Fat fraction mapping using bSSFP Signal Profile Asymmetries for Robust multi-Compartment Quantification (SPARCQ)

Purpose: To develop a novel quantitative method for detection of different tissue compartments based on bSSFP signal profile asymmetries (SPARCQ) and to provide a validation and proof-of-concept for voxel-wise water-fat separation and fat fraction mapping. Methods: The SPARCQ framework uses phase-cycled bSSFP acquisitions to obtain bSSFP signal profiles. For each voxel, the profile is decomposed into a weighted sum of simulated profiles with specific off-resonance and relaxation time ratios. From the obtained set of weights, voxel-wise estimations of the fractions of the different components and their equilibrium magnetization are extracted. For the entire image volume, component-specific quantitative maps as well as banding-artifact-free images are generated. A SPARCQ proof-of-concept was provided for water-fat separation and fat fraction mapping. Noise robustness was assessed using simulations. A dedicated water-fat phantom was used to validate fat fractions estimated with SPARCQ against gold-standard 1H MRS. Quantitative maps were obtained in knees of six healthy volunteers, and SPARCQ repeatability was evaluated in scan rescan experiments. Results: Simulations showed that fat fraction estimations are accurate and robust for signal-to-noise ratios above 20. Phantom experiments showed good agreement between SPARCQ and gold-standard (GS) fat fractions (fF(SPARCQ) = 1.02*fF(GS) + 0.00235). In volunteers, quantitative maps and banding-artifact-free water-fat-separated images obtained with SPARCQ demonstrated the expected contrast between fatty and non-fatty tissues. The coefficient of repeatability of SPARCQ fat fraction was 0.0512. Conclusion: The SPARCQ framework was proposed as a novel quantitative mapping technique for detecting different tissue compartments, and its potential was demonstrated for quantitative water-fat separation.Comment: 20 pages, 7 figures, submitted to Magnetic Resonance in Medicin

Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure

Modelling Identity Rules with Neural Networks

In this paper, we show that standard feed-forward and recurrent neural networks fail to learn abstract patterns based on identity rules. We propose Repetition Based Pattern (RBP) extensions to neural network structures that solve this problem and answer, as well as raise, questions about integrating structures for inductive bias into neural networks. Examples of abstract patterns are the sequence patterns ABA and ABB where A or B can be any object. These were introduced by Marcus et al (1999) who also found that 7 month old infants recognise these patterns in sequences that use an unfamiliar vocabulary while simple recurrent neural networks do not. This result has been contested in the literature but it is confirmed by our experiments. We also show that the inability to generalise extends to different, previously untested, settings. We propose a new approach to modify standard neural network architectures, called Repetition Based Patterns (RBP) with different variants for classification and prediction. Our experiments show that neural networks with the appropriate RBP structure achieve perfect classification and prediction performance on synthetic data, including mixed concrete and abstract patterns. RBP also improves neural network performance in experiments with real-world sequence prediction tasks. We discuss these finding in terms of challenges for neural network models and identify consequences from this result in terms of developing inductive biases for neural network learning