Filtering noise from images with wavelet transforms

Research related to the diagnosis of prostate cancer based on machine learning medical images: A review

BACKGROUND

Prostate cancer is currently the second most prevalent cancer among men. Accurate diagnosis of prostate cancer can provide effective treatment for patients and greatly reduce mortality. The current medical imaging tools for screening prostate cancer are mainly MRI, CT and ultrasound. In the past 20 years, these medical imaging methods have made great progress with machine learning, especially the rise of deep learning has led to a wider application of artificial intelligence in the use of image-assisted diagnosis of prostate cancer.

METHOD

This review collected medical image processing methods, prostate and prostate cancer on MR images, CT images, and ultrasound images through search engines such as web of science, PubMed, and Google Scholar, including image pre-processing methods, segmentation of prostate gland on medical images, registration between prostate gland on different modal images, detection of prostate cancer lesions on the prostate.

CONCLUSION

Through these collated papers, it is found that the current research on the diagnosis and staging of prostate cancer using machine learning and deep learning is in its infancy, and most of the existing studies are on the diagnosis of prostate cancer and classification of lesions, and the accuracy is low, with the best results having an accuracy of less than 0.95. There are fewer studies on staging. The research is mainly focused on MR images and much less on CT images, ultrasound images.

DISCUSSION

Machine learning and deep learning combined with medical imaging have a broad application prospect for the diagnosis and staging of prostate cancer, but the research in this area still has more room for development.

SENSE EPI reconstruction with 2D phase error correction and channel-wise noise removal

PURPOSE

To develop a robust reconstruction pipeline for EPI data that enables 2D Nyquist phase error correction using sensitivity encoding without incurring major noise artifacts in low SNR data.

METHODS

SENSE with 2D phase error correction (PEC-SENSE) was combined with channel-wise noise removal using Marcenko-Pastur principal component analysis (MPPCA) to simultaneously eliminate Nyquist ghost artifacts in EPI data and mitigate the noise amplification associated with phase correction using parallel imaging. The proposed pipeline (coined SPECTRE) was validated in phantom DW-EPI data using the accuracy and precision of diffusion metrics; ground truth values were obtained from data acquired with a spin echo readout. Results from the SPECTRE pipeline were compared against PEC-SENSE reconstructions with three alternate denoising strategies: (i) no denoising; (ii) denoising of magnitude data after image formation; (iii) denoising of complex data after image formation. SPECTRE was then tested using highb $$ b $$ -value (i.e., low SNR) diffusion data (up tob = 3000 $$ b=3000 $$  s/mm2 $$ {}^2 $$ ) in four healthy subjects.

RESULTS

Noise amplification associated with phase error correction incurred a 23% bias in phantom mean diffusivity (MD) measurements. Phantom MD estimates using the SPECTRE pipeline were within 8% of the ground truth value. In healthy volunteers, the SPECTRE pipeline visibly corrected Nyquist ghost artifacts and reduced associated noise amplification in highb $$ b $$ -value data.

CONCLUSION

The proposed reconstruction pipeline is effective in correcting low SNR data, and improves the accuracy and precision of derived diffusion metrics.

3D photon counting integral imaging by using multi-level decomposition

In this paper, we propose three-dimensional (3D) photon counting integral imaging by using multi-level decomposition such as discrete wavelet transform to improve the visual quality and measurement accuracy under photon-starved conditions. Conventional 3D integral imaging can visualize 3D objects and acquire their depth information. However, the amount of irradiated light on the object causes the degradation of visual quality for 3D images under photon-starved conditions. To visualize 3D objects, photon counting integral imaging has been utilized. It can detect photons from 3D scenes by using a computational photon counting model, which is modelled by the Poisson random process. However, photons occur not only from objects but also in areas where objects do not exist. Moreover, photon fluctuation may occur in the scene through shot noise. Since these noise photons are measurement errors, it may decrease the image quality and accuracy. In contrast, our proposed method uses 2D discrete wavelet transform, which can emphasize the object photons effectively. Finally, our proposed method can enhance the visual quality of 3D images and provide more accurate depth information under photon-starved conditions. To prove the feasibility of our proposed method, we implement the optical experiment and calculate various image quality metrics.

