[Show abstract][Hide abstract] ABSTRACT: We propose a novel formulation for relaxed analysis-based sparsity in multiple dictionaries as a general type of prior for images, and apply it for Bayesian estimation in image restoration problems. Our formulation of a L2-relaxed L0 pseudonorm prior allows for an especially simple MAP estimation iterative marginal optimization algorithm, whose convergence we prove. We achieve a significant speed-up over the direct (static) solution by using dynamically evolving parameters through the estimation loop. As an added heuristic twist, we fix in advance the number of iterations, and then empirically optimize the involved parameters according to two performance benchmarks. The resulting constrained dynamic method is not just fast and effective, it is also highly robust and flexible. First, it is able to provide an outstanding trade-off between computational load and performance, in visual and objective -MSE, SSIM- terms, for a large variety of degradation tests, using the same set of parameter values for all tests. Second, the performance benchmark can be easily adapted to specific types of degradation, image classes, and even performance criteria. Third, it allows for using simultaneously several dictionaries with complementary features. This unique combination makes ours a highly practical deconvolution method.
Full-text · Article · Nov 2015 · IEEE Transactions on Image Processing
[Show abstract][Hide abstract] ABSTRACT: Acquisition parameters play a crucial role in Diffusion Tensor Imaging (DTI), as they have a major impact on the values of scalar measures such as Fractional Anisotropy (FA) or Mean Diffusivity (MD) that are usually the focus of clinical studies based on white matter analysis. This paper presents an analysis on the impact of the variation of several acquisition parameters on these scalar measures with a novel double focus. First, a tractography-based approach is employed, motivated by the significant number of clinical studies that are carried out using this technique. Second, the consequences of simultaneous changes in multiple parameters are analyzed: number of gradient directions, b-value and voxel resolution. Results indicate that the FA is most affected by changes in the number of gradients and voxel resolution, while MD is specially influenced by variations in the b-value. Even if the choice of a tractography algorithm has an effect on the numerical values of the final scalar measures, the evolution of these measures when acquisition parameters are modified is parallel.
[Show abstract][Hide abstract] ABSTRACT: GRAPPA is a well-known parallel imaging method that recovers the MR magnitude image from aliasing by using a weighted interpolation of the data in k-space. To estimate the optimal reconstruction weights, GRAPPA uses a band along the center of the k-space where the signal is sampled at the Nyquist rate, the so-called autocalibrated (ACS) lines. However, while the subsampled lines usually belong to the medium- to high-frequency areas of the spectrum, the ACS lines include the low-frequency areas around the DC component. The use for estimation and reconstruction of areas of the k-space with very different features may negatively affect the final reconstruction quality. We propose a simple, yet powerful method to eliminate reconstruction artifacts, based on the discrimination of the low-frequency spectrum.
The proposal to improve the estimation of the weights lays on a proper selection of the coefficients within the ACS lines, which advises discarding those points around the DC component. A simple approach is the elimination of a square window in the center of the k-space, although more developed approaches can be used.
The method is tested using real multiple-coil MRI acquisitions. We empirically show this approach achieves great enhancement rates, while keeping the same complexity of the original GRAPPA and reducing the g-factor. The reconstruction is even more accurate when combined with other reconstruction methods. Improvement rates of 35 % are achieved for 32 ACS and acceleration rate of 3.
The method proposed highly improves the accuracy of the GRAPPA coefficients and therefore the final image reconstruction. The method is fully compatible with the original GRAPPA formulation and with other optimization methods proposed in literature, and it can be easily implemented into the commercial scanning software.
No preview · Article · Mar 2015 · International Journal of Computer Assisted Radiology and Surgery
[Show abstract][Hide abstract] ABSTRACT: Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE is one of the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. However, the SENSE reconstruction process yields to a variance of noise value which is dependent on the position within the image. Hence, the traditional noise estimation methods based on a single noise level for the whole image fail. Accordingly, we propose a novel method to recover the complete spatial pattern of the variance of noise in SENSE reconstructed images up from the sensitivity maps of each receiver coil. Our method fits applications in statistical image processing tasks such as image denoising.
No preview · Article · Jul 2013 · Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference
[Show abstract][Hide abstract] ABSTRACT: Recently, some methods have been proposed for filtering multi-coil MRI acquisitions with correlation between coils. Those methods are based on statistical models of noise to develop a Linear Minimum Mean Square Error (LMMSE) filter. The advantage of LMMSE-based filters stems from their simplicity and robustness. However, they exhibit some drawbacks: their performance strongly depends on the underlying statistical model and on the way the local moments are estimated. The first problem can be avoided when considering effective values provided by recent studies on the models of noise in multi-coil systems with correlation between coils. However, the local moments are estimated in square neighborhoods which can include different kinds of tissues. Thus, the local variance is biased towards upper values, which results in an inaccurate estimate in regions close to tissue boundaries. In this work we propose to overcome this problem by introducing an anisotropic diffusion step in the LMMSE estimate for correlated multi-coil systems which improves the estimation of the signal in regions where other LMMSE methods fail. Results demonstrate the better behavior in different noisy scenarios.
