Picture reconstruction from projections in restricted range

In order to reduce scanning time modern x-ray scanners provide projections only in a restricted range [O, &Phi;] with &Phi;< &pi;. We consider the reconstruction of pictures from p+1 complete projections in [O, &Phi;]. An extrapolation procedure is given to achieve approximations gp of the data in the whole range. We show that the L2-error of the corresponding picture is of order p- &alpha; if the original belongs to the SOBOLEV space H o &alpha;. The validity of our error estimate is investigeted by numerical experiments

Picture reconstruction from projections in restricted range

In order to reduce scanning time modern x-ray scanners provide projections only in a restricted range [O, &Phi;] with &Phi;< &pi;. We consider the reconstruction of pictures from p+1 complete projections in [O, &Phi;]. An extrapolation procedure is given to achieve approximations gp of the data in the whole range. We show that the L2-error of the corresponding picture is of order p- &alpha; if the original belongs to the SOBOLEV space H o &alpha;. The validity of our error estimate is investigeted by numerical experiments

Metric on the space of quantum states from relative entropy. Tomographic reconstruction

In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N = 2, N = 3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher- Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.Comment: 31 pages. No figures. Abstract and Introduction rewritten. Minor corrections. References adde

Lifting symmetric pictures to polyhedral scenes

Scene analysis is concerned with the reconstruction of d-dimensional objects, such as polyhedral surfaces, from (d − 1)-dimensional pictures (i.e., projections of the objects onto a hyperplane). In this paper we study the impact of symmetry on the lifting properties of pictures. We first use methods from group representation theory to show that the lifting matrix of a symmetric picture can be transformed into a block-diagonalized form. Using this result we then derive new symmetry-extended counting conditions for a picture with a non-trivial symmetry group in an arbitrary dimension to be minimally flat (i.e., ‘non-liftable’). These conditions imply very simply stated restrictions on the number of those structural components of the picture that are fixed by the various symmetry operations of the picture. We then also transfer lifting results for symmetric pictures from Euclidean (d − 1)-space to Euclidean d-space via the technique of coning. Finally, we offer some conjectures regarding sufficient conditions for a picture realized generically for a symmetry group to be minimally flat

Determination of 2D implanted ion distributions using inverse radon transform methods

Two methods are presented for the experimental determination of 2D implanted ion distribution resulting from implantations with a line source into amorphous targets. It is shown that the relation between the 2D distribution and the depth profiles resulting from tilted angle implantations is described by the Radon transformation. The inverse transformation has been applied to accurately measured depth profiles. The first method uses a digitization of the 2D distribution and the second method uses a parameterized function for the 2D distribution. The methods are tested for a 400 keV boron implantation in an amorphous layer of silicon. The experimental obtained 2D distributions are compared with a TRIM Monte Carlo simulation. A good agreement between experiment and simulation is observed

Medical ultrasonic tomographic system

An electro-mechanical scanning assembly was designed and fabricated for the purpose of generating an ultrasound tomogram. A low cost modality was demonstrated in which analog instrumentation methods formed a tomogram on photographic film. Successful tomogram reconstructions were obtained on in vitro test objects by using the attenuation of the fist path ultrasound signal as it passed through the test object. The nearly half century tomographic methods of X-ray analysis were verified as being useful for ultrasound imaging