A new unsupervised pseudo-siamese network with two filling strategies for image denoising and quality enhancement

Digital image noise may be introduced during acquisition, transmission, or processing and affects readability and image processing effectiveness. The accuracy of established image processing techniques, such as segmentation, recognition, and edge detection, is adversely impacted by noise. There exists an extensive body of work which focuses on circumventing such issues through digital image enhancement and noise reduction, but this work is limited by a number of constraints including the application of non-adaptive parameters, potential loss of edge detail information, and (with supervised approaches) a requirement for clean, labeled, training data. This paper, developed on the principle of Noise2Void, presents a new unsupervised learning approach incorporating a pseudo-siamese network. Our method enables image denoising without the need for clean images or paired noise images, instead requiring only noise images. Two independent branches of the network utilize different filling strategies, namely zero filling and adjacent pixel filling. Then, the network employs a loss function to improve the similarity of the results in the two branches. We also modify the Efficient Channel Attention module to extract more diverse features and improve performance on the basis of global average pooling. Experimental results show that compared with traditional methods, the pseudo-siamese network has a greater improvement on the ADNI dataset in terms of quantitative and qualitative evaluation. Our method therefore has practical utility in cases where clean images are difficult to obtain.

Improving dermal level images from reflectance confocal microscopy using wavelet-based transformations and adaptive histogram equalization

OBJECTIVES

Reflectance confocal microscopy (RCM) generates scalar image data from serial depths in the skin, allowing in vivo examination of cellular features. The maximum imaging depth of RCM is approximately 250 µm, to the papillary dermis, or upper reticular dermis. Frequently, important diagnostic features are present in the dermis, hence improved visualization of deeper levels is advantageous.

METHODS

Low contrast and noise in dermal images were improved by employing a combination of wavelet-based transformations and contrast-limited adaptive histogram equalization.

RESULTS

Preserved details, noise reduction, increased contrast, and feature enhancement were observed in the resulting processed images.

CONCLUSIONS

Complex and combined wavelet-based enhancement approaches for dermal level images yielded reconstructions of higher quality than less sophisticated histogram-based strategies. Image optimization may improve the diagnostic accuracy of RCM, especially for entities with dermal findings.

Comparison of noise estimation methods used in denoising 99mTc-sestamibi parathyroid images using wavelet transform

The objective of this study was to compare the performance of variance, median absolute deviation, and the square of median absolute deviation methods of noise estimation in denoising of ^99mTc-sestamibi parathyroid images using wavelet transform. Sixty-eight ^99mTc-sestamibi parathyroid images including 33 images acquired at zoom 1.0 and 35 acquired at zoom 2.0 were denoised using the wavethresh package in R. The image decomposition and reconstruction method discrete wavelet transform, wavelet filter db4, shrinkage method hard, and thresholding policy universal were used. The noise estimation in the process was made using var, mad and madmad functions, which use variance, mean absolute deviation, and the square of mean absolute deviation, respectively. The quality of denoised images was assessed both qualitatively and quantitatively. A nonparametric two-sample Kolmogorov–Smirnov test was applied to find whether the difference in image quality produced by these three noise estimation methods was significant at 95% confidence. Noise estimation using madmad function produced the best quality denoised image. Further, the quality of the denoised image using madmad function was significantly better than the quality of the denoised image obtained with var or mad function (P = 1). The estimation of noise using madmad functions in wavelet transforms provides the best-denoised image for both zoom 1.0 and zoom 2.0 ^99mTc-sestamibi parathyroid images.

