On the Construction of Non Linear Adjoint Operators: Application to L1-Penalty Dynamic Image Reconstruction
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Santiago Sanz-Estebanez [1] ; Elisa Moya-Sáez [1] ; Javier Royuela-del-Val [2] ; Carlos Alberola-López [1]
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[1] Universidad de Valladolid
Universidad de Valladolid
Valladolid, España
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[2] Cardiothoracic Imaging Section , Hospital de la Cruz Roja, RESSALTA, Health Time Group, Córdoba
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- Localización: Libro de Actas del XXXVI Congreso Anual de la Sociedad Española de Ingeniería Biomédica / Ma Gloria Bueno García (dir.), 2018, ISBN 978-84-09-06253-9, págs. 3-6
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
The purpose of this work is to develop a methodology for the ad- joint operators application in non linear optimization problems. The use of adjoint operators is very popular for numerical control theory; one of its main applications is devised for image recon- struction. Most of these reconstruction techniques are limited to linear L1-constraints whose adjoints are well-defined. We aim to extend these image reconstruction techniques allowing the terms involved to be non linear. For these purpose, we have general- ized the concept of adjoint operator under the basis of Taylor’s formula, using Gateaux derivatives in order to construct a lin- ˆ earised adjoint operator associated to the non linear operator. The proposed approach has been validated in a Magnetic Reso- nance Imaging (MRI) reconstruction framework with Cartesian subsampled k-space data using Compressed Sensing based tech- niques and a groupwise registration algorithm for motion com- pensation. The proposed algorithm has shown to be able to ef- fectively deal with the presence of both physiological motion and subsampling artefacts, increasing accuracy and robustness of the reconstruction as compared with its linear counterpart.