Full-text · Article · Jul 2013 · Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference
[Show abstract][Hide abstract] ABSTRACT: We present a new method for denoising of Diffusion Weighted Images (DWI) that shares several desirable features of state-of-the-art proposals: 1) it works with the squared-magnitude signal, allowing for a closed-form formulation as a Linear Minimum Mean Squared Error (LMMSE) estimator, a.k.a. Wiener filter; 2) it jointly accounts for the DWI channels altogether, being able to unveil anatomical structures that remain hidden in each separated channel; 3) it uses a Non-Local Means (NLM)-like scheme to discriminate voxels corresponding to different fiber bundles, being able to enhance the anatomical structures of the DWI. We report extensive experiments evidencing the new approach outperforms several related methods for all the range of input signal-to-noise ratios (SNR). An open-source C++ implementation of the algorithm is also provided for the sake of reproducibility.
No preview · Article · Jul 2013 · Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference
[Show abstract][Hide abstract] ABSTRACT: A new technique for multi-point collision response among 3D objects is presented. The method is applied to the interpenetration between deformable and non-deformable models. Accuracy in the response to collided points is a critical premise that determines the fidelity and the stability of the subsequent deformations. Previous approaches assume a set of simplifications in the collision models that usually derives in inadequate model behaviors. The method pursues a twofold objective: (1) to consider the 3D character of the surgical instruments (2) to cope with the complex nature, concavities and convexities, of the interpenetrated volume. For that purpose, an overall approximation of a local deformation is performed. First, the fidelity of each local deformation is modeled as a combination of penetration and sliding forces inferred from a feedback fuzzy logic system, and, second, the stability of the global deformation is ensured by the definition of an homeomorphic transformation which enforces the preservation of the topology of deformable objects. A linear combination of a set of Compact Supported Radial Basis Functions (CS-RBF) provides a customary mathematical description for finding a smooth displacement field. The resulting deformation field is thus expressed as an optimization problem. Preliminary results show its suitability and benefits for surgical simulation.
[Show abstract][Hide abstract] ABSTRACT: Parallel magnetic resonance imaging (MRI) yields noisy magnitude data, described in most cases as following a noncentral χ distribution when the signals received by the coils are combined as the sum of their squares. One well-known case of this noncentral χ noise model is the Rician model, but it is only valid in the case of single-channel acquisition. Although the use of parallel MRI is increasingly common, most of the correction methods still perform Rician noise removal, yielding an erroneous result due to an incorrect noise model. Moreover, the existence of noise correlations in phased array systems renders noise nonstationary and further modifies the noise description in parallel MRI. However, the noncentral χ model has been demonstrated to work as a good approximation as long as effective voxelwise parameters are used. A good correction step, adapted to the right noise model, is of paramount importance, especially when working with diffusion-weighted MR data, whose signal-to-noise ratio is low. In this paper, we present a noise removal technique designed to be fast enough for integration into a real-time reconstruction system, thus offering the convenience of obtaining corrected data almost instantaneously during the MRI scan. Our method employs the noncentral χ noise model and uses a simplified method to account for noise correlations; this leads to an efficient and rapid correction. The method consists of an anisotropic extension of the Linear Minimum Mean Square Error estimator (LMMSE) that is a far better edge-preserving method than the traditional LMMSE and addresses noncentral χ distributions along with empirically computed global effective parameters. The results on simulated and real data demonstrate that this anisotropic extended LMMSE outperforms the original LMMSE on images corrupted by noncentral χ noise. Moreover, in comparison with the existing LMMSE technique incorporating the estimation of voxelwise effective parameters, our method yields improved results.
Full-text · Article · May 2013 · Magnetic Resonance Imaging
[Show abstract][Hide abstract] ABSTRACT: Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k − space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods—based on a single noise level for the whole image—fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.
