Jan Aelterman

Augmented Lagrangian based reconstruction of non-uniformly sub-Nyquist sampled MRI data☆

Abstract MRI has recently been identified as a promising application for compressed-sensing-like regularization because of its potential to speed up the acquisition while maintaining the image quality. Thereby non-uniform k-space trajectories, such as random or spiral trajectories, are becoming more and more important, because they are well suited to be used within the compressed-sensing (CS) acquisition framework. In this paper, we propose a new reconstruction technique for non-uniformly sub-Nyquist sampled k-space data. Several parts make up this technique, such as the non-uniform Fourier transform (NUFT), the discrete shearlet transform and a augmented Lagrangian based optimization algorithm. Because MRI images are real-valued, we introduce a new imaginary value suppressing prior, which attenuates imaginary components of MRI images during reconstruction, resulting in a better overall image quality. Further, a preconditioning based on the Voronoi cell size of each NUFT data point speeds up the conjugate gradient optimization used as part of the optimization algorithm. The resulting algorithm converges in a relatively small number of iterations and guarantees solutions that fully comply to the imposed constraints. The results show that the algorithm is applicable not only to sub-Nyquist sampled k-space reconstruction, but also to MR image fusion and/or resolution enhancement.

Isotropic non-white matter partial volume effects in constrained spherical deconvolution.

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a non-invasive imaging method, which can be used to investigate neural tracts in the white matter (WM) of the brain. Significant partial volume effects (PVEs) are present in the DW signal due to relatively large voxel sizes. These PVEs can be caused by both non-WM tissue, such as gray matter (GM) and cerebrospinal fluid (CSF), and by multiple non-parallel WM fiber populations. High angular resolution diffusion imaging (HARDI) methods have been developed to correctly characterize complex WM fiber configurations, but to date, many of the HARDI methods do not account for non-WM PVEs. In this work, we investigated the isotropic PVEs caused by non-WM tissue in WM voxels on fiber orientations extracted with constrained spherical deconvolution (CSD). Experiments were performed on simulated and real DW-MRI data. In particular, simulations were performed to demonstrate the effects of varying the diffusion weightings, signal-to-noise ratios (SNRs), fiber configurations, and tissue fractions. Our results show that the presence of non-WM tissue signal causes a decrease in the precision of the detected fiber orientations and an increase in the detection of false peaks in CSD. We estimated 35–50% of WM voxels to be affected by non-WM PVEs. For HARDI sequences, which typically have a relatively high degree of diffusion weighting, these adverse effects are most pronounced in voxels with GM PVEs. The non-WM PVEs become severe with 50% GM volume for maximum spherical harmonics orders of 8 and below, and already with 25% GM volume for higher orders. In addition, a low diffusion weighting or SNR increases the effects. The non-WM PVEs may cause problems in connectomics, where reliable fiber tracking at the WM–GM interface is especially important. We suggest acquiring data with high diffusion-weighting 2500–3000 s/mm2, reasonable SNR (~30) and using lower SH orders in GM contaminated regions to minimize the non-WM PVEs in CSD.

A GPU-Accelerated Real-Time NLMeans Algorithm for Denoising Color Video Sequences

The NLMeans filter, originally proposed by Buades et al., is a very popular filter for the removal of white Gaussian noise, due to its simplicity and excellent performance. The strength of this filter lies in exploiting the repetitive character of structures in images. However, to fully take advantage of the repetitivity a computationally extensive search for similar candidate blocks is indispensable. In previous work, we presented a number of algorithmic acceleration techniques for the NLMeans filter for still grayscale images. In this paper, we go one step further and incorporate both temporal information and color information into the NLMeans algorithm, in order to restore video sequences. Starting from our algorithmic acceleration techniques, we investigate how the NLMeans algorithm can be easily mapped onto recent parallel computing architectures. In particular, we consider the graphical processing unit (GPU), which is available on most recent computers. Our developments lead to a high-quality denoising filter that can process DVD-resolution video sequences in real-time on a mid-range GPU.

Efficient design of a low redundant Discrete Shearlet Transform

Recently, there has been a huge interest in multiresolution representations that also perform a multidirectional analysis. The Shearlet transform provides both a multiresolution analysis (such as the wavelet transform), and at the same time an optimally sparse image-independent representation for images containing edges. Existing discrete implementations of the Shearlet transform havemainly focused on specific applications, such as edge detection or denoising, and were not designed with a low redundancy in mind (the redundancy factor is typically larger than the number of orientation subbands in the finest scale). In this paper, we present a novel design of a Discrete Shearlet Transform, that can have a redundancy factor of 2.6, independent of the number of orientation subbands, and that has many interesting properties, such as shift-invariance and self-invertability. This transform can be used in a wide range of applications. Experiments are provided to show the improved characteristics of the transform.

The effect of Gibbs ringing artifacts on measures derived from diffusion MRI.

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a unique method to investigate microstructural tissue properties noninvasively and is one of the most popular methods for studying the brain white matter in vivo. To obtain reliable statistical inferences with diffusion MRI, however, there are still many challenges, such as acquiring high-quality DW-MRI data (e.g., high SNR and high resolution), careful data preprocessing (e.g., correcting for subject motion and eddy current induced geometric distortions), choosing the appropriate diffusion approach (e.g., diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), or diffusion spectrum MRI), and applying a robust analysis strategy (e.g., tractography based or voxel based analysis). Notwithstanding the numerous efforts to optimize many steps in this complex and lengthy diffusion analysis pipeline, to date, a well-known artifact in MRI--i.e., Gibbs ringing (GR)--has largely gone unnoticed or deemed insignificant as a potential confound in quantitative DW-MRI analysis. Considering the recent explosion of diffusion MRI applications in biomedical and clinical applications, a systematic and comprehensive investigation is necessary to understand the influence of GR on the estimation of diffusion measures. In this work, we demonstrate with simulations and experimental DW-MRI data that diffusion estimates are significantly affected by GR artifacts and we show that an off-the-shelf GR correction procedure based on total variation already can alleviate this issue substantially.

