Stacking operators are widely used in seismic imaging and seismic data processing. Examples include Kirchhoff datuming, migration, offset continuation, DMO, and velocity transform. Two primary approaches exist for inverting such operators. The first approach is iterative least-squares optimization, which involves the construction of the adjoint operator. The second approach is asymptotic invers...

We give a finite presentation by generators and relations of unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many...

A unified treatment of the Pauli algebraic forms of the linear operators defined on a unitary linear space of two dimensions over the field of complex numbers C(1) is given. The Pauli expansions of the normal and nonnormal operators, unitary and Hermitian operators, orthogonal projectors, and symmetries are deduced in this frame. A geometrical interpretation of these Pauli algebraical results i...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...