We consider the decomposition of bounded linear operators on Hilbert spaces in terms functions forming frames. Similar to singular-value decomposition, resulting frame decompositions encode information structure and ill-posedness problem can be used as basis for design implementation efficient numerical solution methods. In contrast presented derived explicitly a wide class operators, particula...

Objective: Cone beam computed tomography (CBCT) is applied for the imaging of the maxillofacial and dental structures, particularly for surgical treatments and dental implants. The aim of this study was to assess the effect of slice thickness on the accuracy of CBCT linear measurements. Methods: In this diagnostic accuracy study, forty-two titanium pins with the same dimensions were inserted...

Seismic tomography is a non-linear problem with a significant null-space. Our estimation problem often converges slowly, to a geologically unreasonable model, or not at all. One reason for slow or non-convergence is that we are attempting to simultaneously estimate reflector position (mapping velocity) and image our data (focusiing velocity). By performing tomography in vertical travel-time spa...

abstract necrotizing sarcoid granulomatosis (nsg) is a rare disease which is classified in the spectrum of pulmonary angiitis and granulomatosis. it is a variant of sarcoidosis and differs from it histologically. diagnosis is based on the pathological features, but radiology may help in the differential diagnosis. it is characterized by alveolar infiltrates or parenchymal nodules in multidetect...

We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularizationmethod. Numerical tests are presented for a linear problem related to photoacoustic tomography and a non-linear problem related to the testing of semiconductor ...

The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the measurements are taken with respect to rank one matrices constructed from the elements of a random tight frame. We consider a convex optimization approach and s...

We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization properties and also obtain rates of convergence for our methods. A numerical example concerning a dynamical electrical impedance tomography (EIT) problem is used t...

In this paper we provide for a first time, to our knowledge, a mathematical model for imaging an anisotropic, orthotropic medium with polarization-sensitive optical coherence tomography. The imaging problem is formulated as an inverse scattering problem in three dimensions for reconstructing the electrical susceptibility of the medium using Maxwell's equations. Our reconstruction method is base...