Effect of Noise Adaptive Wavelet Filter on Diagnostic Performance in Stroke Perfusion

Background: Computed tomography perfusion (CTP) images include more noise than routine clinic computed tomography (CT) images. Singular value decomposition based deconvolution algorithms are widely used for obtaining several functional perfusion maps. Recently block circulant singular value decomposition algorithms become popular for its superior property of immunity to contrast bolus lag. It is well known from literature that these algorithms are very sensitive to noise. There are a lot of examples of noise reduction filters in the literature as well as commercial ones. Functional maps which help physicians in the diagnostic process can be obtained with better image quality by de-noising CTP images with adaptive noise reduction filters. Objective: In this study, the effect of a noise adaptive wavelet filtering method on diagnostic performance on CTP stroke patient images is investigated. Method: Images of acute stroke patients were de-noised by this method and their diagnostic value were evaluated by visual means, peak signal-to-noise ratio and time intensity profile metrics. An observer evaluation study was carried out in order to validate quantitative image quality metrics. The results are compared with Gaussian and a bilateral filter based filtering method called TIPS (Time Intensity Profile Similarity) on same images sets to benchmark proposed method. Results: The diagnostic value of the images obtained from noise adaptive wavelet filtering method were better than Gaussian filter method and were compatible with a wellknown time intensity profile similarity bilateral filter method. Diagnostic performance of the both observers were improved compared to both Gaussian and TIPS methods. Conclusion: The noise adaptive wavelet filter method succeeded to reduce noise while preserving details contained in the contrast bolus. Its final effect on the timeintensity profiles and generated perfusion maps are compatible with the literature and showed improvements on diagnostic performance on specificity and overall accuracy when compared to other methods.

A Survey on State-of-the-art Denoising Techniques for Brain Magnetic Resonance Images

The accuracy of the magnetic resonance (MR) image diagnosis depends on the quality of the image, which degrades mainly due to noise and artifacts. The noise is introduced because of erroneous imaging environment or distortion in the transmission system. Therefore, denoising methods play an important role in enhancing the image quality. However, a tradeoff between denoising and preserving the structural details is required. Most of the existing surveys are conducted on a specific MR image modality or on limited denoising schemes. In this context, a comprehensive review on different MR image denoising techniques is inevitable. This survey suggests a new direction in categorizing the MR image denoising techniques. The categorization of the different image models used in medical image processing serves as the basis of our classification. This study includes recent improvements on deep learning-based denoising methods alongwith important traditional MR image denoising methods. The major challenges and their scope of improvement are also discussed. Further, many more evaluation indices are considered for a fair comparison. An elaborate discussion on selecting appropriate method and evaluation metric as per the kind of data is presented. This study may encourage researchers for further work in this domain.

Detection of Methane Plumes Using Airborne Midwave Infrared (3–5 µm) Hyperspectral Data

Methane (CH4) display spectral features in several regions of the infrared range (0.75–14 µm), which can be used for the remote mapping of emission sources through the detection of CH4 plumes from natural seeps and leaks. Applications of hyperspectral remote sensing techniques for the detection of CH4 in the near and shortwave infrared (NIR-SWIR: 0.75–3 µm) and longwave infrared (LWIR: 7–14 µm) have been demonstrated in the literature with multiple sensors and scenarios. However, the acquisition and processing of hyperspectral data in the midwave infrared (MWIR: 3–5 µm) for this application is rather scarce. Here, a controlled field experiment was used to evaluate the potential for CH4 plume detection in the MWIR based on hyperspectral data acquired with the SEBASS airborne sensor. For comparison purposes, LWIR data were also acquired simultaneously with the same instrument. The experiment included surface and undersurface emission sources (ground stations), with flow rates ranging between 0.6–40 m3/h. The data collected in both ranges were sequentially processed using the same methodology. The CH4 plume was detected, variably, in both datasets. The gas plume was detected in all LWIR images acquired over nine gas leakage stations. In the MWIR range, the plume was detected in only four stations, wherein 18 m3/h was the lowest flux sensed. We demonstrate that the interference of target reflectance, the low contrast between plume and background and a low signal of the CH4 feature in the MWIR at ambient conditions possibly explain the inferior results observed for this range when compared to LWIR. Furthermore, we show that the acquisition time and weather conditions, including specific limits of temperature, humidity, and wind speed, proved critical for plume detection using daytime MWIR hyperspectral data.

