ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems

We propose an efficient, hybrid Fourier-wavelet regularized deconvolution (ForWaRD) algorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's economical representation of the colored noise inherent in deconvolution, whereas the wavelet shrinkage exploits the wavelet domain's economical representation of piecewise smooth signals and images. We derive the optimal balance between the amount of Fourier and wavelet regularization by optimizing an approximate mean-squared error (MSE) metric and find that signals with more economical wavelet representations require less Fourier shrinkage. ForWaRD is applicable to all ill-conditioned deconvolution problems, unlike the purely wavelet-based wavelet-vaguelette deconvolution (WVD); moreover, its estimate features minimal ringing, unlike the purely Fourier-based Wiener deconvolution. Even in problems for which the WVD was designed, we prove that ForWaRD's MSE decays with the optimal WVD rate as the number of samples increases. Further, we demonstrate that over a wide range of practical sample-lengths, ForWaRD improves on WVD's performance.     

Multiple resolution image restoration

A new algorithm for solving the deconvolution problem is proposed. This algorithm uses the wavelet transform to induce a multiresolution approach to deconvolve a blurred signal/image. The low resolution part of a signal/image is restored first and then high resolution information is added successively into the estimation process. Two different ways to incorporate the image space positivity constraint, namely loosely and strictly, are discussed. In to most restoration algorithms, the positivity constraint is applied directly in the transformed domain. The performance of the algorithm in the presence of noise is also investigated     

Image Denoising Using Trivariate Shrinkage Filter in the Wavelet Domain and Joint Bilateral Filter in the Spatial Domain

This correspondence proposes an efficient algorithm for removing Gaussian noise from corrupted image by incorporating a wavelet-based trivariate shrinkage filter with a spatial-based joint bilateral filter. In the wavelet domain, the wavelet coefficients are modeled as trivariate Gaussian distribution, taking into account the statistical dependencies among intrascale wavelet coefficients, and then a trivariate shrinkage filter is derived by using the maximum a posteriori (MAP) estimator. Although wavelet-based methods are efficient in image denoising, they are prone to producing salient artifacts such as low-frequency noise and edge ringing which relate to the structure of the underlying wavelet. On the other hand, most spatial-based algorithms output much higher quality denoising image with less artifacts. However, they are usually too computationally demanding. In order to reduce the computational cost, we develop an efficient joint bilateral filter by using the wavelet denoising result rather than directly processing the noisy image in the spatial domain. This filter could suppress the noise while preserve image details with small computational cost. Extension to color image denoising is also presented. We compare our denoising algorithm with other denoising techniques in terms of PSNR and visual quality. The experimental results indicate that our algorithm is competitive with other denoising techniques.     

Spatially adaptive wavelet-based multiscale image restoration

In this paper, we present a new spatially adaptive approach to the restoration of noisy blurred images, which is particularly effective at producing sharp deconvolution while suppressing the noise in the flat regions of an image. This is accomplished through a multiscale Kalman smoothing filter applied to a prefiltered observed image in the discrete, separable, 2-D wavelet domain. The prefiltering step involves constrained least-squares filtering based on optimal choices for the regularization parameter. This leads to a reduction in the support of the required state vectors of the multiscale restoration filter in the wavelet domain and improvement in the computational efficiency of the multiscale filter. The proposed method has the benefit that the majority of the regularization, or noise suppression, of the restoration is accomplished by the efficient multiscale filtering of wavelet detail coefficients ordered on quadtrees. Not only does this lead to potential parallel implementation schemes, but it permits adaptivity to the local edge information in the image. In particular, this method changes filter parameters depending on scale, local signal-to-noise ratio (SNR), and orientation. Because the wavelet detail coefficients are a manifestation of the multiscale edge information in an image, this algorithm may be viewed as an "edge-adaptive" multiscale restoration approach.     

