Optimization of MRI protocols and pulse sequence parameters for eigenimage filtering

The eigenimage filter generates a composite image in which a desired feature is segmented from interfering features. The signal-to-noise ratio (SNR) of the eigenimage equals its contrast-to-noise ratio (CNR) and is directly proportional to the dissimilarity between the desired and interfering features. Since image gray levels are analytical functions of magnetic resonance imaging (MRI) parameters, it is possible to maximize this dissimilarity by optimizing these parameters. For optimization, the authors consider four MRI pulse sequences: multiple spin-echo (MSE); spin-echo (SE); inversion recovery (IR); and gradient-echo (GE). The authors use the mathematical expressions for MRI signals along with intrinsic tissue parameters to express the objective function (normalized SNR of the eigenimage) in terms of MRI parameters. The objective function along with a set of diagnostic or instrumental constraints define a multidimensional nonlinear constrained optimization problem, which the authors solve by the fixed point approach. The optimization technique is demonstrated through its application to phantom and brain images. The authors show that the optimal pulse sequence parameters for a sequence of four MSE and one IR images almost doubles the smallest normalized SNR of the brain eigenimages, as compared to the conventional brain protocol.     

Directional low-pass filtering for improved accuracy and reproducibility of stenosis quantification in coronary arteriograms

Considers the quantification of percent diameter stenosis in digital coronary arteriograms of low spatial resolution. To improve accuracy and reproducibility an edge-preserving smoothing method, called the directional low-pass filter (DLF), was developed to suppress quantum noise by averaging image intensity in a direction parallel to the vessel border. Accuracy of stenosis quantification was assessed by using stenosis phantoms. The standard error of the estimate (SEE) was 0.76 pixel-length (p) without spatial filtering and further reduced to 0.50 p by DLF; the average deviation as a measure of the regularity of border definition was also reduced by DLF from 1.00 to 0.68 p (n=50, P<0.001). It was shown that the DLF outperformed the conventional moving average filter and median filter. Reproducibility in terms of intraframe variability was assessed by using coronary arteriograms obtained from 10 patients. Intraframe variability of the percent stenosis measurements was reduced from 3.5% to 2.9% by DLF (n=10, P<0.005). An analysis of variance showed, however, that the interframe variability cannot be reduced by any of the spatial filters under investigation. The result of this study has provided a guideline for angiographically based quantification of percent stenosis under limited imaging resolution and suggests a new method for improving accuracy and reproducibility by directional low-pass filtering.     

A comparative analysis of several transformations for enhancement and segmentation of magnetic resonance image scene sequences

The performance of the eigenimage filter is compared with those of several other filters as applied to magnetic resonance image (MRI) scene sequences for image enhancement and segmentation. Comparisons are made with principal component analysis, matched, modified-matched, maximum contrast, target point, ratio, log-ratio, and angle image filters. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), segmentation of a desired feature (SDF), and correction for partial volume averaging effects (CPV) are used as performance measures. For comparison, analytical expressions for SNRs and CNRs of filtered images are derived, and CPV by a linear filter is studied. Properties of filters are illustrated through their applications to simulated and acquired MRI sequences of a phantom study and a clinical case; advantages and weaknesses are discussed. The conclusion is that the eigenimage filter is the optimal linear filter that achieves SDF and CPV simultaneously.     

Interframe coding of magnetic resonance images

Presents a new interframe coding method for medical images, in particular magnetic resonance (MR) images. Until now, attempts in using interframe redundancies for coding MR images have been unsuccessful. The authors believe that the main reason for this is twofold: unsuitable interframe estimation models and the thermal noise inherent in magnetic resonance imaging (MRI). The interframe model used here is a continuous affine mapping based on (and optimized by) deforming triangles. The inherent noise of MRI is dealt with by using a median filter within the estimation loop. The residue frames are quantized with a zero-tree wavelet coder, which includes arithmetic entropy coding. This particular method of quantization allows for progressive transmission, which aside from avoiding buffer control problems is very attractive in medical imaging applications.     

Spatial domain filtering for fast modification of the tradeoff between image sharpness and pixel noise in computed tomography

In computed tomography (CT), selection of a convolution kernel determines the tradeoff between image sharpness and pixel noise. For certain clinical applications it is desirable to have two or more sets of images with different settings. So far, this typically requires reconstruction of several sets of images. We present an alternative approach using default reconstruction of sharp images and online filtering in the spatial domain allowing modification of the sharpness-noise tradeoff in real time. A suitable smoothing filter function in the frequency domain is the ratio of smooth and original (sharp) kernel. Efficient implementation can be achieved by a Fourier transform of this ratio to the spatial domain. Separating the two-dimensional spatial filtering into two subsequent one-dimensional filtering stages in the x and y directions using a Gaussian approximation for the convolution kernel further reduces computational complexity. Due to efficient implementation, interactive modification of the filter settings becomes possible, which can completely replace the variety of different reconstruction kernels.     

