Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Family of projected descent methods for optimization problems with simple bounds
Journal of Optimization Theory and Applications
A General and Unifying Framework for Feature Construction, in Image-Based Pattern Classification
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
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We present a new framework for predicting cognitive or other continuous-variable data from medical images. Current methods of probing the connection between medical images and other clinical data typically use voxel-based mass univariate approaches. These approaches do not take into account the multivariate, network-based interactions between the various areas of the brain and do not give readily interpretable metrics that describe how strongly cognitive function is related to neuroanatomical structure. On the other hand, high-dimensional machine learning techniques do not typically provide a direct method for discovering which parts of the brain are used for making predictions. We present a framework, based on recent work in sparse linear regression, that addresses both drawbacks of mass univariate approaches, while preserving the direct spatial interpretability that they provide. In addition, we present a novel optimization algorithm that adapts the conjugate gradient method for sparse regression on medical imaging data. This algorithm produces coefficients that are more interpretable than existing sparse regression techniques.