Wavelet Transform-Based Soft Computational Techniques and Applications in Medical Imaging

The aim of this chapter is to highlight the biomedical applications of wavelet transform based soft computational techniques i.e. wavenet and corresponding research efforts in imaging techniques. A brief introduction of wavelet transform, its properties that are vital for biomedical applications touched by various researchers and basics of neural networks has been discussed. The concept of wavelon and wavenet is also discussed in detail. Recent survey of wavelet based neural networks in medical imaging is another facet of this script, which includes biomedical image denoising, image enhancement and functional neuro-imaging, including positron emission tomography and functional MRI.

Noise Estimation and Reduction in Magnetic Resonance Imaging Using a New Multispectral Nonlocal Maximum-likelihood Filter

Denoising of magnetic resonance (MR) images enhances diagnostic accuracy, the quality of image manipulations such as registration and segmentation, and parameter estimation. The first objective of this paper is to introduce a new, high-performance, nonlocal filter for noise reduction in MR image sets consisting of progressively-weighted, that is, multispectral, images. This filter is a multispectral extension of the nonlocal maximum likelihood filter (NLML). Performance was evaluated on synthetic and in-vivo T₂ - and T₁ -weighted brain imaging data, and compared to the nonlocal-means (NLM) and its multispectral version, that is, MS-NLM, and the nonlocal maximum likelihood (NLML) filters. Visual inspection of filtered images and quantitative analyses showed that all filters provided substantial reduction of noise. Further, as expected, the use of multispectral information improves filtering quality. In addition, numerical and experimental analyses indicated that the new multispectral NLML filter, MS-NLML, demonstrated markedly less blurring and loss of image detail than seen with the other filters evaluated. In addition, since noise standard deviation (SD) is an important parameter for all of these nonlocal filters, a multispectral extension of the method of maximum likelihood estimation (MLE) of noise amplitude is presented and compared to both local and nonlocal MLE methods. Numerical and experimental analyses indicated the superior performance of this multispectral method for estimation of noise SD.

Exploring the complementarity of THz pulse imaging and DCE-MRIs: Toward a unified multi-channel classification and a deep learning framework

We provide a comprehensive account of recent advances in biomedical image analysis and classification from two complementary imaging modalities: terahertz (THz) pulse imaging and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). The work aims to highlight underlining commonalities in both data structures so that a common multi-channel data fusion framework can be developed. Signal pre-processing in both datasets is discussed briefly taking into consideration advances in multi-resolution analysis and model based fractional order calculus system identification. Developments in statistical signal processing using principal component and independent component analysis are also considered. These algorithms have been developed independently by the THz-pulse imaging and DCE-MRI communities, and there is scope to place them in a common multi-channel framework to provide better software standardization at the pre-processing de-noising stage. A comprehensive discussion of feature selection strategies is also provided and the importance of preserving textural information is highlighted. Feature extraction and classification methods taking into consideration recent advances in support vector machine (SVM) and extreme learning machine (ELM) classifiers and their complex extensions are presented. An outlook on Clifford algebra classifiers and deep learning techniques suitable to both types of datasets is also provided. The work points toward the direction of developing a new unified multi-channel signal processing framework for biomedical image analysis that will explore synergies from both sensing modalities for inferring disease proliferation.

A partial differential equation-based general framework adapted to Rayleigh's, Rician's and Gaussian's distributed noise for restoration and enhancement of magnetic resonance image

The proposed framework is obtained by casting the noise removal problem into a variational framework. This framework automatically identifies the various types of noise present in the magnetic resonance image and filters them by choosing an appropriate filter. This filter includes two terms: the first term is a data likelihood term and the second term is a prior function. The first term is obtained by minimizing the negative log likelihood of the corresponding probability density functions: Gaussian or Rayleigh or Rician. Further, due to the ill-posedness of the likelihood term, a prior function is needed. This paper examines three partial differential equation based priors which include total variation based prior, anisotropic diffusion based prior, and a complex diffusion (CD) based prior. A regularization parameter is used to balance the trade-off between data fidelity term and prior. The finite difference scheme is used for discretization of the proposed method. The performance analysis and comparative study of the proposed method with other standard methods is presented for brain web dataset at varying noise levels in terms of peak signal-to-noise ratio, mean square error, structure similarity index map, and correlation parameter. From the simulation results, it is observed that the proposed framework with CD based prior is performing better in comparison to other priors in consideration.

