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PubMed2004

Robust model-based vasculature detection in noisy biomedical images.

This paper presents a set of algorithms for robust detection of vasculature in noisy retinal video images. Three methods are studied for effective handling of outliers. The first method is based on Huber's censored likelihood ratio test. The second is based on the use of a alpha-trimmed test statistic. The third is based on robust model selection algorithms. All of these algorithms rely on a mathematical model for the vasculature that accounts for the expected variations in intensity/texture profile, width, orientation, scale, and imaging noise. These unknown parameters are estimated implicitly within a robust detection and estimation framework. The proposed algorithms are also useful as nonlinear vessel enhancement filters. The proposed algorithms were evaluated over carefully constructed phantom images, where the ground truth is known a priori, as well as clinically recorded images for which the ground truth was manually compiled. A comparative evaluation of the proposed approaches is presented. Collectively, these methods outperformed prior approaches based on Chaudhuri et al. (1989) matched filtering, as well as the verification methods used by prior exploratory tracing algorithms, such as the work of Can et aL (1999). The Huber censored likelihood test yielded the best overall improvement, with a 145.7% improvement over the exploratory tracing algorithm, and a 43.7% improvement in detection rates over the matched filter.

Algorithms↗
PubMed2002

Encoding with frames in MRI and analysis of the signal-to-noise ratio.

Recently, many new encoding techniques have been suggested for magnetic resonance imaging and an important image reconstruction problem has been raised in order to fully exploit the advantages promised by these new encoding techniques. In terms of frames in an L2 (R) space, we treat these encoding techniques in a unified perspective and propose a solution for this image reconstruction problem. We first develop a matrix form of frame theory and apply it to numerically construct the duals of the encoding functions, which are the transverse excitation profiles generated by radio-frequency pulses along a linear magnetic field gradient. An analysis of the signal-to-noise ratio (SNR) is also presented. Simulations have been carried out and they show that our image reconstruction algorithm minimizes the mean square error between the original and reconstructed images. The SNRs evaluated from simulations agree with our theoretical predictions.

Algorithms↗
PubMed2002

Generation of anisotropic-smoothness regularization filters for EIT.

In the inverse conductivity problem, as in any ill-posed inverse problem, regularization techniques are necessary in order to stabilize inversion. A common way to implement regularization in electrical impedance tomography is to use Tikhonov regularization. The inverse problem is formulated as a minimization of two terms: the mismatch of the measurements against the model, and the regularization functional. Most commonly, differential operators are used as regularization functionals, leading to smooth solutions. Whenever the imaged region presents discontinuities in the conductivity distribution, such as interorgan boundaries, the smoothness prior is not consistent with the actual situation. In these cases, the reconstruction is enhanced by relaxing the smoothness constraints in the direction normal to the discontinuity. In this paper, we derive a method for generating Gaussian anisotropic regularization filters. The filters are generated on the basis of the prior structural information, allowing a better reconstruction of conductivity profiles matching these priors. When incorporating prior information into a reconstruction algorithm, the risk is of biasing the inverse solutions toward the assumed distributions. Simulations show that, with a careful selection of the regularization parameters, the reconstruction algorithm is still able to detect conductivities patterns that violate the prior information. A generalized singular-value decomposition analysis of the effects of the anisotropic filters on regularization is presented in the last sections of the paper.

Algorithms↗
PubMed2002

Understanding phase maps in MRI: a new cutline phase unwrapping method.

This paper describes phase maps. A review of the phase unwrapping problem is given. Different structures, in particular fringelines, cutlines, and poles, contained within a phase map are described and their origin and behavior investigated. The problem of phase unwrapping can then be addressed with a better understanding of the source of poles or inconsistencies. This understanding, along with some assumptions about what is being encoded in the phase of a magnetic resonance image, are used to derive a new method for phase unwrapping which relies only on the phase map. The method detects cutlines and distinguishes between noise-induced poles and signal undersampling poles based on the length of the fringelines. The method was shown to be robust to noise and successful in unwrapping challenging clinical cases.

Algorithms↗
PubMed2002

Generalization of median root prior reconstruction.

Penalized iterative algorithms for image reconstruction in emission tomography contain conditions on which kind of images are accepted as solutions. The penalty term has commonly been a function of pairwise pixel differences in the activity in a local neighborhood, such that smooth images are favored. Attempts to ensure better edge and detail preservation involve difficult tailoring of parameter values or the penalty function itself. The previously introduced median root prior (MRP) favors locally monotonic images. MRP preserves sharp edges while reducing locally nonmonotonic noise at the same time. Quantitative properties of MRP are good, because differences in the neighboring pixel values are not penalized as such. The median is used as an estimate for a penalty reference, against which the pixel value is compared when setting the penalty. In order to generalize the class of MRP-type of priors, the standard median was replaced by other order statistic operations, the L and finite-impluse-response median hybrid (FMH) filters. They allow for smoother appearance as they apply linear weighting together with robust nonlinear operations. The images reconstructed using the new MRP-L and MRP-FMH priors are visually more conventional. Good quantitative properties of MRP are not significantly altered by the new priors.

