The Discrete radon transform: A more efficient approach to image reconstruction

The Radon transform and its inversion are the mathematical keys that enable tomography. Radon transforms are defined for continuous objects with continuous projections at all angles in [0,π). In practice, however, we pre-filter discrete projections take

Fast Mojette Transform for Discrete Tomography

A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin

Quantised Angular Momentum Vectors and Projection Angle Distributions for Discrete Radon Transformations

International audienceA quantum mechanics based method is presented to generate sets of digital angles that may be well suited to describe projections on discrete grids. The resulting angle sets are an alternative to those derived using the Farey fractions from number theory. The Farey angles arise naturally through the definitions of the Mojette and Finite Radon Transforms. Often a subset of the Farey angles needs to be selected when reconstructing images from a limited number of views. The digital angles that result from the quantisation of angular momentum (QAM) vectors may provide an alternative way to select angle subsets. This paper seeks first to identify the important properties of digital angles sets and second to demonstrate that the QAM vectors are indeed a candidate set that fulfils these requirements. Of particular note is the rare occurrence of degeneracy in the QAM angles, particularly for the half-integral angular momenta angle sets

Recovering missing slices of the discrete fourier transform using ghosts

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n\log-{2}n) (for an n=N\times N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT

Investigation into Stereoselective Pharmacological Activity of Phenotropil

Phenotropil [N-carbamoylmethyl-4-aryl-2-pyrrolidone (2-(2-oxo-4-phenyl-pyrrolidin-1-yl) acetamide; carphedon)] is clinically used in its racemic form as a nootropic drug that improves physical condition and cognition. The aim of this study was to compare the stereoselective pharmacological activity of R- and S-enantiomers of phenotropil in different behavioural tests. Racemic phenotropil and its enantiomers were tested for locomotor, antidepressant and memory-improving activity and influence on the central nervous system (CNS) using general pharmacological tests in mice. After a single administration, the amount of compound in brain tissue extracts was determined using an ultra performance liquid chromatography-tandem mass spectrometry (UPLC/MS/MS) method in a positive ion electrospray mode. In the open-field test, a significant increase in locomotor activity was observed after a single administration of R-phenotropil at doses of 10 and 50mg/kg and S-phenotropil at a dose of 50mg/kg. In the forced swim test, R-phenotropil induced an antidepressant effect at doses of 100 and 50mg/kg, and S-phenotropil was active at a dose of 100mg/kg. R-phenotropil significantly enhanced memory function in a passive avoidance response test at a dose of 1 mg/kg; the S-enantiomer did not show any activity in this test. However, the concentrations of R- and S-phenotropils in brain tissue were similar. In conclusion, the antidepressant and increased locomotor activity relies on both R- and S-phenotropils, but the memory-improving activity is only characteristic of R-phenotropil. These results may be important for the clinical use of optically pure isomers of phenotropil.publishersversionPeer reviewe