Iterative Wiener filters for image restoration

The iterative Wiener filter, which successively uses the Wiener-filtered signal as an improved prototype to update the covariance estimates, is investigated. The convergence properties of this iterative filter are analyzed. It has been shown that this iterative process converges to a signal which does not correspond to the minimum mean-squared-error solution. Based on the analysis, an alternate iterative filter is proposed to correct for the convergence error. The theoretical performance of the filter has been shown to give minimum mean-squared error. In practical implementation when there is unavoidable error in the covariance computation, the filter may still result in undesirable restoration. Its performance has been investigated and a number of experiments in a practical setting were conducted to demonstrate its effectiveness     

On the robustness of the class of stack filters

A widely held view in the nonlinear signal processing community is that the class of stack filters is robust. Although this is supported by extensive experimental evidence, no systematic theoretical justification exists, despite the availability of analytical tools for studying robustness of individual stack filters. We focus on rank selection probabilities (RSPs) as measures of robustness as it is well known that other statistical characterizations of stack filters, such as output distributions, breakdown probabilities and output distributional influence functions can be represented in terms of RSPs. We show, in a very general sense, that the class of stack filters is highly robust. It is also shown that almost all stack filters have very similar output distributions for independent and identically distributed (i.i.d.) input signals and, thus, very similar statistical behavior     

Partition-based weighted sum filters for image restoration

We develop the concept of partitioning the observation space to build a general class of filters referred to as partition-based weighted sum (PWS) filters. In the general framework, each observation vector is mapped to one of M partitions comprising the observation space, and each partition has an associated filtering function. We focus on partitioning the observation space utilizing vector quantization and restrict the filtering function within each partition to be linear. In this formulation, a weighted sum of the observation samples forms the estimate, where the weights are allowed to be unique within each partition. The partitions are selected and weights tuned by training on a representative set of data. It is shown that the proposed data adaptive processing allows for greater detail preservation when encountering nonstationarities in the data and yields superior results compared to several previously defined filters. Optimization of the PWS filters is addressed and experimental results are provided illustrating the performance of PWS filters in the restoration of images corrupted by Gaussian noise.     

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     

基于层叠滤波的快速图像恢复算法

在层叠滤波理论基础上,根据层叠滤波器的阈值分解和层叠性,提出了一种快速图像恢复算法。此算法在对层叠滤波进行计算机仿真实验时,能有效地提高图像恢复的效率,大大缩短图像恢复时间。     

A vector quantizer for image restoration

This paper presents a novel technique for image restoration based on nonlinear interpolative vector quantization (NLIVQ). The algorithm performs nonlinear restoration of diffraction-limited images concurrently with quantization. It is trained on image pairs consisting of an original image and its diffraction-limited counterpart. The discrete cosine transform is used in the codebook design process to control complexity. Simulation results are presented that demonstrate improvements in visual quality and peak signal-to-noise ratio of the restored images.     

Dual stack filters and the modified difference of estimatesapproach to edge detection

The theory of optimal stack filtering has been used in the difference of estimates (DoE) approach to the detection of intensity edges in noisy images. The DoE approach is modified by imposing a symmetry condition on the data used to train the two stack filters. Under this condition, the stack filters obtained are duals of each other. Only one filter must therefore be trained; the other is simply its dual. This new technique is called the symmetric difference of estimates (SDoE) approach. The dual stack filters obtained under the SDoE approach are shown to be comparable. This allows the difference of these two filters to be represented by a single equivalent edge operator. This latter result suggests that an edge operator can be found by directly training a (possibly nonpositive) Boolean function to be used on each level of the threshold decomposition architecture. This approach, which is called the threshold Boolean filter (TBF) approach, requires less training time but produces operators that are less robust than those produced by the SDoE approach. This is demonstrated and interpreted via comparisons of results for natural images.     

ℒ-M-S filters for image restoration applications

A new filtering architecture is proposed, generalizing some previously introduced multilevel median filters. An efficient design procedure for the new filtering architecture is demonstrated for image restoration application. Simulation results show a good noise rejection performance, combined with a fine detail preservation capability.     

Synthesis of neural pulse interference filters for image restoration

The synthesis of nonlinear pulse interference filters in the form of three-layer and polynomial perceptrons has been considered in this study. Neural filters were used for removing the “salt and pepper“-type pulse interference from half-tone images. It was shown that a three-layer perceptron filter in terms of the filtration accuracy is not inferior to its polynomial analogues and its mathematical model is mush simpler than the Volterra model. Neural and polynomial filters ensure a higher level of pulse interference suppression as compared with median filters.     

Multiple template detection using impulse restoration and discriminative filters

Recently, Ben-Arie and Rao (1993) have proposed a linear filter that, given a template, maximises the energy concentration in a single sample of its output. A two-dimensional generalisation of this method has also been proposed, formulating template matching as a multivariable optimisation problem. In other work, template detection has been looked at as an impulse restoration problem, and closed-form solutions for it have been proposed. An extension that allows multiple template discrimination is proposed. Simulation results suggest that the proposed method is an effective tool for decision problems and can achieve performances only attainable with sophisticated nonlinear methods.     

Order statistic-neural network hybrid filters for gamma camera-bremsstrahlung image restoration

An order statistic and neural network hybrid filter (OSNNH) is proposed for the restoration of gamma camera images using the measured modulation transfer function. Planar images of beta-emitting radionuclides are used to evaluate the filter because they exhibit higher degradation than images of single photon emitters due to increased photon scattering and collimator septal penetration. The filter performance is quantitatively evaluated and compared to that of the Wiener filter by investigating the relationship between the externally measured counts from sources of phosphorous-32 ((32)P) at various depths in water. An effective linear attenuation coefficient for (32)P is determined to be equal to 0.13 cm(-1) and 0.14 cm(-1) for the OSNNH and the Wiener filters, respectively. Evaluation of phantom and patient filtered images demonstrates that the OSNNH filter avoids ring effects caused by the ill-conditioned blur matrix and noise overriding caused by matrix inversion, typical of other restoration filters such as the Wiener.     