Algorithms↗
PubMed2003

Real-time adaptive filtering for projection reconstruction MR fluoroscopy.

Magnetic resonance (MR) imaging has faced a dramatic increase in real-time capabilities over the last years. However, the application of fast pulse sequences still suffers from low signal-to-noise ratios (SNRs), which can be the limiting factor for the actual acquisition speed. In MR fluoroscopy, filtering along the time and/or spatial domain can be applied to increase the image quality. In this paper, a projection-based noise filter is presented that significantly enhances the SNR in projection reconstruction (PR) fluoroscopy without apparent loss of resolution in the reconstructed images. In contrast to an imaged-based approach, this method allows a very efficient computational implementation. The filter algorithm was implemented on a digital signal processor and was applied to real-time processing during PR fluoroscopy. A quantitative analysis of the improvement in SNR and results for different fluoroscopic MR applications are given. Apart from MR fluoroscopy, the proposed technique has the potential to be applied to low dose computed tomography fluoroscopy.

Algorithms↗
PubMed2003

Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series.

This paper addresses the problem of detecting significant changes in fMRI time series that are correlated to a stimulus time course. This paper provides a new approach to estimate the parameters of a semiparametric generalized linear model of fMRI time series. The fMRI signal is described as the sum of two effects: a smooth trend and the response to the stimulus. The trend belongs to a subspace spanned by large scale wavelets. The wavelet transform provides an approximation to the Karhunen-Loève transform for the long memory noise and we have developed a scale space regression that permits to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend. In order to demonstrate that our approach outperforms the state-of-the art detrending technique, we evaluated our method against a smoothing spline approach. Experiments with simulated data and experimental fMRI data, demonstrate that our approach can infer and remove drifts that cannot be adequately represented with splines.

Acoustic Stimulation↗
PubMed2003

A versatile wavelet domain noise filtration technique for medical imaging.

In this paper, we propose a robust wavelet domain method for noise filtering in medical images. The proposed method adapts itself to various types of image noise as well as to the preference of the medical expert; a single parameter can be used to balance the preservation of (expert-dependent) relevant details against the degree of noise reduction. The algorithm exploits generally valid knowledge about the correlation of significant image features across the resolution scales to perform a preliminary coefficient classification. This preliminary coefficient classification is used to empirically estimate the statistical distributions of the coefficients that represent useful image features on the one hand and mainly noise on the other. The adaptation to the spatial context in the image is achieved by using a wavelet domain indicator of the local spatial activity. The proposed method is of low complexity, both in its implementation and execution time. The results demonstrate its usefulness for noise suppression in medical ultrasound and magnetic resonance imaging. In these applications, the proposed method clearly outperforms single-resolution spatially adaptive algorithms, in terms of quantitative performance measures as well as in terms of visual quality of the images.

Algorithms↗
PubMed2003

A linear wavelet filter for parametric imaging with dynamic PET.

This paper describes a new filter for parametric images obtained from dynamic positron emission tomography (PET) studies. The filter is based on the wavelet transform following the heuristics of a previously published method that are here developed into a rigorous theoretical framework. It is shown that the space-time problem of modeling a dynamic PET sequence reduces to the classical one of estimation of a normal multivariate vector of independent wavelet coefficients that, under least-squares risk, can be solved by straightforward application of well established theory. From the study of the distribution of wavelet coefficients of PET images, it is inferred that a James-Stein linear estimator is more suitable for the problem than traditional nonlinear procedures that are incorporated in standard wavelet filters. This is confirmed by the superior performance of the James-Stein filter in simulation studies compared to a state-of-the-art nonlinear wavelet filter and a nonstationary filter selected from literature. Finally, the formal framework is interpreted for the practitioner's point of view and advantages and limitations of the method are discussed.

Aged↗
PubMed2003

Robust estimation of ultrasound pulses using outlier-resistant de-noising.

