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Sparse Projections of Medical Images onto Manifolds

Institution:
Massachusetts Institute of Technology, Cambridge, MA, USA.
Publisher:
Inf Process Med Imaging IPMI 2013
Publication Date:
Jun-2013
Volume Number:
23
Pages:
292-303
Citation:
Inf Process Med Imaging. 2013 Jun; 23:292-303.
PubMed ID:
24683977
PMCID:
PMC3979531
Appears in Collections:
NAC, NA-MIC
Sponsors:
P41 EB015902/EB/NIBIB NIH HHS/United States
P41 RR013218/RR/NCRR NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
Generated Citation:
Chen G.H., Wachinger C., Golland P. Sparse Projections of Medical Images onto Manifolds. Inf Process Med Imaging. 2013 Jun; 23:292-303. PMID: 24683977. PMCID: PMC3979531.
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Manifold learning has been successfully applied to a variety of medical imaging problems. Its use in real-time applications requires fast projection onto the low-dimensional space. To this end, out-of-sample extensions are applied by constructing an interpolation function that maps from the input space to the low-dimensional manifold. Commonly used approaches such as the Nyström extension and kernel ridge regression require using all training points. We propose an interpolation function that only depends on a small subset of the input training data. Consequently, in the testing phase each new point only needs to be compared against a small number of input training data in order to project the point onto the low-dimensional space. We interpret our method as an out-of-sample extension that approximates kernel ridge regression. Our method involves solving a simple convex optimization problem and has the attractive property of guaranteeing an upper bound on the approximation error, which is crucial for medical applications. Tuning this error bound controls the sparsity of the resulting interpolation function. We illustrate our method in two clinical applications that require fast mapping of input images onto a low-dimensional space.

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