Wavelets and statistical analysis of functional magnetic resonance images of the human brain

Wavelets provide an orthonormal basis for multiresolution analysis and decorrelation or ‘whitening’ of nonstationary time series and spatial processes. Wavelets are particularly well suited to analysis of biological signals and images, such as human brain imaging data, which often have fractal or scale-invariant properties. We briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of functional magnetic resonance imaging (fMRI) data. We focus on time series resampling by ‘wavestrapping’ of wavelet coefficients, methods for efficient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing, all of which are somewhat simplified by the decorrelating property of the DWT.

Portal imaging: Performance improvement in noise reduction by means of wavelet processing

This paper discusses the suitability, in terms of noise reduction, of various methods which can be applied to an image type often used in radiation therapy: the portal image. Among these methods, the analysis focuses on those operating in the wavelet domain. Wavelet-based methods tested on natural images--such as the thresholding of the wavelet coefficients, the minimization of the Stein unbiased risk estimator on a linear expansion of thresholds (SURE-LET), and the Bayes least-squares method using as a prior a Gaussian scale mixture (BLS-GSM method)--are compared with other methods that operate on the image domain--an adaptive Wiener filter and a nonlocal mean filter (NLM). For the assessment of the performance, the peak signal-to-noise ratio (PSNR), the structural similarity index (SSIM), the Pearson correlation coefficient, and the Spearman rank correlation (ρ) coefficient are used. The performance of the wavelet filters and the NLM method are similar, but wavelet filters outperform the Wiener filter in terms of portal image denoising. It is shown how BLS-GSM and NLM filters produce the smoothest image, while keeping soft-tissue and bone contrast. As for the computational cost, filters using a decimated wavelet transform (decimated thresholding and SURE-LET) turn out to be the most efficient, with calculation times around 1 s.

Bayesian Models for fMRI Data Analysis

Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This paper provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatio-temporal models for fMRI data that detect task-related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as EEG/MEG and DTI data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics.

Clinician's road map to wavelet EEG as an Alzheimer's disease biomarker

Alzheimer's disease (AD) is considered the main cause of dementia in Western countries. Consequently, there is a need for an accurate, universal, specific and cost-effective biomarker for early AD diagnosis, to follow disease progression and therapy response. This article describes a new diagnostic approach to quantitative electroencephalogram (QEEG) diagnosis of mild and moderate AD. The data set used in this study was composed of EEG signals recorded from 2 groups: (S1) 74 normal subjects, 33 females and 41 males (mean age 67 years, standard deviation = 8) and (S2) 88 probable AD patients (NINCDS-ADRDA criteria), 55 females and 33 males (mean age 74.7 years, standard deviation = 7.8) with mild to moderate symptoms (DSM-IV-TR). Attention is given to sample size and the use of state of the art open source tools (LetsWave and WEKA) to process the EEG data. This innovative technique consists in associating Morlet wavelet filter with a support vector machine technique. A total of 111 EEG features (attributes) were obtained for 162 probands. The results were accuracy of 92.72% and area under the curve of 0.92 (percentage split test). Most important, comparing a single patient versus the total data set resulted in accuracy of 84.56% (leave-one-patient-out test). Particular emphasis was on clinical diagnosis and feasibility of implementation of this low-cost procedure, because programming knowledge is not required. Consequently, this new method can be useful to support AD diagnosis in resource-limited settings.

Laplacian based non-local means denoising of MR images with Rician noise

Magnetic Resonance (MR) image is often corrupted with a complex white Gaussian noise (Rician noise) which is signal dependent. Considering the special characteristics of Rician noise, we carry out nonlocal means denoising on squared magnitude images and compensate the introduced bias. In this paper, we propose an algorithm which not only preserves the edges and fine structures but also performs efficient denoising. For this purpose we have used a Laplacian of Gaussian (LoG) filter in conjunction with a nonlocal means filter (NLM). Further, to enhance the edges and to accelerate the filtering process, only a few similar patches have been preselected on the basis of closeness in edge and inverted mean values. Experiments have been conducted on both simulated and clinical data sets. The qualitative and quantitative measures demonstrate the efficacy of the proposed method.