Informed constrained spherical deconvolution (iCSD)

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a noninvasive imaging method, which can be used to investigate neural tracts in the white matter (WM) of the brain. However, the voxel sizes used in DW-MRI are relatively large, making DW-MRI prone to significant partial volume effects (PVE). These PVEs can be caused both by complex (e.g. crossing) WM fiber configurations and non-WM tissue, such as gray matter (GM) and cerebrospinal fluid. High angular resolution diffusion imaging methods have been developed to correctly characterize complex WM fiber configurations, but significant non-WM PVEs are also present in a large proportion of WM voxels. In constrained spherical deconvolution (CSD), the full fiber orientation distribution function (fODF) is deconvolved from clinically feasible DW data using a response function (RF) representing the signal of a single coherently oriented population of fibers. Non-WM PVEs cause a loss of precision in the detected fiber orientations and an emergence of false peaks in CSD, more prominently in voxels with GM PVEs. We propose a method, informed CSD (iCSD), to improve the estimation of fODFs under non-WM PVEs by modifying the RF to account for non-WM PVEs locally. In practice, the RF is modified based on tissue fractions estimated from high-resolution anatomical data. Results from simulation and in-vivo bootstrapping experiments demonstrate a significant improvement in the precision of the identified fiber orientations and in the number of false peaks detected under GM PVEs. Probabilistic whole brain tractography shows fiber density is increased in the major WM tracts and decreased in subcortical GM regions. The iCSD method significantly improves the fiber orientation estimation at the WM-GM interface, which is especially important in connectomics, where the connectivity between GM regions is analyzed.

Realistic camera noise modeling with application to improved HDR synthesis

Due to the ongoing miniaturization of digital camera sensors and the steady increase of the “number of megapixels”, individual sensor elements of the camera become more sensitive to noise, even deteriorating the final image quality. To go around this problem, sophisticated processing algorithms in the devices, can help to maximally exploit the knowledge on the sensor characteristics (e.g., in terms of noise), and offer a better image reconstruction. Although a lot of research focuses on rather simplistic noise models, such as stationary additive white Gaussian noise, only limited attention has gone to more realistic digital camera noise models. In this article, we first present a digital camera noise model that takes several processing steps in the camera into account, such as sensor signal amplification, clipping, post-processing,.. We then apply this noise model to the reconstruction problem of high dynamic range (HDR) images from a small set of low dynamic range (LDR) exposures of a static scene. In literature, HDR reconstruction is mostly performed by computing a weighted average, in which the weights are directly related to the observer pixel intensities of the LDR image. In this work, we derive a Bayesian probabilistic formulation of a weighting function that is near-optimal in the MSE sense (or SNR sense) of the reconstructed HDR image, by assuming exponentially distributed irradiance values. We define the weighting function as the probability that the observed pixel intensity is approximately unbiased. The weighting function can be directly computed based on the noise model parameters, which gives rise to different symmetric and asymmetric shapes when electronic noise or photon noise is dominant. We also explain how to deal with the case that some of the noise model parameters are unknown and explain how the camera response function can be estimated using the presented noise model. Finally, experimental results are provided to support our findings.

Compass: a joint framework for Parallel Imaging and Compressive Sensing in MRI

Parallel Imaging MRI (pMRI) and Compressive Sensing (CS) are two reconstruction techniques that have recently been applied to increase MRI performance. In this paper we demonstrate that a combined analysis of the pMRI and CS problems leads to a conceptually simple, yet effective technique that outperforms independent approaches to both reconstruction problems. We argue that the proposed technique is also naturally resilient to noise, due to its relation to the MAP image denoising formulation. A modified Basis Pursuit (BP) formulation of the CS-MRI problem allows it to handle the pMRI problem at the same time. We also present an exact solution to this BP problem, using the split Bregman technique, with discrete shearlet transform (DST) regularization. The DST is an excellent choice for natural image applications, due to its optimal sparsity property. Results show that this Compressive Parallel Sensing (COMPASS) reconstruction algorithm outperforms more traditional MRI reconstruction algorithms in both pMRI and CS experiments.

Design of a tight frame of 2D shearlets based on a fast non-iterative analysis and synthesis algorithm

The shearlet transform is a recent sibling in the family of geometric image representations that provides a traditional multiresolution analysis combined with a multidirectional analysis. In this paper, we present a fast DFT-based analysis and synthesis scheme for the 2D discrete shearlet transform. Our scheme conforms to the continuous shearlet theory to high extent, provides perfect numerical reconstruction (up to floating point rounding errors) in a non-iterative scheme and is highly suitable for parallel implementation (e.g. FPGA, GPU). We show that our discrete shearlet representation is also a tight frame and the redundancy factor of the transform is around 2.6, independent of the number of analysis directions. Experimental denoising results indicate that the transform performs the same or even better than several related multiresolution transforms, while having a significantly lower redundancy factor.

Hyperspectral image deblurring with PCA and total variation

In this paper, we propose a novel algorithm for hyper-spectral (HS) image deblurring with principal component analysis (PCA) and total variation (TV). We first decorrelate the HS images and separate the information content from the noise by means of PCA. Then, we employ the TV method to jointly denoise and deblur the first principal components (PCs). Subsequently, noise in the last principal components is suppressed using a simple soft-thresholding scheme, for computational efficiency. Experimental results on simulated and real HS images are very encouraging.