基于自适应稀疏表示的被动毫米波图像恢复

为了克服傅立叶域和小波域正则化方法不能同时保持目标特征和有效滤除噪声的缺点,提出一种被动毫米波图像恢复的新方法。它利用稀疏表示表达信号灵活的特点,对逆滤波后的毫米波图像采用基于奇异值分解的K聚类(K-SVD)算法进行学习,自适应地得到图像恢复需要的基函数。与傅立叶域和小波域正则化方法相比,论文方法采用了自适应的处理方法,因此能够更好地保持目标特征,更有效地抑制噪声,进而更好地恢复图像。将论文方法用于被动毫米波仿真图像的恢复,得到了很好的结果。因此,它是一种有效的被动毫米波成像方法。     

织物图像增强技术的研究

对具有不同特性的织物数字图像利用二维离散傅立叶变换进行图像增强和图像复原等操作,能有效地改善图像的 质量,突出所需要的细节,为织物密度的自动测量提供最佳质量的图像.研究了二维离散快速傅立叶变换算法,以及利用该 算法在频率域中进行图像增强和图像复原的新方法.实验结果分析表明,利用提出的方法可以较好地改善织物图像的质量.     

复小波域HMT模型图像复原

提出了基于二元树复小波变换（DT-CWT）的复小波域隐马尔可夫树（HMT）模型线性图像复原算法,并采用一种简单可行的快速算法来估计HMT模型参数。该方法较好地再现了各种边缘信息,其复原结果较传统的复原方法有不同程度的提高,其运行效率较传统的HMT模型参数估计方法有明显的提高。     

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child-parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.     

一种基于小波-Contourlet变换的图像去噪算法

提出了一种基于小波-Contourlet变换的图像去噪算法.实验证明,该算法相对于小波变换和Contourlet变换能更稀疏的表达图像,并利用此优越性进行图像去噪,可以达到更好的效果和更高的PSNR值.     

An efficient algorithm for MR image reconstruction without low spatial frequencies

It is demonstrated that if the image to be reconstructed is known to have some zero-valued pixels, the dynamic ranges can be better used by disregarding the largest signals and using signal restoration methods. Low-frequency and high-frequency signals are related, using the knowledge that some pixels are zero, by a set of linear equations in which the number of equations is equal to the number of zero pixels, and the number of unknowns is equal to the number of low-frequency signal samples rejected. An improved Fourier transform (FT), magnetic resonance (MR) imaging method based on a least-square-error (LSE) technique, and an efficient algorithm for signal restoration when the low-frequency components are discarded are presented. In this method, the regions of support in both the image domain and the frequency domain can have arbitrary shapes, and all zero pixels in the image domain can be taken into account. The algorithm has been tested on simulated and experimental data with acceptable results     

一种有效抵抗裁剪攻击的小波域盲水印算法

该文提出了一种有效抵抗裁剪攻击的小波域盲水印算法,能从小的图像块上检测出水印。首先将图像进行小波变换,选择两个所需要的子带,利用相邻特征平均值和奇偶判决法在两个子带上各自重复内嵌一半水印,在水印检测过程中不需要原始图像。实验结果表明,该算法具有较好的透明性,对各种攻击有较强的鲁棒性,尤其是明显增强了小波域水印在面临裁剪攻击和联合攻击时的鲁棒性。     

基于多方向小波期望最大融合的图像边缘检测算法

针对传统图像边缘检测算法抗噪能力差,定位准确性不高的缺点.提出了一种基干多方向多尺腰小波变换的图像边缘检测算法.该算法利用小波变换各尺度间边缘梯度信息的关联及备方向上边缘梯度信息的互补,首先从多个方向对图像进行多尺度小波变换.然后将各个方向上小波系数根据期望最大规则进行融合,再通过最大墒阈值处理,形成图像的边缘。宾验结果表明,由于算法省去了求模值过程,使计算更加简单.同时通过多方向小波变换能尽可能地搜索各方向的图像边界,使边缘定位更加准确.     