Statistical characterization of portal images and noise from portal imaging systems

In this paper, we consider the statistical characteristics of the so-called portal images, which are acquired prior to the radiotherapy treatment, as well as the noise that present the portal imaging systems, in order to analyze whether the well-known noise and image features in other image modalities, such as natural image, can be found in the portal imaging modality. The study is carried out in the spatial image domain, in the Fourier domain, and finally in the wavelet domain. The probability density of the noise in the spatial image domain, the power spectral densities of the image and noise, and the marginal, joint, and conditional statistical distributions of the wavelet coefficients are estimated. Moreover, the statistical dependencies between noise and signal are investigated. The obtained results are compared with practical and useful references, like the characteristics of the natural image and the white noise. Finally, we discuss the implication of the results obtained in several noise reduction methods that operate in the wavelet domain.

A CURE for noisy magnetic resonance images: chi-square unbiased risk estimation

n this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon most state-of-the-art methods for both simulated and actual magnetic resonance image data.

Improved DCT-based nonlocal means filter for MR images denoising

The nonlocal means (NLM) filter has been proven to be an efficient feature-preserved denoising method and can be applied to remove noise in the magnetic resonance (MR) images. To suppress noise more efficiently, we present a novel NLM filter based on the discrete cosine transform (DCT). Instead of computing similarity weights using the gray level information directly, the proposed method calculates similarity weights in the DCT subspace of neighborhood. Due to promising characteristics of DCT, such as low data correlation and high energy compaction, the proposed filter is naturally endowed with more accurate estimation of weights thus enhances denoising effectively. The performance of the proposed filter is evaluated qualitatively and quantitatively together with two other NLM filters, namely, the original NLM filter and the unbiased NLM (UNLM) filter. Experimental results demonstrate that the proposed filter achieves better denoising performance in MRI compared to the others.

Wavelet-based de-noising techniques in MRI

The paper deals with techniques for the enhancement of magnetic resonance (MR) images using the wavelet analysis, which is assessed from the viewpoint of choosing the mother wavelet and the thresholding technique. Three parameters are used as objective criteria of the quality of image enhancement: the signal-to-noise ratio (SNR), image contrast, and linear approximation of edge steepness. Unlike most of the standard methods, which work exclusively with image magnitude, we also examined the influence of image phase, i.e. the image is processed as a complex signal. In addition to the interpretation of results, a short summary is given that deals with the choice of the optimal mother wavelet and thresholding technique for different types of MR images.

A wavelet multiscale denoising algorithm for magnetic resonance (MR) images

Based on the Radon transform, a wavelet multiscale denoising method is proposed for MR images. The approach explicitly accounts for the Rician nature of MR data. Based on noise statistics we apply the Radon transform to the original MR images and use the Gaussian noise model to process the MR sinogram image. A translation invariant wavelet transform is employed to decompose the MR 'sinogram' into multiscales in order to effectively denoise the images. Based on the nature of Rician noise we estimate noise variance in different scales. For the final denoised sinogram we apply the inverse Radon transform in order to reconstruct the original MR images. Phantom, simulation brain MR images, and human brain MR images were used to validate our method. The experiment results show the superiority of the proposed scheme over the traditional methods. Our method can reduce Rician noise while preserving the key image details and features. The wavelet denoising method can have wide applications in MRI as well as other imaging modalities.

