Anamorphic Projection: Analogical/Digital Algorithms

The Anamorphic Universe the Anamorphic Universe

We introduce “anamorphic” cosmology, an approach for explaining the smoothness and flatness of the universe on large scales and the generation of a nearly scale-invariant spectrum of adiabatic density perturbations. The defining feature is a smoothing phase that acts like a contracting universe based on some Weyl frame-invariant criteria and an expanding universe based on other frame-invariant ...

Projection algorithms with correction

We present in this paper two versions of a general correction procedure applied to a classical iterative method, which gives us the possibility, under certain assumptions, to obtain an extension of it to inconsistent linear least-squares problems. We prove that some well known extended projection type algorithms from image reconstruction in computerized tomography fit into one or the other of t...

Kernel Affine Projection Algorithms

The combination of the famed kernel trick and affine projection algorithms (APA) yields powerful nonlinear extensions, named collectively here KAPA. This paper is a follow-up study of the recently introduced kernel leastmean-square algorithm (KLMS). KAPA inherits the simplicity and online nature of KLMS while reducing its gradient noise, boosting performance. More interestingly, it provides a u...

Projection Algorithms for Variational Inclusions

A Family of Selective Partial Update Affine Projection Adaptive Filtering Algorithms

In this paper we present a general formalism for the establishment of the family of selective partial update affine projection algorithms (SPU-APA). The SPU-APA, the SPU regularized APA (SPU-R-APA), the SPU partial rank algorithm (SPU-PRA), the SPU binormalized data reusing least mean squares (SPU-BNDR-LMS), and the SPU normalized LMS with orthogonal correction factors (SPU-NLMS-OCF) algorithms...