A different approach to the problem of estimation of the ultrasound pulse spectrum, which usually arises as a part of ultrasound image restoration algorithms, is presented. It is shown that this estimation problem can be reformulated in terms of a de-noising problem. In this formulation, the log-spectrum of a radio-frequency line (RF-line) is viewed as a noisy measurement of the signal that needs to be estimated, i.e., the ultrasound pulse log-spectrum. The log-spectrum of the tissue reflectivity function (i.e., tissue response) is considered as the noise to be rejected. The contribution of the paper is twofold. First, it provides statistical description of the reflectivity function log-spectrum for the case, when the samples of the reflectivity function are independent identically distributed (i.i.d.) Gaussian random variables. Moreover, it is shown that the problem of the pulse spectrum recovery is essentially a de-noising problem. Consequently, it is suggested to solve the problem within the framework of the de-noising by wavelet shrinkage. Second, a computationally efficient algorithm is proposed for the pulse-spectrum estimation, which can be viewed as a modified version of the classical Donoho's three-step de-noising procedure. This modification is necessary, because of specific properties of the noise to be rejected. It is shown, that whenever the samples of the reflectivity function can be assumed to be i.i.d. Gaussian random variables, the samples of its log-spectrum obey the Fisher-Tippet distribution. For this type of noise, straightforward implementation of the standard de-noising can cause serious estimation errors. In order to overcome this difficulty, an outlier-resistant de-noising is performed. The unique properties of this modified de-noising algorithm allow estimating the pulse spectrum adaptively to its properties, as they are continuously influenced by the frequency-dependent attenuation process. The performance of the proposed algorithm is examined in a series of computer-simulations. It is shown that this algorithm, developed on the assumption of the "Gaussian" reflectivity function, remains applicable for broader classes of distributions. The results obtained in a series of in vivo experiments reveal superior performance of the novel approach over some of alternative estimation techniques, e.g., cepstrum-based estimation.

Adult↗
PubMed2003

Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging.

The nonparametric multiscale platelet algorithms presented in this paper, unlike traditional wavelet-based methods, are both well suited to photon-limited medical imaging applications involving Poisson data and capable of better approximating edge contours. This paper introduces platelets, localized functions at various scales, locations, and orientations that produce piece-wise linear image approximations, and a new multiscale image decomposition based on these functions. Platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries. For smoothness measured in certain Hölder classes, it is shown that the error of m-term platelet approximations can decay significantly faster than that of m-term approximations in terms of sinusoids, wavelets, or wedgelets. This suggests that platelets may outperform existing techniques for image denoising and reconstruction. Fast, platelet-based, maximum penalized likelihood methods for photon-limited image denoising, deblurring and tomographic reconstruction problems are developed. Because platelet decompositions of Poisson distributed images are tractable and computationally efficient, existing image reconstruction methods based on expectation-maximization type algorithms can be easily enhanced with platelet techniques. Experimental results suggest that platelet-based methods can outperform standard reconstruction methods currently in use in confocal microscopy, image restoration, and emission tomography.

Algorithms↗
PubMed2003

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.

Algorithms↗
PubMed2004

Denoising functional MR images: a comparison of wavelet denoising and Gaussian smoothing.

We present a general wavelet-based denoising scheme for functional magnetic resonance imaging (fMRI) data and compare it to Gaussian smoothing, the traditional denoising method used in fMRI analysis. One-dimensional WaveLab thresholding routines were adapted to two-dimensional (2-D) images, and applied to 2-D wavelet coefficients. To test the effect of these methods on the signal-to-noise ratio (SNR), we compared the SNR of 2-D fMRI images before and after denoising, using both Gaussian smoothing and wavelet-based methods. We simulated a fMRI series with a time signal in an active spot, and tested the methods on noisy copies of it. The denoising methods were evaluated in two ways: by the average temporal SNR inside the original activated spot, and by the shape of the spot detected by thresholding the temporal SNR maps. Denoising methods that introduce much smoothness are better suited for low SNRs, but for images of reasonable quality they are not preferable, because they introduce heavy deformations. Wavelet-based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions. We also performed statistical parametric mapping on the denoised simulated time series, as well as on a real fMRI data set. False discovery rate control was used to correct for multiple comparisons. The results show that the methods that produce smooth images introduce more false positives. The less smoothing wavelet-based methods, although generating more false negatives, produce a smaller total number of errors than Gaussian smoothing or wavelet-based methods with a large smoothing effect.

Algorithms↗
PubMed2004

Noise equalization for detection of microcalcification clusters in direct digital mammogram images.

