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.     

A multidimensional nonlinear edge-preserving filter for magneticresonance image restoration

The paper presents a multidimensional nonlinear edge-preserving filter for restoration and enhancement of magnetic resonance images (MRI). The filter uses both interframe (parametric or temporal) and intraframe (spatial) information to filter the additive noise from an MRI scene sequence. It combines the approximate maximum likelihood (equivalently, least squares) estimate of the interframe pixels, using MRI signal models, with a trimmed spatial smoothing algorithm, using a Euclidean distance discriminator to preserve partial volume and edge information. (Partial volume information is generated from voxels containing a mixture of different tissues.) Since the filter's structure is parallel, its implementation on a parallel processing computer is straightforward. Details of the filter implementation for a sequence of four multiple spin-echo images is explained, and the effects of filter parameters (neighborhood size and threshold value) on the computation time and performance of the filter is discussed. The filter is applied to MRI simulation and brain studies, serving as a preprocessing procedure for the eigenimage filter. (The eigenimage filter generates a composite image in which a feature of interest is segmented from the surrounding interfering features.) It outperforms conventional pre and post-processing filters, including spatial smoothing, low-pass filtering with a Gaussian kernel, median filtering, and combined vector median with average filtering.     

Adding explicit content classification to nonlinear filters

Nonlinear filters are known for better edge-preserving performance in image processing applications as they can adapt to some local image content. Instead of trying to find a single optimal filter that can adapt to all the image content, some classification-based approaches first apply a pre-classification on the image content and then employ an optimal linear filter for each content class. It is interesting to extend the linear filter in such approaches to a nonlinear filter and see if the explicit content classification, can still add to such inherently adapting nonlinear filters. In this paper, we investigate several categories of nonlinear filters: order statistics filters, hybrid filters, neural filters, and bilateral filters with different forms of content classification in various image processing applications, including image de-blocking, noise reduction, and image interpolation.     

Inclusion filters: a class of self-dual connected operators.

In this paper, we define a connected operator that either fills or retains the holes of the connected sets depending on application-specific criteria that are increasing in the set theoretic sense. We refer to this class of connected operators as inclusion filters, which are shown to be increasing, idempotent, and self dual (gray-level inversion invariance). We demonstrate self duality for 8-adjacency on a discrete Cartesian grid. Inclusion filters are defined first for binary-valued images, and then the definition is extended to grayscale imagery. It is also shown that inclusion filters are levelings, a larger class of connected operators. Several important applications of inclusion filters are demonstrated-automatic segmentation of the lung cavities from magnetic resonance imagery, user interactive shape delineation in content-based image retrieval, registration of intravital microscopic video sequences, and detection and tracking of cells from these sequences. The numerical performance measures on 100-cell tracking experiments show that the use of inclusion filter improves the total number of frames successfully tracked by five times and provides a threefold reduction in the overall position error.     

Optimal Gabor filters for texture segmentation

Texture segmentation involves subdividing an image into differently textured regions. Many texture segmentation schemes are based on a filter-bank model, where the filters, called Gabor filters, are derived from Gabor elementary functions. The goal is to transform texture differences into detectable filter-output discontinuities at texture boundaries. By locating these discontinuities, one can segment the image into differently textured regions. Distinct discontinuities occur, however, only if the Gabor filter parameters are suitably chosen. Some previous analysis has shown how to design filters for discriminating simple textures. Designing filters for more general natural textures, though, has largely been done ad hoc. We have devised a more rigorously based method for designing Gabor filters. It assumes that an image contains two different textures and that prototype samples of the textures are given a priori. We argue that Gabor filter outputs can be modeled as Rician random variables (often approximated well as Gaussian rv's) and develop a decision-theoretic algorithm for selecting optimal filter parameters. To improve segmentations for difficult texture pairs, we also propose a multiple-filter segmentation scheme, motivated by the Rician model. Experimental results indicate that our method is superior to previous methods in providing useful Gabor filters for a wide range of texture pairs.     

Wavelet filter evaluation for image compression

Choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design. Although regularity is sometimes used in filter evaluation, its success at predicting compression performance is only partial. A more reliable evaluation can be obtained by considering an L-level synthesis/analysis system as a single-input, single-output, linear shift-variant system with a response that varies according to the input location module (2(L),2(L)). By characterizing a filter bank according to its impulse response and step response in addition to regularity, we obtain reliable and relevant (for image coding) filter evaluation metrics. Using this approach, we have evaluated all possible reasonably short (less than 36 taps in the synthesis/analysis pair) minimum-order biorthogonal wavelet filter banks. Of this group of over 4300 candidate filter banks, we have selected and present here the filters best suited to image compression. While some of these filters have been published previously, others are new and have properties that make them attractive in system design.     

