相关论文: Inversion of finite filters
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
Diffraction limited resolution adaptive optics (AO) correction in visible wavelengths requires a high performance control. In this paper we investigate infinite impulse response filters that optimize the wavefront correction: we tested…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
It has been argued that, for a spatially invariant imaging system, the information one can gain about the separation of two incoherent point sources decays quadratically to zero with decreasing separation, an effect termed Rayleigh's curse.…
We shall characterize the structure of invertible substitutions on three-letter alphabet. We show that any invertible substitution, after some cyclic operation, can be written as a finite product of permutations and Fibonacci's…
Phase aberration is an inherent side effect of ultrasound imaging due to the speed of sound inhomogeneity nature of human tissues, resulting in focusing error and reduced image contrast. This work introduces a phase aberration correction…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
Context. Narrow-band interference filters can be tuned toward shorter wavelengths by tilting them from the perpendicular to the optical axis. This can be used as a cheap alternative to real tunable filters, such as Fabry-P\'erot…
The point-spread function (PSF) is a fundamental property of any astronomical instrument. In interferometers, differing array configurations combined with their $uv$ coverage, and various weighting schemes can produce an irregular but…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
The transmission characteristics of commercial interference filters are not quite what we expected from the specifications provided by manufacturers. The unexpectedly sharp dependences of the transmission coefficient on the incidence angle,…
Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…
Marine Controlled Source Electromagnetic (CSEM) is employed both in large-scale geophysical applications as well as within exploration of hydrocarbons and gas hydrates. Due to the diffusive character of the EM field only very low…
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
When inverting solar spectra, image degradation effects that are present in the data are usually approximated or not considered. We develop a data reduction method that takes these issues into account and minimizes the resulting errors. By…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
We answer a question by Judith Packer about the irreducibility of the wavelet representation associated to the Cantor set. We prove that if the QMF filter does not have constant absolute value, then the wavelet representations is reducible.
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…