Direct multi-dimensional Chebyshev polynomial based reconstruction for magnetic particle imaging.

Magnetic Particle Imaging is a tomographic imaging technique that measures the voltage induced due to magnetization changes of magnetic nanoparticle distributions. The relationship between the received signal and the distribution of the nanoparticels is described by the system function. A common method for image reconstruction is using a measured system function to create a system matrix and set up a regularized linear system of equations. Since the measurement of the system matrix is time-consuming, different methods for acceleration have been proposed. These include modeling the system matrix or using a direct reconstruction method in time, known as X-space reconstruction. In this work, based on the simplified Langevin model of paramagnetism and certain approximations, a direct reconstruction technique for Magnetic Particle Imaging in the frequency domain with two- and three-dimensional Lissajous trajectory excitation is presented. The approach uses Chebyshev polynomials of second kind. During reconstruction, they are weighted with the frequency components of the voltage signal and additional factors and then summed up. To obtain the final nanoparticle distribution, this result is rescaled and deconvolved. It is shown that the approach works for both simulated data and real measurements. The obtained image quality is comparable to a modeled system matrix approach using the same simplified physical assumptions and no relaxation effects. The reconstruction of a 31 × 31 × 31 volume takes less than a second and is up to 25 times faster than the state-of-the-art Kaczmarz reconstruction. Besides, the derivation of the proposed method shows some new theoretical aspects of the system function and its well-known observed similarity to tensor products of Chebyshev polynomials of second kind.

Multiresolution vessel detection in magnetic particle imaging using wavelets and a Gaussian mixture model.

PURPOSE: Magnetic particle imaging is a tomographic imaging technique that allows one to measure the spatial distribution of superparamagnetic nanoparticles, which are used as tracer. The magnetic particle imaging scanner measures the voltage induced due to the nonlinear magnetization behavior of the nanoparticles. The tracer distribution can be reconstructed from the voltage signal by solving an inverse problem. A possible application is the imaging of vessel structures. In this and many other cases, the tracer is only located inside the structures and a large part of the image is related to background. A detection of the tracer support in early stages of the reconstruction process could improve reconstruction results. METHODS: In this work, a multiresolution wavelet-based reconstruction combined with a segmentation of the foreground structures is performed. For this, different wavelets are compared with respect to their reconstruction quality. For the detection of the foreground, a segmentation with a Gaussian mixture model is performed, which leads to a threshold-based binary segmentation. This segmentation is done on a coarse level of the reconstruction and then transferred to the next finer level, where it is used as prior knowledge for the reconstruction. This is repeated until the finest resolution is reached. RESULTS: The approach is evaluated on simulated vessel phantoms and on two real measurements. The results show that this method improves the structural similarity index of the reconstructed images significantly. Among the compared wavelets, the 9/7 wavelets led to the best reconstruction results. CONCLUSIONS: The early detection of the vessel structures at low resolution helps to improve the image quality. For the wavelet decomposition, the use of 9/7 wavelets is recommended.

Segmentation of mouse skin layers in optical coherence tomography image data using deep convolutional neural networks.

Optical coherence tomography (OCT) enables the non-invasive acquisition of high-resolution three-dimensional cross-sectional images at micrometer scale and is mainly used in the field of ophthalmology for diagnosis as well as monitoring of eye diseases. Also in other areas, such as dermatology, OCT is already well established. Due to its non-invasive nature, OCT is also employed for research studies involving animal models. Manual evaluation of OCT images of animal models is a challenging task due to the lack of imaging standards and the varying anatomy among models. In this paper, we present a deep learning algorithm for the automatic segmentation of several layers of mouse skin in OCT image data using a deep convolutional neural network (CNN). The architecture of our CNN is based on the U-net and is modified by densely connected convolutions. We compared our adapted CNN with our previous algorithm, a combination of a random forest classification and a graph-based refinement, and a baseline U-net. The results showed that, on average, our proposed CNN outperformed our previous algorithm and the baseline U-net. In addition, a reduction of outliers could be observed through the use of densely connected convolutions.