A local structure measure for anisotropic regularization of tensor fields

Abstract

Acquisition systems are not fully reliable since any real sensor will provide noisy and possibly incomplete and degraded data. Therefore, in tensor measurements, all problems dealt with in conventional multidimensional statistical signal processing are present with tensor signals. In this chapter we describe some noniterative approaches to tensor signal processing. Our schemes are achieved by the estimation of a local structure tensor, which is used as a key element in regularization. A stochastic point of view as well as a phase-invariant implementation are presented. This work also covers tensor extensions for common scalar operations such as anisotropic interpolation and filtering. An application of the structure tensor for regularization of deformation fields in tensor image registration is also shown. The techniques presented in this chapter suppose an alternative to variational and PDEs schemes, and another point of view of the tensor signal processing.