Restoration Filter Research Articles

Subspace partition weighted sum filters for image restoration

The previously proposed partition-based weighted sum (PWS) filters combine vector quantization (VQ) and linear finite impulse response (FIR) Wiener filtering concepts. By partitioning the observation space and applying a tuned Wiener filter to each partition, the PWS is spatially adaptive and has been shown to perform well in noise reduction applications. In this letter, we propose the subspace PWS (SPWS) filter and evaluate the efficacy of the SPWS filter in image deconvolution and noise reduction applications. In the SPWS filter, we project the observation vectors into a subspace using principal component analysis (PCA), or other methods, prior to partitioning. This subspace projection can dramatically reduce the computational burden associated with partitioning, especially for large window sizes. In some cases, performance is also enhanced due to improved partitioning.

Defining paramaters for an adaptative 3D Wiener filter in image restoration of SPECT cerebral blood flow studies: A novel approach

Multiple factors (attenuation, scattering, scanner response, etc) significantly degrade SPECT images. and multiple techniques have been proposed to correct for those and therefore yield more quantitatively exact SPECT studies, with the aim of improving clinical classification of patients as well as results from research using this technique. Application of a Wiener filter during reconstruction, which minimizes the mean square error between the original object and its estimate (the image), is a well-validated and relatively simple approach to this problem. Optimal use of this technique requires a priori information such as the point spread function (PSF) of the imaging system and the power spectrum ratio of the original object to image noise, but this information is not generally available. We have applied a new adaptation of this approach to cerebral blood flow studies obtained in SPECT with 99mTc labeled agents. Here, we start with a Gaussian function to model the PSF of the SPECT system, and a constant to replace the noise-to-signal power spectrum ratio 1. The PSF width and power-spectrum ratio are then iteratively optimized to improve image contrast between white and gray matter while keeping image mottle (or variance) within each region at a tolerable level (as defined in 2, 3). To track precisely the contrast and mottle, the white and gray matter regions are identified from an anatomical MRI of the same patient previously co-registered to the SPECT study 4. Simulation results with a realistic brain model (digital Hoffman phantom 5, with 3D Gaussian noise (at such count levels, Poisson noise would yield comparable results) and then blurred with a 3D Gaussian function to simulate an actual SPECT study) show marked contrast improvement while maintaining the mottle at an acceptable level: with object contrast between white and gray matter (as defined in 2) set at 0.427 and degraded to 0.074 post blurring, filtering increased contrast to 0.378, with the mottle (proportionally averaged for gray and white matter) actually decreasing (0.224 to 0.182). Tests conducted with actual clinical SPECT cases exhibit similar contrast improvement (0.045 to 0.104) with a limited (and still acceptable 2) mottle increase (0.198 to 0.276). We believe that this technique for defining the parameters of a 3D adaptive Wiener filter will be useful in clinical practice, where significant data degradation limits detection of anomalies with SPECT, because it automatically generates the best combination of those parameters, leading to significantly improved contrast quantification with little noise amplification.

A MODIFIED WIENER FILTER FOR MULTI-FRAME RESTORATION OF BLURRED AND NOISY IMAGES

This paper proposes the use of a modified Wiener digital restoration technique for multi-frame image sequences that are degraded by both blur and noise. The proposed multi-channel Wiener restoration filter accounts for both intra-frame (spatial) and inter-frame (temporal) correlation. A modified cross-correlation formula between consecutive frames, which directly utilizes the motion vectors in the calculation of correlation among frames is derived and implemented in a multi-frame Wiener filter. Our modification estimates the motion vectors (horizontal and vertical) between consecutive frames using the three-step method, and then uses the estimated motion vectors to modify the cross-correlation terms in the formula for restoration. The performed simulations verified that the multi-frame restoration algorithm, that uses the motion information among different frames in restoration, gives improved results than both of the single frame independent restoration and the multi-channel restoration without considering the motion vectors.

