  PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a
particularly interesting framework of physically meaningful diffeomorphic
registration methods. Newton-Krylov optimization has shown an excellent
numerical accuracy and an extraordinarily fast convergence rate in this
framework. However, the most significant limitation of PDE-constrained LDDMM is
the huge computational complexity, that hinders the extensive use in
Computational Anatomy applications. In this work, we propose two
PDE-constrained LDDMM methods parameterized in the space of band-limited vector
fields and we evaluate their performance with respect to the most related state
of the art methods. The parameterization in the space of band-limited vector
fields dramatically alleviates the computational burden avoiding the
computation of the high-frequency components of the velocity fields that would
be suppressed by the action of the low-pass filters involved in the computation
of the gradient and the Hessian-vector products. Besides, the proposed methods
have shown an improved accuracy with respect to the benchmark methods.