Implementation of cascaded and recursive stack filters

Systematic methods are developed for simplified implementations of cascaded stack and WOS filters. For recursive stack and WOS filters, corresponding nonrecursive implementations are given, with linear complexity with respect to the number of iterations. Dynamic domino logic is proposed for VLSI hardware implementation of positive Boolean functions, and a pipelined stack filter architecture is described.     

Some representation properties of stack filters

Stack filters, a class of nonlinear filters which are based on positive Boolean functions as the window operators, are considered. The representations of these window operations are presented via the structures of on-set and off-set of the positive Boolean functions, which can be expressed as a Boolean expression containing no complements of the input variables. A fast algorithm for finding the representation of stack filters is designed. This algorithm can be easily extended to find the representation of morphological filters mentioned by P. Maragos (1989)     

On the accuracy of PSF representation in image restoration

Point spread function (PSF) models derived from physical optics provide a more accurate representation of real blurs than simpler models based on geometrical optics. However, the physical PSF models do not always result in a significantly better restoration, due to the coarse sampling of the recording device and insufficiently high signal-to-noise ratio (SNR) levels. Low recording resolutions result in aliasing errors in the PSF and suboptimal restorations. A high-resolution representation of the PSF where aliasing errors are minimized is used to obtain improved restorations. The SNR is the parameter which ultimately limits the restoration quality and determines the need for an accurate PSF model. As a rule of thumb, the geometrical PSF can be used in place of the physical PSF without significant loss in restoration quality when the SNR is less than 30 dB.     

On the numerical feasibility of digital image restoration

Computational aspects of the image restoration schemes described by Sondhi are discussed. It is shown that severe numerical difficulties limit their direct use in practical applications.     

Nonlinear order statistic filters for image filtering and edge detection

A novel class of nonlinear filters for image processing is proposed. This class is a combination of nonlinear mean and order statistic filters. Median, homomorphic, α-trimmed mean, nonlinear mean, order statistic, and linear filters can be considered as special cases of this class. The properties of these filters in the presence of different kinds of noise are investigated. It is shown that these filters can be used for the reduction of additive white noise, signal-dependent noise, and impulse noise. It is also shown that they preserve edges better than linear filters. Such filters can successfully be used as edge detectors, by appropriate adjustment of some of their parameters. Edge information can be used as an input to these filters to perform in an adaptive manner, changing their behaviour near the edges of an image. It is finally shown that many of the filters proposed have a reasonable (and in certain cases small) computational complexity.     

Generalized matched filters and univariate Neyman-Pearson detectorsfor image target detection

I derive two-stage, statistically suboptimal target detectors for images. The first, or transformation, stage is a “generalized matched filter” (GMF) that linearly transforms the input image. I propose three rational signal-to-noise-ratio criteria whose maximization yields the three GMFs. The second, or detection, stage is a univariate “Neyman-Pearson detector” (NPD), which executes a pointwise likelihood ratio test on the GMF transformed images. Experiments on infrared and synthetic-aperture radar imagery compare GMF/NPDs with several established detectors     

Design of optimal stack filters under the MAE criterion

The design of optimal stack filters under the MAE criterion is addressed in this paper. In our work, the Hasse diagram is adopted to represent the positive Boolean functions to solve the optimization problem. After problem transformation, the finding of the optimal stack filter is equivalent to the finding of the optimal on-set such that the total cost of the on-set is minimal. An efficient algorithm is developed that makes use of an important property of the optimal on-set to avoid fruitless search. It thereby greatly reduces the complexity in finding the corresponding optimal stack filter. A design example is illustrated in detail to demonstrate the optimization procedures. The proposed algorithm can generate the optimal stack filter in 1 s for the window size of 14 pixels. It can still generate the optimal stack filter for the window size of 21, although it takes about 4 h. Experimental results for real images reveal that the proposed algorithm essentially extends the maximum filter window size to make the stack filter optimization problem computationally tractable     

On the detection of edges in vector images

A novel method for edge detection in vector images is proposed that does not require any prior knowledge of the imaged scenes. In the derivation, it is assumed that the observed vector images are realizations of spatially quasistationary processes, and that the vector observations are generated by parametric probability distribution functions of known form whose parameters are in general unknown. The method detects and estimates the edge locations using a criterion derived by Bayesian theory. It chooses the number of edges and their locations according to the maximum a posteriori probability (MAP) principle. We provide results that demonstrate its performance on synthesized and real images.     

A robust structure-adaptive hybrid vector filter for color image restoration.

A robust structure-adaptive hybrid vector filter is proposed for digital color image restoration in this paper. At each pixel location, the image vector (i.e., pixel) is first classified into several different signal activity categories by applying a modified quadtree decomposition to luminance component (image) of the input color image. A weight-adaptive vector filtering operation with an optimal window is then activated to achieve the best tradeoff between noise suppression and detail preservation. Through extensive simulation experiments conducted using a wide range of test color images, the filter has demonstrated superior performance to that of a number of well known benchmark techniques, in terms of both standard objective measurements and perceived image quality, in suppressing several distinct types of noise commonly considered in color image restoration, including Gaussian noise, impulse noise, and mixed noise.