Adaptive Fuzzy Filtering for Artifact Reduction in Compressed Images and Videos

A fuzzy filter adaptive to both sample's activity and the relative position between samples is proposed to reduce the artifacts in compressed multidimensional signals. For JPEG images, the fuzzy spatial filter is based on the directional characteristics of ringing artifacts along the strong edges. For compressed video sequences, the motion compensated spatiotemporal filter (MCSTF) is applied to intraframe and interframe pixels to deal with both spatial and temporal artifacts. A new metric which considers the tracking characteristic of human eyes is proposed to evaluate the flickering artifacts. Simulations on compressed images and videos show improvement in artifact reduction of the proposed adaptive fuzzy filter over other conventional spatial or temporal filtering approaches.      

基于均值漂移的自适应滤波及其在光谱信号处理中的应用

该文给出了一种基于均值漂移的自适应双边滤波方法,其性能仅取决于空域的核尺度参数,幅度域的核尺度是根据信号的局部特征自适应选取的。该方法能够去除脉冲噪声,能有效抑制非脉冲噪声,并有较强的边缘保护能力。实验和分析表明本文方法的整体性能优于高斯滤波和中值滤波。该文将所提出方法用于天体光谱的去噪,并与均值漂移滤波和小波硬阈值法进行了比较,结果表明:该方法能够有效抑制光谱中天光背景噪声和随机噪声,并能较好地保护谱线信息,更适于天体光谱信号的处理。     

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.     

Error propagation in eigenimage filtering

Mathematical derivation of error (noise) propagation in eigenimage filtering is presented. Based on the mathematical expressions, a method for decreasing the propagated noise given a sequence of images is suggested. The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of the final composite image are compared to the SNRs and CNRs of the images in the sequence. The consistency of the assumptions and accuracy of the mathematical expressions are investigated using sequences of simulated and real magnetic resonance (MR) images of an agarose phantom and a human brain.     

Efficient multiframe Wiener restoration of blurred and noisy imagesequences

Computationally efficient multiframe Wiener filtering algorithms that account for both intraframe (spatial) and interframe (temporal) correlations are proposed for restoring image sequences that are degraded by both blur and noise. One is a general computationally efficient multiframe filter, the cross-correlated multiframe (CCMF) Wiener filter, which directly utilizes the power and cross power spectra of only NxN matrices, where N is the number of frames used in the restoration. In certain special cases the CCMF lends itself to a closed-form solution that does not involve any matrix inversion. A special case is the motion-compensated multiframe (MCMF) filter, where each frame is assumed to be a globally shifted version of the previous frame. In this case, the interframe correlations can be implicitly accounted for using the estimated motion information. Thus the MCMF filter requires neither explicit estimation of cross correlations among the frames nor matrix inversion. Performance and robustness results are given.     

Recursive Temporal Filtering and Frame Rate Reduction for Image Coding

The effect of temporal recursive filtering and frame rate reduction on a sequence of moving images is investigated. Following a well-known first-order Markov model for the temporal domain data, the effect of filtering and frame rate reduction on the values of variance, correlation coefficient, filtering distortion, and interframe prediction error are mathematically derived. The validity of these derivations is verified by the experimental results using a CCITT standard sequence which closely follows the first-order Markov model. The effect of temporal filtering and frame rate reduction to the coding rate is examined by encoding the CCITT standard sequence using a combined interframe and intraframe Scene Adaptive Coding system. At a frame rate of 30 frames per second, a 2:1 reduction in coding rate is obtained with a filtering coefficient of 0.5. At a frame rate of 10 frames per second, an additional reduction factor of nearly 2 is obtained using the same filtering coefficient. Selected images are presented to demonstrate the subjective effect.     

量子彩色图像的频域滤波

为解决量子彩色图像滤波问题,该文提出一种基于量子傅里叶变换的频域滤波方法。首先采用新颖的增强量子描述(NEQR)方案将彩色图像描述为量子图像,然后对该量子图像实施傅里叶变换,采用基于滤波函数定义的量子Oracle将变换后的图像划分为不同频率的图像,最后通过逆量子傅里叶变换将这些不同频率的量子图像变换到空域,通过对空域量子图像实施测量即可得到不同频率的经典滤波图像。文中给出了具体的量子滤波线路,以彩色图像平滑、锐化、周期噪声消除为例,验证了提出方案的正确性。     

Multiexposure image fusion using intensity enhancement and detail extraction

In this study, a multiexposure image fusion approach using intensity enhancement and detail extraction is proposed. The N input low dynamic range (LDR) RGB color images are transformed into HSI color space. Intensity enhancement is achieved by CLAHE and homomorphic filtering. Gamma correction is used to compensate the nonlinear response of display devices, whereas “cross-image” median filtering is used to generate the reference intensity image. L₀ smoothing filter and weighted least squares (WLS) optimization are used to perform local and global detail extractions on the N processed LDR images, respectively. The N weighting maps of the N processed LDR images are estimated by spatial and cross-image consistencies and then refined by cross bilateral filtering. Finally, the multiresolution spline based scheme is used to perform multiexposure image fusion. Based on the experimental results obtained in this study, the performance of the proposed approach is better than those of four comparison approaches.     