Improving 3D PET imaging by restoration: a phantom study

The main objective of our work is to improve 3D PET imaging. Compared with 2D PET, 3D PET imaging has slightly worse axial resolution and a significantly higher contribution of scatter and randoms, but 3D PET has much better sensitivity than 2D PET imaging. A Jaszczak deluxe phantom was acquired in 3D mode on our GE Advance PET system. Activity of 333 MBq of 18F was uniformly distributed. Prior to the emission scan, blank and transmission scans had been acquired. They were used for attenuation correction. The duration of the emission scan was 20 min, transmission 10 min, and blank 20 min. Standard FBP reconstruction software provided by the vendor was used to obtain slice images. Point spread function was also acquired in a 21 cm diameter cylinder phantom filled with water 6.0 cm from the center and used to create restoration filters. Two restoration filters were applied, medium and sharp. Results showed significant improvement in resolution, contrast and detectability of the cold rods. The artifacts outside the phantom were also significantly reduced. For 11.1 mm rods, average contrast was 0.49±0.02 in the original image, 0.52±0.04 in the medium restored image, and in the sharply restored image 0.75±0.05. For 7.9 mm rods, average contrast was 0.07±0.01 in the original image, 0.21±0.03 in the medium restored image, and 0.50±0.04 in the sharply restored image. The amount of noise in the uniform slices, measured as the coefficient of variation (COV), was 5.5, 7.1 and 10.8% in the original image and in the images restored with medium and sharp filters, respectively. In conclusion, restoration can significantly improve the resolution and contrast of 3D PET imaging.

Adaptive filter design for image deblurring by using multi-criteria blurred image information

This paper introduces a novel method to enhance the quality of blurred images. The proposed method is based on the estimation of the multi-criteria information of the degraded images. The multi-criteria information is extracted from the distribution model and the boundaries of the input image. The actual image blurred by an unknown distribution is correlated with predetermined reference models in order to choose the restoration filter model. The filter coefficient is then estimated using the edge information of the degraded image. Experiments have been conducted using simulated and real world images to evaluate the performance of the proposed method and the results are presented.

Adaptive histogram-based filter for image restoration

A novel filter for image restoration is proposed in this paper. The filter estimates histogram of original image via input image. It gets a membership function through the histogram, and the membership function contains a lot of information of original image. Then a weighted fuzzy mean filter is established based on this membership function; meanwhile, the filter adaptively adopts different filter scale according to the character divergence of image region and intensity of impulsive noise. Experimental result shows that new filter gives superior performance to conventional filters and currently used fuzzy filter.

Temporal filtering for restoration of wavelet-compressed motion imagery

Temporal filtering of motion imagery can alleviate the effects of noise and artifacts in the data by incorporating observations of the imagery data from several distinct frames. If the noise that is expected to occur in the data is well-modeled by independent and identically distributed (IID) Gaussian noise, then straightforward algorithms can be designed that filter along motion trajectories in an optimal fashion. This paper addresses the restoration of motion imagery that have been compressed by scalar quantization of the data's discrete wavelet transform coefficients. Noise due to compression in such situations is neither independent nor identically distributed, and thus straightforward filters designed for the IID case are suboptimal. This paper provides a statistical characterization of the quantization error and shows how the improved noise modeling can be used in temporal filtering to improve visual quality of the decompressed motion imagery. Example restoration results include the cases where the data have been compressed by quantization of two- and three-dimensional wavelet transform coefficients. Although not developed in this work, the noise model is also directly applicable to other restoration algorithms that incorporate information from other time instants, such as super-resolution.

Image quality improvement using edge and distribution information of degraded image

The basic blur distribution approach considered in the restoration of degraded images uses a Gaussian structure to cover a large class of possible distributions. In contrast to this general hypothesis, a common problem encountered in restoration is that the restoration algorithm, especially working in real time, might have large errors with unexpected results if the distribution of image blur based on different media such as atmosphere, x rays, etc. is not known. From this point of view, information about the distribution of blur operating on image is an essential step toward a better restoration to obtain a high-quality image from the degraded one. We introduce a novel approach for restoration of images by using edge and distribution information of the degraded image. For that purpose, first, the distribution model of the degradation process is estimated by a correlation between actual image and reference distribution test models. Then, the proposed algorithm estimates restoration filter model coefficients according to the estimated distribution model and edge information of the degraded image. Simulation results of image restoration illustrate the performance of the proposed method.

Robust incremental compensation of the light attenuation with depth in 3D fluorescence microscopy.

Summary Fluorescent signal intensities from confocal laser scanning microscopes (CLSM) suffer from several distortions inherent to the method. Namely, layers which lie deeper within the specimen are relatively dark due to absorption and scattering of both excitation and fluorescent light, photobleaching and/or other factors. Because of these effects, a quantitative analysis of images is not always possible without correction. Under certain assumptions, the decay of intensities can be estimated and used for a partial depth intensity correction. In this paper we propose an original robust incremental method for compensating the attenuation of intensity signals. Most previous correction methods are more or less empirical and based on fitting a decreasing parametric function to the section mean intensity curve computed by summing all pixel values in each section. The fitted curve is then used for the calculation of correction factors for each section and a new compensated sections series is computed. However, these methods do not perfectly correct the images. Hence, the algorithm we propose for the automatic correction of intensities relies on robust estimation, which automatically ignores pixels where measurements deviate from the decay model. It is based on techniques adopted from the computer vision literature for image motion estimation. The resulting algorithm is used to correct volumes acquired in CLSM. An implementation of such a restoration filter is discussed and examples of successful restorations are given.