Quasi-Monte Carlo estimation approach for denoising MRI data based on regional statistics

An important postprocessing step for MR data is noise reduction. Noise in MR data is difficult to suppress due to its signal-dependence. To address this issue, a novel stochastic approach to noise reduction for MR data is presented. The estimation of the noise-free signal is formulated as a general bayesian least-squares estimation problem and solved using a quasi-Monte Carlo method that takes into account the statistical characteristics of the underlying noise and the regional statistics of the observed signal in a data-adaptive manner. A set of experiments were performed to compare the proposed quasi-Monte Carlo estimation (QMCE) method to state-of-the-art wavelet-based MR noise reduction (WAVE) and nonlocal means MR noise reduction (NLM) methods using MR data volumes with synthetic noise, as well as real noise-contaminated MR data. Experimental results show that QMCE is capable of achieving state-of-the-art performance when compared to WAVE and NLM methods quantitatively in SNR, mean structural similarity (MSSIM), and contrast measures. Visual comparisons show that QMCE provides effective noise suppression, while better preserving tissue structural boundaries and restoring contrast.

Optimization of k-space trajectories for compressed sensing by Bayesian experimental design

The optimization of k-space sampling for nonlinear sparse MRI reconstruction is phrased as a Bayesian experimental design problem. Bayesian inference is approximated by a novel relaxation to standard signal processing primitives, resulting in an efficient optimization algorithm for Cartesian and spiral trajectories. On clinical resolution brain image data from a Siemens 3T scanner, automatically optimized trajectories lead to significantly improved images, compared to standard low-pass, equispaced, or variable density randomized designs. Insights into the nonlinear design optimization problem for MRI are given.

Wavelet-domain medical image denoising using bivariate laplacian mixture model

In this paper, we proposed novel noise reduction algorithms that can be used to enhance image quality in various medical imaging modalities such as magnetic resonance and multidetector computed tomography. The noisy captured 3-D data are first transformed by discrete complex wavelet transform. Using a nonlinear function, we model the data as the sum of the clean data plus additive Gaussian or Rayleigh noise. We use a mixture of bivariate Laplacian probability density functions for the clean data in the transformed domain. The MAP and minimum mean-squared error (MMSE) estimators allow us to efficiently reduce the noise. The employed prior distribution is mixture and bivariate, and thus accurately characterizes the heavy-tail distribution of clean images and exploits the interscale properties of wavelets coefficients. In addition, we estimate the parameters of the model using local information; as a result, the proposed denoising algorithms are spatially adaptive, i.e., the intrascale dependency of wavelets is also well exploited in the enhancement process. The proposed approach results in significant noise reduction while the introduced distortions are not noticeable as a result of accurate statistical modeling. The obtained shrinkage functions have closed form, are simple in implementation, and efficiently enhances data. Our experiments on CT images show that among our derived shrinkage functions usually BiLapGausMAP produces images with higher peak SNR. However, BiLapGausMMSE is preferred especially for CT images, which have high SNRs. Furthermore, BiLapRayMAP yields better noise reduction performance for low SNR MR datasets such as high-resolution whole heart imaging while BiLapGauMAP results in better performance in MR data with higher intrinsic SNR such as functional cine data.

Partitioned image filtering for reduction of the Gibbs phenomenon

The aim of this paper is to propose a partitioned-image filtering technique that is a new way of reducing the Gibbs phenomenon in filtered images.

METHODS

This technique relies on exploiting the properties of the Gibbs phenomenon and on assumptions about the structure of the image. The amplitude of the Gibbs ringing is directly proportional to the height of the image discontinuity. If the height of the discontinuity can be reduced, then the subsequent ringing will also be reduced. Separating the image into stratified layers or partitions reduces the height of the discontinuity significantly. Each partition is filtered separately and recombined nonlinearly to yield the final filtered image. This method weakens filtering of image edges that have large discontinuities, thus reducing the Gibbs phenomenon while simultaneously reducing the image noise.

RESULTS

The proposed filtering method has been applied to a simple image with only 2 intensity values to illustrate the implementation steps. The method has also been applied to 2 SPECT patient studies to show the effectiveness of the proposed filtering method, which can significantly reduce the Gibbs artifacts.

CONCLUSION

The Gibbs phenomenon in a filtered image can be reduced by partitioning the image so that the amplitude of the discontinuity is controlled. The proposed method is efficient and simple in implementation, with fast Fourier transform.