Nonlinear scale-space filtering and multiresolution system

We derive and demonstrate a nonlinear scale-space filter and its application in generating a nonlinear multiresolution system. For each datum in a signal, a neighborhood of weighted data is used for clustering. The cluster center becomes the filter output. The filter is governed by a single scale parameter that dictates the spatial extent of nearby data used for clustering. This, together with the local characteristic of the signal, determines the scale parameter in the output space, which dictates the influences of these data on the output. This filter is thus adaptive and data driven. It provides a mechanism for (a) removing impulsive noise, (b) improved smoothing of nonimpulsive noise, and (c) preserving edges. Comparisons with Gaussian scale-space filtering and median filters are made using real images. Using the architecture of the Laplacian pyramid and this nonlinear filter for interpolation, we construct a nonlinear multiresolution system that has two features: (1) edges are well preserved at low resolutions, and (2) difference signals are small and spatially localized. This filter implicitly presents a new mechanism for detecting discontinuities differing from techniques based on local gradients and line processes. This work shows that scale-space filtering, nonlinear filtering, and scale-space clustering are closely related and provides a framework within which further image processing, image coding, and computer vision problems can be investigated.     

基于高斯混合概率假设密度的运动参数估计组合平滑滤波算法

针对高斯混合概率假设密度(GM-PHD)滤波器在目标速度未知或不准确时,目标状态估计性能较差,该文提出一种基于GM-PHD的运动参数估计组合平滑滤波算法。该算法通过目标状态提取速度信息,经过中值平滑和线性平滑组合处理提升速度估计准确性,然后将速度反馈给GM-PHD滤波器的状态转移方程,提高状态预测精度。仿真结果表明,目标速度未知或不准确时,所提算法能够明显改善GM-PHD滤波器状态估计性能。     

An improved median filter

A modified median filtering technique offering improved smoothing performance while maintaining the edge-preserving ability of the conventional median filter is presented. It is shown how a mean filter outperforms a median filter in noise reduction except on or near the image boundaries. Along with the edge-preserving ability of the median filter, this observation forms the basis of the three-stage filtering algorithm which is described.     

Prescanned minmax centre-weighted filters for image restoration

The prescanned minmax centre-weighted (PMCW) filter, which is capable of restoring images severely corrupted by impulsive noise, is presented. Before filtering, the input image is scanned by a running window; the maximum and minimum of each ranked set in the running window are grouped as the first subset, and the rest as the second subset. Then, the two subsets are filtered in sequence by a centered weight filter. It is shown that filtering results in the first subset provide the extension property by which the effective smoothing region for the subsequent filtering in the second subset is extended. The detail-control property of the PMCW is characterised and some relationships between PMCW and ranked-order based filters are derived. Quantitative comparisons demonstrate that the PMCW filter offers a more desirable combination of noise suppression and detail preservation properties than can other median-type filters     

一种改进型图像降噪方法

针对图像获取中易受到噪声干扰的问题,介绍了图像去噪处理的几种常用算法（邻域平均法、中值滤波法、图像间的平均滤波）,对比阐述了各自的优缺点及适用范围。提出了一种基于平滑滤波的小波阈值图像去噪算法,该算法采用中值滤波和小波阈值相结合的方式对图像进行平滑处理。实验结果表明,该方法不仅有利于图像噪声的去除,而且边缘信息也得到了较好的保留,使图像具有更好的视觉效果,还原出图像的本来面目。     

A blind particle filtering detector of signals transmitted over flat fading channels

A new particle filtering detector (PFD) is proposed for blind signal detection over flat Rayleigh fading channels whose model coefficients are unknown. The detector employs a hybrid importance function and a mixture Kalman filter. It also incorporates an auxiliary particle filtering strategy with a smoothing kernel in the resampling step. Further, by considering practical information of communication systems and the physical interpretation of the adopted second-order autoregressive (AR) channel model, a fully blind particle filtering implementation is developed. The structure of the proposed PFD can be easily adapted to other system requirements. Simulations are provided that demonstrate the performance of the new PFD.     

Fast impulsive noise removal

A generic n-dimensional filter with the primary purpose of eliminating impulsive-like noise is presented. This recursive nonlinear filter is composed of two conditional rules, which are applied independently, in any order, one after the other. It identifies noisy items by inspection of their surrounding neighborhood, and afterwards it replaces their values with the most "conservative" ones out of their neighbors' values. In this way, no new values are introduced and the histogram distribution range is conserved. This n-dimensional filter can be decomposed recursively to a lower dimensional space, each time generating two sets of n(n-1)-dimensional filters. This study, which focuses on the case of two-dimensional signals (gray scale images), explores one possible implementation of this new filter and orients the evaluation of its performance toward the median filter, as this filter is the basis of many more sophisticated filters for impulsive noise reduction. Tests were carried out using both real and artificial images. We found this new filter to be much faster than the median filter while performing comparably in terms of both image information conservation and noise reduction, which suggests that it could replace the median filter for the preliminary processing included in state-of-the-art noise removal filters. This new filter should either eliminate or attenuate most noisy pixels in synthetic and natural images not excessively contaminated. It has a slight smoothing effect on nonnoisy image regions. In addition, it is scalable, easily implemented, and adaptable to specific applications.