Equalizing image noise is shown to be an important step in the automatic detection of microcalcifications in digital mammography. This study extends a well established film-screen noise equalization scheme developed by Veldkamp et al. for application to full-field digital mammogram (FFDM) images. A simple noise model is determined based on the assumption that quantum noise is dominant in direct digital X-ray imaging. Estimation of the noise as a function of the gray level is improved by calculating the noise statistics using a truncated distribution method. Experimental support for the quantum noise assumption is presented for a set of step wedge phantom images. Performance of the noise equalization technique is also tested as a preprocessing stage to a microcalcification detection scheme. It is shown that the square root model based approach which FFDM allows leads to a robust estimation of the high frequency image noise. This provides better microcalcification detection performance when compared to the film-screen noise equalization method developed by Veldkamp. Substantially better results are obtained than when noise equalization is omitted. A database of 124 direct digital mammogram images containing 28 microcalcification clusters was used for evaluation of the method.

Algorithms↗
PubMed2004

Emission image reconstruction for randoms-precorrected PET allowing negative sinogram values.

Most positron emission tomography (PET) emission scans are corrected for accidental coincidence (AC) events by real-time subtraction of delayed-window coincidences, leaving only the randoms-precorrected data available for image reconstruction. The real-time randoms precorrection compensates in mean for AC events but destroys the Poisson statistics. The exact log-likelihood for randoms-precorrected data is inconvenient, so practical approximations are needed for maximum likelihood or penalized-likelihood image reconstruction. Conventional approximations involve setting negative sinogram values to zero, which can induce positive systematic biases, particularly for scans with low counts per ray. We propose new likelihood approximations that allow negative sinogram values without requiring zero-thresholding. With negative sinogram values, the log-likelihood functions can be nonconcave, complicating maximization; nevertheless, we develop monotonic algorithms for the new models by modifying the separable paraboloidal surrogates and the maximum-likelihood expectation-maximization (ML-EM) methods. These algorithms ascend to local maximizers of the objective function. Analysis and simulation results show that the new shifted Poisson (SP) model is nearly free of systematic bias yet keeps low variance. Despite its simpler implementation, the new SP performs comparably to the saddle-point model which has shown the best performance (as to systematic bias and variance) in randoms-precorrected PET emission reconstruction.

Algorithms↗
PubMed2004

Nonuniform noise propagation by using the ramp filter in fan-beam computed tomography.

It is observed that when the homogeneity property of the ramp filter is used to derive a filtered backprojection algorithm in fan-beam tomography, the reconstructed images have nonstationary frequency components and nonstationary noise. When a short focal-length is used, higher frequency components are amplified more at the edge of the image than at the center of the image, resulting in higher noise at the edge of the image.

Algorithms↗
PubMed2004

Image denoising based on multiscale singularity detection for cone beam CT breast imaging.

It was recently reported that the real-time flat panel detector-based cone-beam computed tomography (CBCT) breast imaging can help improve the detectability of small breast tumors with an X-ray dose comparable to that of the conventional mammography. In this paper, an efficient denoising algorithm is proposed to further reduce the X-ray exposure level required by a CBCT scan to acquire acceptable image quality. The proposed wavelet-based denoising algorithm possesses three significant characteristics: 1) wavelet coefficients at each scale are classified into two categories: irregular coefficients, and edge-related and regular coefficients; 2) noise in irregular coefficients is reduced as much as possible without producing artifacts to the denoised images; and 3) for the edge-related and regular coefficients, if they are at the first decomposition level, they are further denoised, otherwise, no modifications are made to them so as to obtain good visual quality for diagnosis. By applying the proposed denoising algorithm to the filtered projection images, the X-ray exposure level necessary for the CBCT scan can be reduced by up to 60% while obtaining clinically acceptable image quality. This denoising result indicates that in the clinical application of CBCT breast imaging, the patient radiation dose can be significantly reduced.

Algorithms↗
PubMed2004

Adaptive averaging for improved SNR in real-time coronary artery MRI.

A technique has been developed for combining a series of low signal-to-noise ratio (SNR) real-time magnetic resonance (MR) images to produce composite images with high SNR and minimal artifact in the presence of motion. The main challenge is identifying a set of real-time images with sufficiently small systematic differences to avoid introducing significant artifact into the composite image. To accomplish this task, one must: 1) identify images identical within the limits of noise; 2) detect systematic errors within such images with sufficient sensitivity. These steps are achieved by evaluating the correlation coefficient (CC) between regions in prospective images and a template containing the anatomy of interest. Images identical within noise are selected by comparing the measured CC values to the theoretical distribution expected due to noise. Sensitivity for systematic error depends on the SNR of the CC (=SNR(CCmax)), which in turn depends on the noise, and the template size and structure. By varying the template size, SNR(CCmax) may be altered. Experiments on phantoms and coronary artery images demonstrate that the SNR(CCmax) necessary to avoid introducing significant artifact varies with the target composite SNR. The future potential of this technique is demonstrated on high-resolution (approximately 0.9 mm), reduced field-of-view real-time coronary images.

Algorithms↗