In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be interpreted as another twisted convolution on a finite cyclic group. In analogy with the twisted convolution of finite discrete signals, we derive an anti-homomo...

When transforming data one often wants certain information in the data source to be preserved, i.e., we identify parts of the source data and require these parts to be transformed without loss of information. We characterize the preservation of selected information in terms of the notions of invertibility and query preservation, in a setting when transformations are specified as a view V (a set...

We consider Calderón’s inverse problem with partial data in dimensions n ≥ 3. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility of a broken geodesic ray transform. In Euclidean space, sets satisfying the flatness condition include parts of cylindrical sets, conical sets, and surfaces of re...

In this paper we study decision problems and invertibility for two notions of equivalence of recursive types. In particular, for recursive types presented by means of a recursion operator μ, we describe an algorithm showing that the natural equivalence generated by finitely many steps of folding and unfolding of μ-types is decidable. For recursive types presented by finite systems of recursive ...

We describe a sampling technique particularly suitable for active vision: Dimensionally-Independent Exponential Mapping (DIEM), in which each dimension of the original data is sampled in an exponentially increasing or decreasing series of steps, with bilateral symmetry about the data mid-point. Multidimensional data sampling is achieved by combining single dimension sampling coordinates. DIEM i...