A study of the generalized morphological filter

A new class of morphological filters is proposed for image enhancement. The filter, known as the generalized morphological filter (GMF), uses multiple structuring elements and combines linear and morphological operations. The GMF can be designed to suppress various types of noise yet preserve geometrical structure in an image. A study of several aspects of the performance of the filter is presented. The study includes geometrical feature preservation, noise suppression, structuring element selection, and the root signal structure. For the sake of comparison, averaging and median filters are also used in the experiments and corresponding figures of merit of the performance of the filter. The empirical study shows that the generalized morphological filter possesses effective noise suppression with reduced geometrical feature blurring.This work was supported by the National Science Foundation, under Grant No. CDR-8803017 to the Engineering Research Center for Intelligent Manufacturing Systems.     

Segmentation of Gabor-filtered textures using deterministicrelaxation

A supervised texture segmentation scheme is proposed in this article. The texture features are extracted by filtering the given image using a filter bank consisting of a number of Gabor filters with different frequencies, resolutions, and orientations. The segmentation model consists of feature formation, partition, and competition processes. In the feature formation process, the texture features from the Gabor filter bank are modeled as a Gaussian distribution. The image partition is represented as a noncausal Markov random field (MRF) by means of the partition process. The competition process constrains the overall system to have a single label for each pixel. Using these three random processes, the a posteriori probability of each pixel label is expressed as a Gibbs distribution. The corresponding Gibbs energy function is implemented as a set of constraints on each pixel by using a neural network model based on Hopfield network. A deterministic relaxation strategy is used to evolve the minimum energy state of the network, corresponding to a maximum a posteriori (MAP) probability. This results in an optimal segmentation of the textured image. The performance of the scheme is demonstrated on a variety of images including images from remote sensing.     

A STATISTICAL NOISE MODEL AND MATHEMATICAL MODEL OF SPECKLE PATTERN AND ADAPTIVE FILTERING APPROACH

A statistical noise model and a mathematical model for real speckle pattern are presented in this paper, and then, in view of the models, a new adaptive suboptimal image filtering approach is proposed. The proposed approach, with the local direction features of speckle pattern, combines the characteristics of optimal linear filter with non-linear filter and is an adaptive approximation to linear minimum mean square error filter. Experimental results show that the proposed approach has fairly good edge-preserved performance, compared with other present image filters, as well as much better filtering performance and robustness for speckle pattern.     

Quadratic-linear filters for signal detection

The second-order Volterra series (quadratic-linear) filter was synthesized under three different optimization criteria for signal detection. The performance of the filters is shown to exceed that of quadratic-only or linear-only filters when the noise process is characterized by both separation in the mean and separation in variance. The applications are in object detection and image segmentation, especially in model-drive approaches to these problems. For 2-D applications, the mapping order of pixels into the signal vector is shown to have no effect on the optimality of the filters, regardless of nonlinearity     

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.     

Multi-focus image fusion with joint guided image filtering

Multi-focus image fusion is the activity of synthesizing multiple images of different focusing settings to construct a fully focused image. Many of the latest methods for image fusion rarely consider the structural differences between the guidance image and the input image, and do not retain well the important source image features while producing a fully focused image. To address this issue, a method exploiting a combination of static and dynamic filters (SDF) is proposed herein. This combination has good edge smoothing characteristics and strong robustness against artifacts such as gradient inversion and global strength migration. First, SDF is utilized in order to decompose the source image into structure and texture layers. Secondly, a morphological gradient operator filter is used to calculate the significance map of different levels of the source. Thirdly, the maximum pixel value of the significance map is used to construct the binary decision graph of the two source images. Then, the structure and texture layers are fused with the aid of the binary decision graph, and subsequently the final fusion image is created by combining the fused structure layer and texture layer. This process ensures that spatial consistency is preserved. Tests on grayscale and color multi-focus image sets show that the proposed method has better performance than that of any of the existing methods according to both objective and subjective evaluation.     

Order statistic filter banks

Filter banks play a major role in multirate signal processing where these have been successfully used in a variety of applications. In the past, filter banks have been developed within the framework of linear filters. It is well known, however, that linear filters may have less than satisfactory performance whenever the underlying processes are non-Gaussian. We introduce the nonlinear class of order statistic (OS) filter banks that exploit the spectral characteristics of the input signal as well as its rank-ordering structure. The attained subband signals provide frequency and rank information in a localized time interval. OS filter banks can lead to significant gains over linear filter banks, particularly when the input signals contain abrupt changes and details, as is common with image and video signals. OS filter banks are formed using traditional linear filter banks as fundamental building blocks. It is shown that OS filter banks subsume linear filter banks and that the latter are obtained by simple linear transformations of the former. To illustrate the properties of OS filter banks, we develop simulations showing that the learning characteristics of the LMS algorithm, which are used to optimize the weight taps of OS filters, can be significantly improved by performing the adaptation in the OS subband domain.     