A non-parametric filter for digital image restoration, using cluster analysis

We introduce a method to restore digital images with contaminated pixels. One particular characteristic of this method is that it does not change the pixels that are not considered contaminated, thus avoiding excessive intervening of the original image. Each pixel is analyzed by studying its eight point neighborhood. A cluster analysis is performed on the group of eight pixels contained in the neighborhood. After deciding how many clusters there are in the neighborhood, a decision is made whether the center pixel is an outlier or not. If so, to assign a new value, another decision is made, on a probabilistic basis, as to which cluster it belongs.This method can be applied to black and white images as well as to color and multiphase images.

Optimal noise removal using an adaptive Wiener filter based on a locally stationary Gaussian mixture distribution model for images

AbstractThis paper proposes an adaptive Wiener filter (AWF) based on the Gaussian mixture distribution model (GMM) as a realization of an optimum restoration filter. The proposed method is a kind of simple adaptive WF that classifies image blocks according to their local statistical properties and selects a matched WF from a class of a priori deduced WFs. In this method, the optimum filter is realized based on the fact that the minimum mean square error filter is reduced to a WF when the image and noise signals are both Gaussian. In addition, the probability distribution function of the signals in each class can be transformed to Gaussian by using the GMM as a statistical model for the image. In order to improve the accuracy of variance estimation and to reduce the computational complexity in deducing the WFs, a universal mixture model obtained from various kinds of training images is used as the underlying mixture model. In this paper, in restoring images corrupted with white noise, the method of estimating the covariance matrices in locally stationary processes and the method of designing the mixture model are studied, and the adaptive WF is designed. Finally, simulation results show the efficiency of the proposed method compared with conventional methods. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 49–60, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10082

Road vectors update using SAR imagery: a snake-based method

The paper presents an approach for roads detection based on synthetic aperture radar (SAR) images and road databases. The vectors provided by the database are refined using active contours (snakes). In this framework, we firstly develop a restoration filter based on the frost filter achieving an acceptable compromise between speckle elimination and lines preserving. This is followed by a line plausibility calculation step which is used to deform the snake from its initial location toward the final solution. The snake is reformulated using finite elements method. The setting of the snake parameters is not an obvious problem especially when they are tuned by trial-and-error process. We propose a new automatic computational rule for the snake parameters. Our approach is validated by a series of tests on synthetic and SAR images.

Local Multichannel Deconvolution

We introduce a method to locally restore multiple blurred images that yields an extended boundary of the restored image. In particular, we provide a method for finding solutions that are compactly (finitely) supported to the multichannel deconvolution equation when the impulse responses are also compactly supported distributions. This method allows us to broaden the scope of calculating solutions for any particular type of function beyond what was possible in D.F. Walnut (J. Fourier Anal. Appl., Vol. 4, No. 6, pp. 669–709, 1998). During reconstruction, noise from the blurred images is added locally in neighborhoods dependent on the support of the restoration filters. Numerical simulations indicate that these filters may highly increase the magnitude of the noise but with a slight regularization of the filters, the results obtained show the effectiveness of this method.

A unified method for optimizing linear image restoration filters

Image restoration from degraded images lies at the foundation of image processing, pattern recognition, and computer vision, so it has been extensively studied. A large number of image restoration filters have been devised so far. It is known that a certain filter works excellently for a certain type of original image or degradation. However, the same filter may not be suitable for other images, so the selection of filters is exceedingly important in practice. Moreover, if a filter includes adjustable parameters such as the regularization parameter or threshold, its restoration performance relies heavily on the choice of the parameter values. In this paper, we therefore discuss the problem of optimizing the filter type and parameter values. Our method is based on the subspace information criterion (SIC), which is an unbiased estimator of the expected squared error between the restored and original images. Since SIC is applicable to any linear filters, one can optimize the filter type and parameter values in a consistent fashion. Our emphasis in this article is laid on the practical concerns of SIC, such as the noise variance estimation, computational issues, and comparison with existing methods. Specifically, we derive an analytic form of the optimal parameter values for the moving-average filter, which will greatly reduce the computational cost. Experiments with the regularization filter show that SIC is comparable to existing methods in the small degradation case, and SIC tends to outperform existing methods in the severe degradation case.