No preview · Article · Jan 2013 · Magnetic Resonance Imaging
[Show abstract][Hide abstract] ABSTRACT: Modern magnetic resonance (MR) imaging protocols based on multiple-coil acquisitions have carried on a new attention to noise and signal statistical modeling, as long as most of the existing techniques for data processing are model based. In particular, nonaccelerated multiple-coil and GeneRalized Autocalibrated Partially Parallel Acquisitions (GRAPPA) have brought noncentral-χ (nc-χ) statistics into stake as a suitable substitute for traditional Rician distributions. However, this model is only valid when the signals received by each coil are roughly uncorrelated. The recent literature on this topic suggests that this is often not the case, so nc-χ statistics are in principle not adequate. Fortunately, such model can be adapted through the definition of a set of effective parameters, namely, an effective noise power (greater than the actual power of thermal noise in the Radio Frequency receiver) and an effective number of coils (smaller than the actual number of RF receiving coils in the system). The implications of these artifacts in practical algorithms have not been discussed elsewhere. In the present paper, we aim to study their actual impact and suggest practical rules to cope with them. We define the main noise parameters in this context, introducing a new expression for the effective variance of noise which is of capital importance for the two image processing problems studied: first, we propose a new method to estimate the effective variance of noise from the composite magnitude signal of MR data when correlations are assumed. Second, we adapt several model-based image denoising techniques to the correlated case using the noise estimation techniques proposed. We show, through a number of experiments with synthetic, phantom, and in vivo data, that neglecting the correlated nature of noise in multiple-coil systems implies important errors even in the simplest cases. At the same time, the proper statistical characterization of noise through effective parameters drives to improved accuracy (both qualitatively and quantitatively) for both of the problems studied.
No preview · Article · Oct 2012 · Magnetic Resonance Imaging
[Show abstract][Hide abstract] ABSTRACT: Linear Minimum Mean Squared Error Estimation (LMMSE) is a simple, yet powerful denoising technique within MRI. It is based on the computation of the mean and variance of the data being filtered according to a noise model assumed, which is usually accomplished by calculating local moments over squared neighborhoods. When these neighborhoods are centered in pixels corresponding to image contours, the estimation is not accurate due to the presence of two or more tissues with different statistical properties. We overcome this limitation by introducing an anisotropic LMMSE scheme: the gray levels of each tissue in the MRI volume are modeled as a Gamma-mixture, such that we can discriminate between thedifferent matters to construct anisotropic neighborhoods containing only one kind of tissue. The potential of the Gamma distribution relies on its ability to fit both the Rician distribution traditionally used to model the noise in MRI and the non-central Chi noise found in modern parallel MRI systems.
[Show abstract][Hide abstract] ABSTRACT: Least Squares (LS) and its minimum variance counterpart, Weighted Least Squares (WLS), have become very popular when estimating the Diffusion Tensor (DT), to the point that they are the standard in most of the existing software for diffusion MRI. They are based on the linearization of the Stejskal-Tanner equation by means of the logarithmic compression of the diffusion signal. Due to the Rician nature of noise in traditional systems, a certain bias in the estimation is known to exist. This artifact has been made patent through some experimental set-ups, but it is not clear how the distortion translates in the reconstructed DT, and how important it is when compared to the other source of error contributing to the Mean Squared Error (MSE) in the estimate, i.e. the variance. In this paper we propose the analytical characterization of log-Rician noise and its propagation to the components of the DT through power series expansions. We conclude that even in highly noisy scenarios the bias for log-Rician signals remains moderate when compared to the corresponding variance. Yet, with the advent of Parallel Imaging (pMRI), the Rician model is not always valid. We make our analysis extensive to a number of modern acquisition techniques through the study of a more general Non Central-Chi (nc-χ) model. Since WLS techniques were initially designed bearing in mind Rician noise, it is not clear whether or not they still apply to pMRI. An important finding in our work is that the common implementation of WLS is nearly optimal when nc-χ noise is considered. Unfortunately, the bias in the estimation becomes far more important in this case, to the point that it may nearly overwhelm the variance in given situations. Furthermore, we evidence that such bias cannot be removed by increasing the number of acquired gradient directions. A number of experiments have been conducted that corroborate our analytical findings, while in vivo data have been used to test the actual relevance of the bias in the estimation.
[Show abstract][Hide abstract] ABSTRACT: Diffusion tensor imaging (DTI) constitutes the most used paradigm among the diffusion-weighted magnetic resonance imaging (DW-MRI) techniques due to its simplicity and application potential. Recently, real-time estimation in DW-MRI has deserved special attention, with several proposals aiming at the estimation of meaningful diffusion parameters during the repetition time of the acquisition sequence. Specifically focusing on DTI, the underlying model of the noise present in the acquired data is not taken into account, leading to a suboptimal estimation of the diffusion tensor. In this paper, we propose an optimal real-time estimation framework for DTI reconstruction in single-coil acquisitions. By including an online estimation of the time-changing noise variance associated to the acquisition process, the proposed method achieves the sequential best linear unbiased estimator. Results on both synthetic and real data show that our method outperforms those so far proposed, reaching the best performance of the existing proposals by processing a substantially lower number of diffusion images.
