Investigating Intensity Normalisation for PET Reconstruction with Supervised Deep Learning

Deep learning methods have shown great promise in the field of Positron Emission Tomography (PET) reconstruction, but the successful application of these methods depends heavily on the intensity scale of the images. Normalisation is a crucial step that aims to adjust the intensity of network inputs to make them more uniform and comparable across samples, acquisition times, and activity levels. In this work, we study the influence of different linear intensity normalisation approaches. We focus on two popular deep learning based image reconstruction methods: an unrolled algorithm (Learned Primal-Dual) and a post-processing method (OSEMConvNet). Results on the out-ofdistribution test dataset demonstrate that the choice of intensity normalisation significantly impacts on generalisability of these methods. Normalisation using the mean of acquisition data or corrected acquisition data led to improved peak-signal-to-noiseratio (PSNR) and data-consistency (KLDIV). Through evaluation of lesion-specific metrics of contrast recovery coefficients (CRC) and standard deviation (STD) an increase in CRC and STD is observed. These findings highlight the importance of carefully selecting an appropriate normalisation method for supervised deep learning-based PET reconstruction applications

PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization

Learning neural networks using only few available information is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a powerful regularizer for the variational modeling of inverse problems in imaging. Our regularizer, called patch normalizing flow regularizer (patchNR), involves a normalizing flow learned on small patches of very few images. In particular, the training is independent of the considered inverse problem such that the same regularizer can be applied for different forward operators acting on the same class of images. By investigating the distribution of patches versus those of the whole image class, we prove that our model is indeed a MAP approach. Numerical examples for low-dose and limited-angle computed tomography (CT) as well as superresolution of material images demonstrate that our method provides very high quality results. The training set consists of just six images for CT and one image for superresolution. Finally, we combine our patchNR with ideas from internal learning for performing superresolution of natural images directly from the low-resolution observation without knowledge of any high-resolution image

Spectral Background-Subtracted Activity Maps

High-resolution solar spectroscopy provides a wealth of information from photospheric and chromospheric spectral lines. However, the volume of data easily exceeds hundreds of millions of spectra on a single observation day. Therefore, methods are needed to identify spectral signatures of interest in multidimensional datasets. Background-subtracted activity maps (BaSAMs) have previously been used to locate features of solar activity in time series of images and filtergrams. This research note shows how this method can be extended and adapted to spectral data.Comment: 3 pages, 1 figure, initial version submitted to Research Notes of the AA

An Educated Warm Start For Deep Image Prior-Based Micro CT Reconstruction

Deep image prior (DIP) was recently introduced as an effective unsupervised approach for image restoration tasks. DIP represents the image to be recovered as the output of a deep convolutional neural network, and learns the network's parameters such that the output matches the corrupted observation. Despite its impressive reconstructive properties, the approach is slow when compared to supervisedly learned, or traditional reconstruction techniques. To address the computational challenge, we bestow DIP with a two-stage learning paradigm: (i) perform a supervised pretraining of the network on a simulated dataset; (ii) fine-tune the network's parameters to adapt to the target reconstruction task. We provide a thorough empirical analysis to shed insights into the impacts of pretraining in the context of image reconstruction. We showcase that pretraining considerably speeds up and stabilizes the subsequent reconstruction task from real-measured 2D and 3D micro computed tomography data of biological specimens. The code and additional experimental materials are available at https://educateddip.github.io/docs.educated_deep_image_prior/

Invertible residual networks in the context of regularization theory for linear inverse problems

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility enables investigating the influence of the training and architecture choices on the resulting reconstruction scheme. For example, assuming local approximation properties of the network, we show that these schemes become convergent regularizations. In addition, the investigations reveal a formal link to the linear regularization theory of linear inverse problems and provide a nonlinear spectral regularization for particular architecture classes. On the numerical side, we investigate the local approximation property of selected trained architectures and present a series of experiments on the MNIST dataset that underpin and extend our theoretical findings

Ultrafast Demagnetization of Iron Induced by Optical versus Terahertz Pulses

We study ultrafast magnetization quenching of ferromagnetic iron following excitation by an optical versus a terahertz pump pulse. While the optical pump (photon energy of 3.1 eV) induces a strongly nonthermal electron distribution, terahertz excitation (4.1 meV) results in a quasithermal perturbation of the electron population. The pump-induced spin and electron dynamics are interrogated by the magneto-optic Kerr effect (MOKE). A deconvolution procedure allows us to push the time resolution down to 130 fs, even though the driving terahertz pulse is about 500 fs long. Remarkably, the MOKE signals exhibit an almost identical time evolution for both optical and terahertz pump pulses, despite the 3 orders of magnitude different number of excited electrons. We are able to quantitatively explain our results using a nonthermal model based on quasielastic spin-flip scattering. It shows that, in the small-perturbation limit, the rate of demagnetization of a metallic ferromagnet is proportional to the excess energy of the electrons, independent of the precise shape of their distribution. Our results reveal that, for simple metallic ferromagnets, the dynamics of ultrafast demagnetization and of the closely related terahertz spin transport do not depend on the pump photon energy

Alpha scattering and capture reactions in the A = 7 system at low energies

Differential cross sections for $^3$He-$\alpha$ scattering were measured in the energy range up to 3 MeV. These data together with other available experimental results for $^3$He $+ \alpha$ and $^3$H $+ \alpha$ scattering were analyzed in the framework of the optical model using double-folded potentials. The optical potentials obtained were used to calculate the astrophysical S-factors of the capture reactions $^3$He$(\alpha,\gamma)^7$Be and $^3$H$(\alpha,\gamma)^7$Li, and the branching ratios for the transitions into the two final $^7$Be and $^7$Li bound states, respectively. For $^3$He$(\alpha,\gamma)^7$Be excellent agreement between calculated and experimental data is obtained. For $^3$H$(\alpha,\gamma)^7$Li a $S(0)$ value has been found which is a factor of about 1.5 larger than the adopted value. For both capture reactions a similar branching ratio of $R = \sigma(\gamma_1)/\sigma(\gamma_0) \approx 0.43$ has been obtained.Comment: submitted to Phys.Rev.C, 34 pages, figures available from one of the authors, LaTeX with RevTeX, IK-TUW-Preprint 930540