Image reconstruction by an alternating minimisation

This paper focuses on the problem of incomplete data in the applications of the circular cone-beam computed tomography. This problem is frequently encountered in medical imaging sciences and some other industrial imaging systems. For example, it is crucial when the high density region of objects can only be penetrated by X-rays in a limited angular range. As the projection data are only available in an angular range, the above mentioned incomplete data problem can be attributed to the limited angle problem, which is an ill-posed inverse problem. This paper reports a modified total variation minimisation method to reduce the data insufficiency in tomographic imaging. This proposed method is robust and efficient in the task of reconstruction by showing the convergence of the alternating minimisation method. The results demonstrate that this new reconstruction method brings reasonable performance. (C) 2010 Elsevier B.V. All rights reserved.

A Relay Level Set Method for Automatic Image Segmentation

This paper presents a new image segmentation method that applies an edge-based level set method in a relay fashion. The proposed method segments an image in a series of nested subregions that are automatically created by shrinking the stabilized curves in their previous subregions. The final result is obtained by combining all boundaries detected in these subregions. The proposed method has the following three advantages: 1) It can be automatically executed without human-computer interactions; 2) it applies the edge-based level set method with relay fashion to detect all boundaries; and 3) it automatically obtains a full segmentation without specifying the number of relays in advance. The comparison experiments illustrate that the proposed method performs better than the representative level set methods, and it can obtain similar or better results compared with other popular segmentation algorithms.

Structure image of single crystal of polyethylene

High-resolution electron macroscopic images of lamellar single crystal of polyethylene (PE) have been successfully obtained using high-resolution electron microscopy (HREM), although so far the feasibility of obtaining HREM images from such a radiation sensitive polymer is still drastically questioned. The HREM images with a clear two-dimensional periodic structure reported here were recorded in a transmission electron microscope operated at 200 kV. The images consisted of lattice fringes derived from the <001> zone, and the structure images of different lattice fringes were resolved. To our knowledge, this is the first time that such clear structure images of PE have been reported at a molecular level.

Application of digital image analysis to the study of banded spherulite during growing and melting process

A digital image analysis(DIA) technique can be applied directly to the image obtained by polarizing microscope. The time-resolved DIA apparatus including image collecting, showing and data analysis has been home-made. As an example, it has been used to study the banded spherulite in the blends of poly(epsilon-caprolactone) (PCL) and poly(styrene-ran-acrylonitrile) (SAN).

STM image of tungstosilicic acid molecular layer on highly oriented pyrolytic graphite

Molecular layer of tungstosilicic acid (H4SiW12O40) deposited on freshly-cleaved highly oriented pyrolytic graphite (HOPG) was observed by scanning tunneling microscopy (STM) in air at room temperature. The molecular dimension (11.5 Angstrom) of H4SiW12O40 measured by STM is consistent with known crystallographic parameter. We also imaged the boundary of H4SiW12O40 molecular layer on HOPG showing that molecular layer of H4SiW12O40 was formed. It has been proved that individual tungstosilicic acid species is imaged. The probable reason for the formation of the molecular layer is also discussed.

IN-SITU SCANNING-TUNNELING-MICROSCOPY IMAGE OF A HIGHLY ORIENTED PYROLYTIC-GRAPHITE ELECTRODE MODIFIED WITH POTASSIUM BIS(11-MOLYBDOSILICATO) DYSPROSATE(III) IN SODIUM-SULFATE SOLUTION

The variation in molecule adsorption mode on pretreated highly oriented pyrolytic graphite electrodes, modified with the title complex K10H3[Dy(SiMo11O39)(2)] by cyclic voltammetry in the title complex solution, was observed in situ by electrochemical scanning tunnelling microscopy (ECSTM) with molecular resolution in sodium sulphate solution. According to the ECSTM images and the known molecular structure we conclude that the adsorption mode of the title complex modified electrode changed during potential cycling from ''vertical'' to ''inclined'' and then ''horizontal'' or ''flat'' mode, i.e. the title complex adsorbed on the surface of electrode by one ligand of the complex at first, then began to incline and was finally adsorbed by two ligands of the complex. This result indicates that the adsorption mode on the modified electrode surface changed during potential cycling in the sulphate solution and a much more stable molecular layer was formed. The change in adlattice of adsorbates on the modified electrode surface from hexagonal to rectangular was also observed by ECSTM. A plausible model was given to explain this process.

Influence of mean water depth and a subsurface sandbar on the onset and strength of wave breaking

Wave breaking in the open ocean and coastal zones remains an intriguing yet incompletely understood process, with a strong observed association with wave groups. Recent numerical study of the evolution of fully nonlinear, two-dimensional deep water wave groups identified a robust threshold of a diagnostic growth-rate parameter that separated nonlinear wave groups that evolved to breaking from those that evolved with recurrence. This paper investigates whether these deep water wave-breaking results apply more generally, particularly in finite-water-depth conditions. For unforced nonlinear wave groups in intermediate water depths over a flat bottom, it was found that the upper bound of the diagnostic growth-rate threshold parameter established for deep water wave groups is also applicable in intermediate water depths, given by k(0) h greater than or equal to 2, where k(0) is the mean carrier wavenumber and h is the mean depth. For breaking onset over an idealized circular arc sandbar located on an otherwise flat, intermediate-depth (k(0) h greater than or equal to 2) environment, the deep water breaking diagnostic growth rate was found to be applicable provided that the height of the sandbar is less than one-quarter of the ambient mean water depth. Thus, for this range of intermediate-depth conditions, these two classes of bottom topography modify only marginally the diagnostic growth rate found for deep water waves. However, when intermediate-depth wave groups ( k(0) h greater than or equal to 2) shoal over a sandbar whose height exceeds one-half of the ambient water depth, the waves can steepen significantly without breaking. In such cases, the breaking threshold level and the maximum of the diagnostic growth rate increase systematically with the height of the sandbar. Also, the dimensions and position of the sandbar influenced the evolution and breaking threshold of wave groups. For sufficiently high sandbars, the effects of bottom topography can induce additional nonlinearity into the wave field geometry and associated dynamics that modifies the otherwise robust deep water breaking-threshold results.

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

On the nonlinear integral transform of an ocean wave spectrum into an along-track interferometric synthetic aperture radar image spectrum

We present a new nonlinear integral transform relating the ocean wave spectrum to the along-track interferometric synthetic aperture radar (AT-INSAR) image spectrum. The AT-INSAR, which is a synthetic aperture radar (SAR) employing two antennas displaced along the platform's flight direction, is considered to be a better instrument for imaging ocean waves than the SAR. This is because the AT-INSAR yields the phase spectrum and not only the amplitude spectrum as with the conventional SAR. While the SAR and AT-INSAR amplitude spectra depend strongly on the modulation of the normalized radar cross section (NRCS) by the long ocean waves, which is poorly known, the phase spectrum depends only weakly on this modulation. By measuring the phase difference between the signals received by both antennas, AT-INSAR measures the radial component of the orbital velocity associated with the ocean waves, which is related to the ocean wave height field by a well-known transfer function. The nonlinear integral transform derived in this paper differs from the one previously derived by Bao et al. [1999] by an additional term containing the derivative of the radial component of the orbital velocity associated with the long ocean waves. By carrying out numerical simulations, we show that, in general, this additional term cannot be neglected. Furthermore, we present two new quasi-linear approximations to the nonlinear integral transform relating the ocean wave spectrum to the AT-INSAR phase spectrum.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.