No preview · Article · Feb 2012 · Magnetic Resonance Imaging
[Show abstract][Hide abstract] ABSTRACT: Noise in the composite magnitude signal from multiple-coil systems is usually assumed to follow a noncentral χ distribution when sum of squares is used to combine images sensed at different coils. However, this is true only if the variance of noise is the same for all coils, and no correlation exists between them. We show how correlations may be obviated from this model if effective values are considered. This implies a reduced effective number of coils and an increased effective variance of noise. In addition, the effective variance of noise becomes signal-dependent.
No preview · Article · Feb 2012 · Magnetic Resonance in Medicine
[Show abstract][Hide abstract] ABSTRACT: The Funk-Radon Transform allows to approximate the central section integral of the diffusion signal to compute probabilistic Orientation Distribution Functions (ODF) of fiber populations, provided the behavior for the b-values not acquired is known. To relax the latter demand, it has been proposed to compute instead the integral inside the disk defined in the central section by the b-value acquired. The price to pay is low-pass filtering the ODF, cropping the information it provides. We propose a method to palliate this problem with negligible computational overload. Not only it improves the accuracy in the determination of the diffusion directions, but it also refines the crossing angles that can be resolved.
No preview · Article · Jan 2012 · Proceedings / IEEE International Symposium on Biomedical Imaging: from nano to macro. IEEE International Symposium on Biomedical Imaging
[Show abstract][Hide abstract] ABSTRACT: The nonlocal means (NLM) filter has become a popular approach for denoising medical images due to its excellent performance. However, its heavy computational load has been an important shortcoming preventing its use. NLM works by averaging pixels in nonlocal vicinities, weighting them depending on their similarity with the pixel of interest. This similarity is assessed based on the squared difference between corresponding pixels inside local patches centered at the locations compared. Our proposal is to reduce the computational load of this comparison by checking only a subset of salient features associated to the pixels, which suffice to estimate the actual difference as computed in the original NLM approach. The speedup achieved with respect to the original implementation is over one order of magnitude, and, when compared to more recent NLM improvements for MRI denoising, our method is nearly twice as fast. At the same time, we evidence from both synthetic and in vivo experiments that computing of appropriate salient features make the estimation of NLM weights more robust to noise. Consequently, we are able to improve the outcomes achieved with recent state of the art techniques for a wide range of realistic Signal-to-Noise ratio scenarios like diffusion MRI. Finally, the statistical characterization of the features computed allows to get rid of some of the heuristics commonly used for parameter tuning.
Full-text · Article · Sep 2011 · Computer methods and programs in biomedicine
[Show abstract][Hide abstract] ABSTRACT: The characterization of the distribution of noise in the magnitude MR image is a very important problem within image processing algorithms. The Rician noise assumed in single-coil acquisitions has been the keystone for signal-to-noise ratio estimation, image filtering, or diffusion tensor estimation for years. With the advent of parallel protocols such as sensitivity encoding or Generalized Autocalibrated Partially Parallel Acquisitions that allow accelerated acquisitions, this noise model no longer holds. Since Generalized Autocalibrated Partially Parallel Acquisitions reconstructions yield the combination of the squared signals recovered at each receiving coil, noncentral Chi statistics have been previously proposed to model the distribution of noise. However, we prove in this article that this is a weak model due to several artifacts in the acquisition scheme, mainly the correlation existing between the signals obtained at each coil. Alternatively, we propose to model such correlations with a reduction in the number of degrees of freedom of the signal, which translates in an equivalent nonaccelerated system with a minor number of independent receiving coils and, consequently, a lower signal-to-noise ratio. With this model, a noncentral Chi distribution can be assumed for all pixels in the image, whose effective number of coils and effective variance of noise can be explicitly computed in a closed form from the Generalized Autocalibrated Partially Parallel Acquisitions interpolation coefficients. Extensive experiments over both synthetic and in vivo data sets have been performed to show the goodness of fit of out model.
No preview · Article · Apr 2011 · Magnetic Resonance in Medicine
[Show abstract][Hide abstract] ABSTRACT: In a recent paper, Siddiqui et al. introduced a kernel function to be used as a radial basis function (RBF) in image registration tasks. This function is mainly designed so that the resulting deformation is fairly distributed inside its support. The important property of positive definiteness is checked in the paper erroneously, so that the conclusions inferred are wrong. In this communication, we discuss this point and some other methodological errors in the formulation. In addition, we provide some insights into the importance of positive definiteness, concluding that this property may not be critical, or may even be worthless, in certain interpolation problems.
No preview · Article · Mar 2011 · Pattern Recognition Letters
[Show abstract][Hide abstract] ABSTRACT: A new method to estimate the variance of noise from the composite magnitude signal of GRAPPA reconstructed images is presented. Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. However, the reconstruction process yields to a variance of noise value which is dependent on the position within the image. The proposed method uses information of the GRAPPA reconstruction coefficients and assumes a final non-central chi distribution to recover the spatial pattern of noise.