Research topics

See the updated list of my current and past research topics on the official department web pages

Past and current research

Simulation and visualization of atomic collision cascades in solids - This work was conducted in the frame of my MSc thesis
Simulation of atomic excitations in collision cascades  
Denoising of BEEM (ballistic electron emission microscopy) images
Automatic grain segmentation of BEEM images
Image processing in conservation of an old medieval mosaic
Multichannel blind restoration of astronomical images  
Removal of fractal noise (cloud)
Multichannel blind restoration of spatially misaligned images 

Simulation and Visualization of collision cascades

Atomic collision cascades are similar too a large 3D billiard game with thousands of balls. Individual balls represent atoms of the crystal set up in a lattice. Because of inter-atomic forces, particles hold together and the lattice is stable. An accelerated impinging particle (ion) collides with the surface which has the same impact as a stroke with a billiard cue. Atoms start to collide and the whole crystal "shivers". Some atoms sputter, i.e., they gather enough energy to leave the surface of the crystal. This so called sputtering yield is a experimentally measurable quantity. Using the mathematical simulation, we are able to analyze with a precision of a surgical knife individual collisions and trajectories. This is of course not possible in laboratory experiments. The simulation part of the project is a numerical solution to a large set of differential equations implemented in parallel. For this purpose PVM technology was used which is platform independent). The visualization part (SIM) was implemented in OpenGL and C++ with GUI written in Qt. See an example of one collision cascade (Ar ion bombarding Ag 20x20x10 cluster) recorded as an avi file.  The visualization application SIM has three display modes: standard (color image of a perspective projection), anaglyph (two mutually translated and rotated images that through red and green filters provide 3D gray-scaled perception), and stereo (3D color perception with the shutter glasses). The stereo mode is only available on the SGI platform. The source code of SIM for UNIX (gcc compiler) is available.           

Simulation of atomic excitations

The simulation is based on SPUT93 Molecular Dynamics Program. Several enhancements were inserted to SPUT93 to be able to calculate excitation probability of sputtered particles. The part of the calculation in SPUT93 consists of tracking critical collisions, i.e., position and time of events when particles get closer then 1.2A to each other. These critical collisions are considered as "excitation generators" (delta functions) from which the excitation probabilities diffuse into the space. The post-simulation analysis of sputtered particles and their excitation probabilities is done in Matlab.  Excitation.avi (1MB) shows evolution of one excitation probability isosurface in time (0-200fs) averaged  over 10000 collision cascades Ar-Ag. The surface of the cluster is facing you. Excitationslice.avi (0.5MB) depicts the excitation probability on the surface and on the diagonal cut section as a function of time for the same configuration as above.         

Denoising of BEEM images

Using the BEEM/BEES microscope, we can measure the tunnel or the ballistic current. Images of the tunnel measurement (so called STM) are relatively sharp and any further analysis can be applied immediately. In the case of the ballistic current, the situation is more complicated, since the measurement is extremely noisy. One way how to suppress noise would be to measure for a long period of time and average. However, this is not possible since the measurement should be fast, otherwise temperature fluctuations prevail. To be able to get any meaningful results, we have applied an anisotropic denoising method based on total variation and we compared obtained results with wavelet-based denoising. Few examples of noisy and denoised images can be found here.

We have also developed a system for automatic grain segmentation of STM images. Using a seed-growing technique and boundary smoothing PDEs, individual grains were recovered followed by a radius estimation procedure. Distribution of grain size was then estimated.  The segmentation part was a MSc. thesis of M. Toman. 

Restoration of astronomical images in the multichannel framework

Multichannel blind deconvolution is a topic my PhD. thesis and a classical application of this theory can be found for example in astronomy. Observed stellar objects are blurred by the atmosphere which is a time-varying inhomogeneous medium and by acquiring the objects at different time instants we obtain several degraded images.  According to the multichannel deconvolution theory in a noiseless environment, it is possible to recover exactly the original image if channels are coprime, i.e., channel blurs do not have any common factor except of a scalar. We have improved the classical direct multichannel restoration method  by introducing a minimization algorithm based on total variation denoising and including multichannel constraints. Our algorithm shows great noise robustness. We tested its capabilities on sun-spot images.      

Removal of fractal noise

Removal of clouds is based on anisotropic denoising with constraints formed from a fractal noise model. See several examples.

Multichannel blind restoration of spatially misaligned images

Multichannel blind deconvolution approaches published so far assume perfectly registered channels.   We have proofed that the inaccurate registration of channels can be alleviated by properly overestimating a blur size. A novel blind deconvolution algorithm that can deal with the overestimated blur size  was proposed. It solves a MAP  problem.  Applicability of the novel algorithm is demonstrated on real data experiment.

We have developed a MATLAB Toolbox "MBD_GUI", which is free for research and/or educational purposes.

Superresolution and Blind Deconvolution in one framework

Imaging plays a key role in many diverse application areas, such as astronomy, remote sensing, microscopy or tomography, just to name few. Due to imperfections of measuring devices (optical degradations, limited size of CCD sensors) and instability of observed scene (object motion, media turbulence) acquired images are blurred, noisy and may exhibit  insufficient spatial and/or temporal resolution.

In order to recover the original image, techniques called blind deconvolution and super-resolution remove the blur and increase the resolution, respectively. A necessary condition for the methods to be stable is to have more than one image of the scene (multiframe imaging). Differences between images are necessary to provide new information but they can be almost imperceivable, e.g., subtle spatial shifts or slight modification of acquisition parameters (focus length, aperture size).

Current multiframe blind deconvolution techniques require no or very little prior information about the blurs and they are sufficiently robust to noise to provide satisfying results in most of the real applications. However, they can hardly cope with low-resolution images since in this case a standard convolution model is violated. On the contrary, state-of-the-art super-resolution techniques achieve remarkable results in resolution enhancement by estimating the subpixel shifts between images but lack any apparatus for calculating the blurs. The super-resolution methods either assume that there is no blur or that it can be estimated by other means.

We propose a unifying system that simultaneously estimates blurs and the original undistorted image, all in high resolution, without any prior knowledge of the blurs or original image. We accomplish this by formulating the problem as constrained least squares energy minimization with appropriate regularization terms, which guarantee close-to-perfect solution in the noiseless case. Considering the problem in the 3D domain allows us to apply the proposed method not only to volumes (confocal microscopy, electron tomography) but also to video sequences, where the third dimension is the time.

We have also developed a MATLAB Toolbox "BSR_GUI".
See examples here.