Hierarchical Bayesian image restoration from partially known blurs

We examine the restoration problem when the point-spread function (PSF) of the degradation system is partially known. For this problem, the PSF is assumed to be the sum of a known deterministic and an unknown random component. This problem has been examined before; however, in most previous works the problem of estimating the parameters that define the restoration filters was not addressed. In this paper, two iterative algorithms that simultaneously restore the image and estimate the parameters of the restoration filter are proposed using evidence analysis (EA) within the hierarchical Bayesian framework. We show that the restoration step of the first of these algorithms is in effect almost identical to the regularized constrained total least-squares (RCTLS) filter, while the restoration step of the second is identical to the linear minimum mean square-error (LMMSE) filter for this problem. Therefore, in this paper we provide a solution to the parameter estimation problem of the RCTLS filter. We further provide an alternative approach to the expectation-maximization (EM) framework to derive a parameter estimation algorithm for the LMMSE filter. These iterative algorithms are derived in the discrete Fourier transform (DFT) domain; therefore, they are computationally efficient even for large images. Numerical experiments are presented that test and compare the proposed algorithms.     

Image Denoising Using Mixtures of Projected Gaussian Scale Mixtures

We propose a new statistical model for image restoration in which neighborhoods of wavelet subbands are modeled by a discrete mixture of linear projected Gaussian Scale Mixtures (MPGSM). In each projection, a lower dimensional approximation of the local neighborhood is obtained, thereby modeling the strongest correlations in that neighborhood. The model is a generalization of the recently developed Mixture of GSM (MGSM) model, that offers a significant improvement both in PSNR and visually compared to the current state-of-the-art wavelet techniques. However, the computation cost is very high which hampers its use for practical purposes. We present a fast EM algorithm that takes advantage of the projection bases to speed up the algorithm. The results show that, when projecting on a fixed data-independent basis, even computational advantages with a limited loss of PSNR can be obtained with respect to the BLS-GSM denoising method, while data-dependent bases of Principle Components offer a higher denoising performance, both visually and in PSNR compared to the current wavelet-based state-of-the-art denoising methods.      

运动模糊图像复原算法的改进及性能研究*

为提高运动模糊图像复原算法的有效性和实时性,分析了常见图像复原算法的优缺点。在此基础上,提出了一种基于小波分解和维纳滤波相结合的图像复原算法。新算法充分利用了小波变换的多分辨率分析特性和维纳滤波复原算法的高效性,既有效抑制了噪声,又减小了图像的灰度失真。仿真结果表明,本文算法不仅提升了图像复原质量,也能满足系统实时性的要求,是一种有效的图像复原算法。     

Accelerated image reconstruction using ordered subsets of projection data

The authors define ordered subset processing for standard algorithms (such as expectation maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass through all the subsets, in each subset using the current estimate to initialize application of EM with that data subset. This approach is similar in concept to block-Kaczmarz methods introduced by Eggermont et al. (1981) for iterative reconstruction. Simultaneous iterative reconstruction (SIRT) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET). In simulation studies in SPECT, the OS-EM algorithm provides an order-of-magnitude acceleration over EM, with restoration quality maintained.     

一维小波变换在时域光学相干层析成像中的应用

时域光学相干层析(OCT)系统通常采用短时傅里叶变换(STFT)完成干涉信号的解调和图像重构。短时傅里叶变换算法简单,但是在干涉信号解调时难以获得好的去噪效果,通常还需在二维(2D)图像域对重构图像进行去噪。该方法数据运算量大,集成度不高。将一维(1D)小波变换(WT)应用于时域光学相干层析成像技术,同时实现干涉信号解调、去噪和图像重构。算法将时域光学相干层析的干涉信号分解到各个不同的频率空间,保留包含调制频率的频率空间的小波系数,对保留的小波系数进行滤波去噪后进行逆变换即可实现对干涉信号的解调和去噪,对解调信号等间距采样实现图像重构。该方法数据运算量小,集成度高,结合先进的小波去噪技术可以大大提高重构图像的分辨率,具有良好的应用前景。     

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.     

Two-dimensional matched filtering for motion estimation

In this work, we describe a frequency domain technique for the estimation of multiple superimposed motions in an image sequence. The least-squares optimum approach involves the computation of the three-dimensional (3-D) Fourier transform of the sequence, followed by the detection of one or more planes in this domain with high energy concentration. We present a more efficient algorithm, based on the properties of the Radon transform and the two-dimensional (2-D) fast Fourier transform, which can sacrifice little performance for significant computational savings. We accomplish the motion detection and estimation by designing appropriate matched filters. The performance is demonstrated on two image sequences.