A fast multilevel algorithm for wavelet-regularized image restoration

We present a multilevel extension of the popular "thresholded Landweber" algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targeted towards large-scale linear inverse problems, such as 3-D deconvolution microscopy. The algorithm is derived within the framework of bound optimization. The key idea is to successively update the coefficients in the various wavelet channels using fixed, subband-adapted iteration parameters (step sizes and threshold levels). The optimization problem is solved efficiently via a proper chaining of basic iteration modules. The higher level description of the algorithm is similar to that of a multigrid solver for PDEs, but there is one fundamental difference: the latter iterates though a sequence of multiresolution versions of the original problem, while, in our case, we cycle through the wavelet subspaces corresponding to the difference between successive approximations. This strategy is motivated by the special structure of the problem and the preconditioning properties of the wavelet representation. We establish that the solution of the restoration problem corresponds to a fixed point of our multilevel optimizer. We also provide experimental evidence that the improvement in convergence rate is essentially determined by the (unconstrained) linear part of the algorithm, irrespective of the type of wavelet. Finally, we illustrate the technique with some image deconvolution examples, including some real 3-D fluorescence microscopy data.

A nonlocal maximum likelihood estimation method for Rician noise reduction in MR images

Postacquisition denoising of magnetic resonance (MR) images is of importance for clinical diagnosis and computerized analysis, such as tissue classification and segmentation. It has been shown that the noise in MR magnitude images follows a Rician distribution, which is signal-dependent when signal-to-noise ratio (SNR) is low. It is particularly difficult to remove the random fluctuations and bias introduced by Rician noise. The objective of this paper is to estimate the noise free signal from MR magnitude images. We model images as random fields and assume that pixels which have similar neighborhoods come from the same distribution. We propose a nonlocal maximum likelihood (NLML) estimation method for Rician noise reduction. Our method yields an optimal estimation result that is more accurate in recovering the true signal from Rician noise than NL means algorithm in the sense of SNR, contrast, and method error. We demonstrate that NLML performs better than the conventional local maximum likelihood (LML) estimation method in preserving and defining sharp tissue boundaries in terms of a well-defined sharpness metric while also having superior performance in method error.

Wavelet denoising in voxel-based parametric estimation of small animal PET images: a systematic evaluation of spatial constraints and noise reduction algorithms

Voxel-based estimation of PET images, generally referred to as parametric imaging, can provide invaluable information about the heterogeneity of an imaging agent in a given tissue. Due to high level of noise in dynamic images, however, the estimated parametric image is often noisy and unreliable. Several approaches have been developed to address this challenge, including spatial noise reduction techniques, cluster analysis and spatial constrained weighted nonlinear least-square (SCWNLS) methods. In this study, we develop and test several noise reduction techniques combined with SCWNLS using simulated dynamic PET images. Both spatial smoothing filters and wavelet-based noise reduction techniques are investigated. In addition, 12 different parametric imaging methods are compared using simulated data. With the combination of noise reduction techniques and SCWNLS methods, more accurate parameter estimation can be achieved than with either of the two techniques alone. A less than 10% relative root-mean-square error is achieved with the combined approach in the simulation study. The wavelet denoising based approach is less sensitive to noise and provides more accurate parameter estimation at higher noise levels. Further evaluation of the proposed methods is performed using actual small animal PET datasets. We expect that the proposed method would be useful for cardiac, neurological and oncologic applications.

A fast thresholded landweber algorithm for wavelet-regularized multidimensional deconvolution

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the l(1)-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alternating between a Landweber iteration and a wavelet-domain soft-thresholding operation. While having the advantage of simplicity, they are known to converge slowly. By expressing the cost functional in a Shannon wavelet basis, we are able to decompose the problem into a series of subband-dependent minimizations. In particular, this allows for larger (subband-dependent) step sizes and threshold levels than the previous method. This improves the convergence properties of the algorithm significantly. We demonstrate a speed-up of one order of magnitude in practical situations. This makes wavelet-regularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3-D deconvolution microscopy, where the size of typical data sets does not permit more than a few tens of iterations.