Assessment of the Wiener-Retinex process.

We assess the performance of the Retinex transformation, the Wiener restoration, and the combined Wiener-Retinex process in the context of the end-to-end model of color visual-communication channels for near-surface acquisition. We extend the formulations of panchromatic imaging for the nonlinear Retinex transformation and the linear Wiener and Wiener-Retinex restoration filters to color imaging. We further assess the accuracy by which colors are restored in the cases of uniform and spatially varying irradiance levels, and the shadow depth for which color consistency is still possible with reasonable accuracy. Finally, we assess the sensitivity of these processes to perturbations in the visual channel, including the image-gathering design and the spatial support of the Retinex transformation.

Histogram-based fuzzy filter for image restoration

In this paper, we present a novel approach to the restoration of noise-corrupted image, which is particularly effective at removing highly impulsive noise while preserving image details. This is accomplished through a fuzzy smoothing filter constructed from a set of fuzzy membership functions for which the initial parameters are derived in accordance with input histogram. A principle of conservation in histogram potential is incorporated with input statistics to adjust the initial parameters so as to minimize the discrepancy between a reference intensity and the output of defuzzification process. Similar to median filters (MF), the proposed filter has the benefits that it is simple and it assumes no a priori knowledge of specific input image, yet it shows superior performance over conventional filters (including MF) for the full range of impulsive noise probability. Unlike in many neuro-fuzzy or fuzzy-neuro filters where random strategy is employed to choose initial membership functions for subsequent lengthy training, the proposed filter can achieve satisfactory performance without any training.

Improvement of aperiodic models of deconvolution using an extended size deconvolution method

This paper proposes a methodology for estimating the restoration filter of a degraded image by using an iterative approach involving spatial deconvolution in an aperiodic restoration model environment. This methodology consists of an improvement to the generic aperiodic restoration model, based on operating with a truncated blurring matrix to generate a restoration filter by means of iterations. As a result, we have the operational advantages of the circulant model besides of better restoration results than using the pure aperiodic model in noisy conditions, therefore, there is a reduction of the condition number of the matrices involved for the usual values for the filter mask found in the literature. Some tests have been carried out to validate the proposed model, adding different quantities of gaussian noise to the degraded image. Comparisons have been made between the generic aperiodic model, the circulant model, and the improved aperiodic model proposed in this paper, using the restoration filters in an approach to the Wiener restoration scheme. The results obtained with the improved aperiodic model proposed in this paper show ISNR improvements both with respect to the generic aperiodic model and the circulant model.

Adaptive 3-D median filtering for restoration of an image sequence corrupted by impulse noise

An adaptive 3-D median filtering, which achieves optimal image quality as well as fast computing time, is proposed to remove the impulse noise from a highly corrupted image sequence. The proposed algorithm is compared with the widely used impulse noise removal algorithms with respect to the peak signal-to-noise ratio and the number of computations. The proposed algorithm preserves the image details which are not expected to be corrupted by impulse noise so that the number of computations can be minimized. It has good restoration performance whether the number of pixels corrupted by impulse noise is large or small. In the proposed algorithm, the impulse noise ratio, which is the ratio of the number of pixels corrupted by impulse noise to the total number of pixels, is estimated, and the restoration filtering is adaptively applied based on the estimated impulse noise ratio.

Hybrid order statistic filter and its application to image restoration

We introduce a new nonlinear filter for signal and image restoration, the hybrid order statistic (HOS) filter. Because it exploits both rank- and spatial-order information, the HOS realizes the advantages of nonlinear filters in edge preservation and reduction of impulsive noise components while retaining the ability of the linear filter to suppress Gaussian noise. We show that the HOS filter exhibits improved performance over both the linear Wiener and the nonlinear L filters in reducing mean-squared error in the presence of contaminated Gaussian noise. In many cases it also performs favorably compared with the Ll and rank-conditioned rank selection filters.

A new adaptive filter and quality evaluation index for image restoration

This paper presents a new technique for image adaptive restoration called 3 σ-multiresolution plane fitting (3 σ-MPF) and the global restoration index (GRI) index, which evaluates the restoration performance of smoothing methods. The 3 σ-MPF filter is based on an adaptive plane fitting technique using variable-sized windows with different behavior for continuous regions or discontinuities. The criteria used to select the window size and detect discontinuities is the 3 σ- fidelity test. The GRI, integrates two independent indices measuring restoration smoothness and fidelity. Using this index, the 3 σ-MPF filter performance is compared with other traditional methods, demonstrating better performance under Gaussian noise and robustness against outliers.