Super-Resolution and Self-Similarity in Magnetic Resonance Imaging

This thesis is about super-resolution reconstruction (SRR) and self-similarity in MRI. These are two overlapping fields of research and in the studies described here, one has naturally lead to the other. From investigating basic properties of conventional approaches to SRR in MRI and applying these methods to specific research problems, we saw a potential improvement to SRR in MRI by employing the selfsimilarity of the images. Self-similarity is a versatile methodology, and beside using it for SRR, we have performed a thorough investigation of its application to voxelwise classification in MRI. In this introductory chapter, we will briefly give some background on SRR and self-similarity in MRI and introduce the five studies included in the thesis

Multiple sparse representations classification

Sparse representations classification (SRC) is a powerful technique for pixelwise classification of images and it is increasingly being used for a wide variety of image analysis tasks. The method uses sparse representation and learned redundant dictionaries to classify image pixels. In this empirical study we propose to further leverage the redundancy of the learned dictionaries to achieve a more accurate classifier. In conventional SRC, each image pixel is associated with a small patch surrounding it. Using these patches, a dictionary is trained for each class in a supervised fashion. Commonly, redundant/overcomplete dictionaries are trained and image patches are sparsely represented by a linear combination of only a few of the dictionary elements. Given a set of trained dictionaries, a new patch is sparse coded using each of them, and subsequently assigned to the class whose dictionary yields the minimum residual energy.We propose a generalization of this scheme. The method, which we call multiple sparse representations classification (mSRC), is based on the observation that an overcomplete, class specific dictionary is capable of generating multiple accurate and independent estimates of a patch belonging to the class. So instead of finding a single sparse representation of a patch for each dictionary, we find multiple, and the corresponding residual energies provides an enhanced statistic which is used to improve classification. We demonstrate the efficacy of mSRC for three example applications: pixelwise classification of texture images, lumen segmentation in carotid artery magnetic resonance imaging (MRI), and bifurcation point detection in carotid artery MRI. We compare our method with conventional SRC, K-nearest neighbor, and support vector machine classifiers. The results show that mSRC outperforms SRC and the other reference methods. In addition, we present an extensive evaluation of the effect of the main mSRC parameters: patch size, dictionary size, and sparsity level

Simultaneous Reconstruction and Segmentation of CT Scans with Shadowed Data

International audienceWe propose a variational approach for simultaneous reconstruction and multiclass segmentation of X-ray CT images, with limited field of view and missing data. We propose a simple energy minimi-sation approach, loosely based on a Bayesian rationale. The resulting non convex problem is solved by alternating reconstruction steps using an iterated relaxed proximal gradient, and a proximal approach for the segmentation. Preliminary results on synthetic data demonstrate the potential of the approach for synchrotron imaging applications

Multiple sparse representations classification

textabstractSparse representations classification (SRC) is a powerful technique for pixelwise classification of images and it is increasingly being used for a wide variety of image analysis tasks. The method uses sparse representation and learned redundant dictionaries to classify image pixels. In this empirical study we propose to further leverage the redundancy of the learned dictionaries to achieve a more accurate classifier. In conventional SRC, each image pixel is associated with a small patch surrounding it. Using these patches, a dictionary is trained for each class in a supervised fashion. Commonly, redundant/overcomplete dictionaries are trained and image patches are sparsely represented by a linear combination of only a few of the dictionary elements. Given a set of trained dictionaries, a new patch is sparse coded using each of them, and subsequently assigned to the class whose dictionary yields the minimum residual energy.We propose a generalization of this scheme. The method, which we call multiple sparse representations classification (mSRC), is based on the observation that an overcomplete, class specific dictionary is capable of generating multiple accurate and independent estimates of a patch belonging to the class. So instead of finding a single sparse representation of a patch for each dictionary, we find multiple, and the corresponding residual energies provides an enhanced statistic which is used to improve classification. We demonstrate the efficacy of mSRC for three example applications: pixelwise classification of texture images, lumen segmentation in carotid artery magnetic resonance imaging (MRI), and bifurcation point detection in carotid artery MRI. We compare our method with conventional SRC, K-nearest neighbor, and support vector machine classifiers. The results show that mSRC outperforms SRC and the other reference methods. In addition, we present an extensive evaluation of the effect of the main mSRC parameters: patch size, dictionary size, and sparsity level

Super-resolution reconstruction using cross-scale self-similarity in multi-slice MRI

In MRI, the relatively thick slices of multi-slice acquisitions often hamper visualization and analysis of the underlying anatomy. A group of post-processing techniques referred to as super-resolution reconstruction (SRR) have been developed to address this issue. In this study, we present a novel approach to SRR in MRI, which exploits the high-resolution content usually available in the 2D slices of MRI slice stacks to reconstruct isotropic high-resolution 3D images. Relying on the assumption of local self-similarity of anatomical structures, the method can be applied both to a single slice stack and to the combination of multiple slice stacks that differ in the orientation of their field of view. We evaluate the method quantitatively on synthetic brain MRI and qualitatively on MRI of the lungs. The results show that the method outperforms state-of-the-art MRI super-resolution methods

Heatmaps of carotid artery bifurcation detection results for parameter tuning.

<p>Numerical and color coded distances to the ground truth are shown for dictionary sizes of {500, 1000, 2000, 4000} atoms, patch sizes of {7 × 7 × 7, 9 × 9 × 9, 11 × 11 × 11} voxels, and sparsity levels of {1, 3, 5, 7}.</p

Performance of SRC, mSRC, <i>K</i>-NN, and SVM in the carotid artery lumen segmentation experiments.

<p>The results are shown as boxplots, where the blue box indicates the 25–75 percentile, the red bar indicates the median, the whiskers are determined by the default MATLAB boxplot settings (see MATLAB documentation), and the individual red plus-markers are outliers.</p