Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/47443
Title: A homomorphic filtering framework for DT-MRI
Authors: Castaño-Moraga, Carlos Alberto
Westin, Carl Fredrik
Ruiz-Alzola, Juan 
UNESCO Clasification: 3307 Tecnología electrónica
Keywords: Restoration And Deblurring
Image Quality
Magnetic Resonance
Diffusion Tensor Magnetic Resonance Imaging
Neurological
Issue Date: 2006
Journal: Progress in Biomedical Optics and Imaging - Proceedings of SPIE 
Conference: Medical Imaging 2006: Image Processing 
Abstract: In this paper we develop a new filtering framework for tensor signal processing using the theory of vector spaces. From this point of view, signals are regarded as elements of vector spaces and operators as mappings from the input space to the output space. Hence, it is possible to generalize the principle of superposition to any operator defined on the signal spaces. Systems that obey that generalization of the principle of superposition are referred to as homomorphic and they can be decomposed in a cascade of three homomorphic subsystems: the first one operates on the input signal space, the second one is a linear system in the usual sense and the third one operates on the output signal space. Thus, suitable input and output subsystems can be chosen to deal with input signals, which defines a whole family of homomorphic filters. To apply this idea for DT-MRI signals, which consist of positive semi-definite matrices, we identify input and output signal spaces as the set of those real symmetric positive semi-definite matrices. Our homomorphic filtering framework not only guarantees a positive-semidefinite output tensor field whatever linear filter is used to regularize the noisy input, but also reduces the swelling effect produced by a faster regularization of diffusivities rather than orientations, as demonstrate the encouraging results that have been obtained.
URI: http://hdl.handle.net/10553/47443
ISBN: 0819464236
ISSN: 1605-7422
DOI: 10.1117/12.652094
Source: Progress in Biomedical Optics and Imaging - Proceedings of SPIE[ISSN 1605-7422],v. 6144 I (61441A)
Appears in Collections:Actas de congresos
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