Ondřej Olšák from the Institute of Computer Systems will defend his dissertation in February.

We invite you to the defense of the dissertation of Ing. Ondřej Olšák from the Department of Computer Systems, FIT BUT, which will take place on Thursday, February 5, 2026, at 1:00 p.m. in meeting room C209. The supervisor of the dissertation entitled "Acceleration of wave propagation simulation calculations using pruned Fourier transform" is Prof. Jiří Jaroš.

Ondřej Olšák's research is closely linked to possible practical applications, particularly in the highly monitored field of medicine. In his work, he focuses on optimizing wave propagation simulations, which are key to planning neuromodulation procedures and tissue ablation using ultrasound waves. The SC@FIT research group led by Prof. Jiří Jaroš, of which Ondřej Olšák is a member, focuses not only on the development and optimization of wave propagation simulators at FIT. The group is involved in the development of the open-source toolkit k-Wave, which is one of the most highly regarded tools in the field of wave propagation simulation. k-Wave uses a k-space pseudo-spectral method based on Fourier transformation to calculate wave propagation simulations, which allows for high computational accuracy. However, the Fourier transform calculation accounts for approximately 60% of the total simulation computation time and presents a challenge for optimization.

Simulating wave propagation in high-resolution domains is a computationally demanding task—a single simulation can take from seconds to hours or days, depending on its parameters. When planning medical procedures, it is necessary to perform dozens of such simulations. This is where the key challenge behind Ondřej Olšák's research comes in: to find a new optimization approach to speed up wave propagation simulations using spectrum pruning techniques. When asked for a layman's explanation of the research goal, Ondřej Olšák begins broadly: "In order to simulate the propagation of ultrasound waves in the human body, we must convert the real structure of tissues into digital form—into a regular grid of points. Each point carries information about the type of tissue at that location. The finer the grid we use, the more accurately we can capture the actual shapes and transitions between different types of tissue, and the more accurate the result of the simulation itself will be. However, as the fineness of the grid increases, so does the computational complexity. The key to optimization was understanding how the coefficients in the spectral (frequency) domain of the propagated wave change and what influences their position. After conversion using a fast Fourier transform, the wave is mathematically expressed as a set of spectral coefficients. When we increase the resolution of the domain, the spectral region will contain more of these coefficients. However, for high-resolution domains, we do not need to calculate all the coefficients that occur in the spectral domain to achieve an acceptable result. When calculating the Fourier transform, we can therefore neglect certain parts of the spectrum and calculate only those coefficients that are truly important for the result. This technique, called spectrum pruning, allows for a significant acceleration of the simulation while maintaining acceptable accuracy.

This is the core of the optimization that Ondřej Olšák designed and experimentally verified for the k-Wave tool. The result of his work is a modification of the existing k-Wave implementation for both 2D and 3D simulations. Experiments performed on anatomical models of the human head and liver with different sizes of computational domains – up to a resolution of 9216×12288 points for 2D and 567×672×448 points for 3D – showed acceleration of up to 1.9× for two-dimensional and 1.7× for three-dimensional simulations. However, the spectrum pruning technique comes with a trade-off: neglecting part of the spectral coefficients introduces a certain error into the calculation. The key is to find the right balance between the range of the neglected part of the spectrum and the acceptable accuracy of the simulation results. Determining the acceptable error limit is not a trivial task and provides an incentive for further research in this area.

According to Olšák, the above-described optimization of calculations can be used, for example, in situations where the appropriate position of the ultrasound transmitter is sought before the actual procedure, so that the ultrasound waves are focused as accurately as possible on the desired part of the brain or other tissue and no damage is caused to the surrounding tissue. In this process, it is possible to use an optimized version of the simulation to quickly explore different configurations, and once the appropriate position of the transmitter has been found, to perform a control calculation using a non-optimized simulation to ensure maximum accuracy of the result. This procedure thus significantly reduces the time and costs required for treatment planning. It should be added that the results of Olšák's research can be applied not only in the medical field, but also in other areas requiring wave propagation simulations in sparse heterogeneous media.

Ondřej Olšák takes a pragmatic view of his doctorate and its imminent completion: "I like the fact that someone will now read my work as a whole and give me further feedback on my research. I was already involved in the research during my master's studies. I enjoyed searching for solutions and testing hypotheses the whole time." He himself admits that it was not always an easy journey: "At the beginning of my dissertation research, I reached a dead end and felt like I was at a loss. Then one day, a video I happened to see gave me an idea for a different method. It was a wonderful, indescribable feeling." He would like to continue his research, but his next steps will be in industry, where he sees interesting challenges. "I would like to thank my family for their support throughout my studies. And then, in addition to my supervisor, Professor Jaroš, I would like to thank all my colleagues from the research group for their long-term help and support," Ondřej Olšák recalls with gratitude at the end of our interview. We will keep our fingers crossed for him, and not just for his public defense of his dissertation. We wish him the joy of discovering new paths in his professional practice as well.