Noise-Driven Anisotropic Diffusion Filtering of MRI

A new filtering method to remove Rician noise from magnetic resonance images is presented. This filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for MRI, as the speckle reducing anisotropic diffusion did for ultrasound images. The parameters of the filter are automatically chosen from the estimated noise. This property improves the convergence rate of the diffusion while preserving contours, leading to more robust and intuitive filtering. The partial derivative equation of the filter is extended to a new matrix diffusion filter which allows a coherent diffusion based on the local structure of the image and on the corresponding oriented local standard deviations. This new filter combines volumetric, planar, and linear components of the local image structure. The numerical scheme is explained and visual and quantitative results on simulated and real data sets are presented. In the experiments, the new filter leads to the best results.     

静止图像的一种混合滤波及其改进算法

本文结合线性滤波器和非线性滤波器的优点，提出了一种基于线性、非线性的混合滤波算法。该算法比均值滤波器和中值滤波器具有更好的抑制噪声的，能较好地保持图像的边缘，反映图像的几何结构和细节特性。在此基础上又提出了改进算法及其快速实现，进一步改善了滤波性能。该滤波器计算量适中，具有较好的实时性。     

一种散斑模式的噪声统计模型与自适应滤波方法

本文介绍了一种实际散斑模式的数学模型和噪声统计模型,并提出了一种针对这种模型的自适应次优滤波方法。文中在分析了散斑模式及其噪声性质的基础上,利用其局部方向性特征,结合最优线性滤波器和非线性滤波器的特点,对线性最小均方误差滤波器进行了自适应逼近。实验结果表明,对散斑模式而言,本文的滤波方法与其它常用的图象滤波方法相比,具有更好的去噪和边缘保护性能,并且具有较好的滤波韧性。     

Interactive image segmentation via adaptive weighted distances.

An interactive algorithm for soft segmentation of natural images is presented in this paper. The user first roughly scribbles different regions of interest, and from them, the whole image is automatically segmented. This soft segmentation is obtained via fast, linear complexity computation of weighted distances to the user-provided scribbles. The adaptive weights are obtained from a series of Gabor filters, and are automatically computed according to the ability of each single filter to discriminate between the selected regions of interest. We present the underlying framework and examples showing the capability of the algorithm to segment diverse images.     

Automated object detection with a correlation filter designed from a noisy image

Correlation filters used for object detection are commonly designed using explicit knowledge of the target appearance and the target shape. This assumption requires that the image of a target used for the filter design be manually processed. In this paper, we suppose that the target is given at unknown coordinates in a reference image corrupted by additive noise. Optimum correlation filter with respect to the peak-to-output energy ratio for object detection is derived. Computer simulation results are presented comparing the performance of the proposed filter with that of common correlation filters.     

A Hybrid Geometric–Statistical Deformable Model for Automated 3-D Segmentation in Brain MRI

We present a novel 3-D deformable model-based approach for accurate, robust, and automated tissue segmentation of brain MRI data of single as well as multiple magnetic resonance sequences. The main contribution of this study is that we employ an edge-based geodesic active contour for the segmentation task by integrating both image edge geometry and voxel statistical homogeneity into a novel hybrid geometric-statistical feature to regularize contour convergence and extract complex anatomical structures. We validate the accuracy of the segmentation results on simulated brain MRI scans of both single T1-weighted and multiple T1/T2/PD-weighted sequences. We also demonstrate the robustness of the proposed method when applied to clinical brain MRI scans. When compared to a current state-of-the-art region-based level-set segmentation formulation, our white matter and gray matter segmentation resulted in significantly higher accuracy levels with a mean improvement in Dice similarity indexes of 8.55% (p<0.0001) and 10.18% (p<0.0001), respectively.     

直方图加权均值滤波器

本文提出了一种适合于消除图像盐椒噪声的滤波器——直方图加权均值(HWM)滤波器.该算法以加权均值滤波器为基础,利用被污染图像的直方图函数作为权值进行加权运算.实验表明,对于噪声率在5％到90％的的噪声图像,HWM滤波器具有良好而稳健的去噪效果,当噪声率超过70％时,其优越性更加突出.