompose the given 2-D frequency domain design specifications into one-dimensional (1-D) ones, and then approximate the resulting 1-D magnitude specifications using the well-developed 1-D filter design techniques. Finally, by interconnecting the designed 1-D filters one can obtain a 2-D digital filter. However, since the magnitude responses of digital filters must be nonnegative, it is required that the decomposition of 2-D magnitude specifications result in nonnegative 1-D magnitude specifications. We call such a decomposition the nonnegative decomposition. This paper proposes a nonnegative decomposition method for decomposing the given 2-D magnitude specifications into 1-D ones, and then transforms the problem of designing a 2-D digital filter into that of designing 1-D filters. Consequently, the original problem of designing a 2-D filter is significantly simplified.     

Design of arbitrary-phase variable digital filters using SVD-based vector-array decomposition

This paper proposes a straightforward method for designing variable digital filters with arbitrary variable magnitude as well as arbitrary fixed-phase or variable fractional delay (VFD) responses. The basic idea is to avoid the complicated direct design of one-dimensional (1-D) variable digital filters by decomposing the original variable filter design problem into easier subproblems that only require constant 1-D filter designs and multidimensional polynomial approximations. Through constant 1-D filter designs and multidimensional polynomial fits, we can easily obtain a variable digital filter satisfying the given variable design specifications. To decompose the original variable filter design into constant 1-D filter designs and multidimensional polynomial fits, a new multidimensional complex array decomposition called vector array decomposition (VAD) is proposed, which is based on two new theorems using the singular value decomposition (SVD). Once the VAD is obtained, the subproblems can be easily solved. Furthermore, we show that the VAD can also be generalized to the weighted least squares (WLS) case (WLS-VAD) for the WLS variable filter design. Three design examples are given to illustrate that the WLS-VAD and VAD-based techniques are considerably efficient for designing variable digital filters with arbitrary variable magnitude and arbitrary fixed-phase or VFD responses.     

The nonsubsampled contourlet transform: theory, design, and applications.

In this paper, we develop the nonsubsampled contourlet transform (NSCT) and study its applications. The construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks. The result is a flexible multiscale, multidirection, and shift-invariant image decomposition that can be efficiently implemented via the à trous algorithm. At the core of the proposed scheme is the nonseparable two-channel nonsubsampled filter bank (NSFB). We exploit the less stringent design condition of the NSFB to design filters that lead to a NSCT with better frequency selectivity and regularity when compared to the contourlet transform. We propose a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases. In addition, our design ensures that the corresponding frame elements are regular, symmetric, and the frame is close to a tight one. We assess the performance of the NSCT in image denoising and enhancement applications. In both applications the NSCT compares favorably to other existing methods in the literature.     

Wavelets, ridgelets, and curvelets for Poisson noise removal.

In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance. This new transform, which can be deemed as an extension of the Anscombe transform to filtered data, is simple, fast, and efficient in (very) low-count situations. We combine this VST with the filter banks of wavelets, ridgelets and curvelets, leading to multiscale VSTs (MS-VSTs) and nonlinear decomposition schemes. By doing so, the noise-contaminated coefficients of these MS-VST-modified transforms are asymptotically normally distributed with known variances. A classical hypothesis-testing framework is adopted to detect the significant coefficients, and a sparsity-driven iterative scheme reconstructs properly the final estimate. A range of examples show the power of this MS-VST approach for recovering important structures of various morphologies in (very) low-count images. These results also demonstrate that the MS-VST approach is competitive relative to many existing denoising methods.     

Differential morphology and image processing

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.     

Multiscale contrast enhancement for radiographies: Laplacian Pyramid versus fast wavelet transform

Contrast enhancement of radiographies based on a multiscale decomposition of the images recently has proven to be a far more versatile and efficient method than regular unsharp-masking techniques, while containing these as a subset. In this paper, we compare the performance of two multiscale-methods, namely the Laplacian Pyramid and the fast wavelet transform (FWT). We find that enhancement based on the FWT suffers from one serious drawback-the introduction of visible artifacts when large structures are enhanced strongly. By contrast, the Laplacian Pyramid allows a smooth enhancement of large structures, such that visible artifacts can be avoided. Only for the enhancement of very small details, for denoising applications or compression of images, the FWT may have some advantages over the Laplacian Pyramid.     

No-reference image quality assessment using statistical characterization in the shearlet domain

Image and video quality measurements are crucial for many applications, such as acquisition, compression, transmission, enhancement, and reproduction. Nowadays, no-reference (NR) image quality assessment (IQA) methods have drawn extensive attention because it does not rely on any information of original images. However, most of the conventional NR-IQA methods are designed only for one or a set of predefined specific image distortion types, which are unlikely to generalize for evaluating image/video distorted with other types of distortions. In order to estimate a wide range of image distortions, in this paper, we present an efficient general-purpose NR-IQA algorithm which is based on a new multiscale directional transform (shearlet transform) with a strong ability to localize distributed discontinuities. This is mainly based on distorted natural image that leads to significant variation in the spread discontinuities in all directions. Thus, the statistical property of the distorted image is significantly different from that of natural images in fine scale shearlet coefficients, which are referred to as ‘distorted parts’. However, some ‘natural parts’ are reserved in coarse scale shearlet coefficients. The algorithm relies on utilizing the natural parts to predict the natural behavior of distorted parts. The predicted parts act as ‘reference’ and the difference between the reference and distorted parts is used as an indicator to predict the image quality. In order to achieve this goal, we modify the general sparse autoencoder to serve as a predictor to get the predicted parts from natural parts. By translating the NR-IQA problem into classification problem, the predicted parts and distorted parts are utilized to form features and the differences between them are identified by softmax classifier. The resulting algorithm, which we name SHeArlet based No-reference Image quality Assessment (SHANIA), is tested on several database (LIVE, Multiply Distorted LIVE and TID2008) and shown to be suitable for many common distortions, consistent with subjective assessment and comparable to full-reference IQA methods and state-of-the-art general purpose NR-IQA algorithms.