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In this paper, we study collision-free graph exploration in an anonymous pot labeled network. Two identical mobile agents, starting from different nodes in $G$ have to explore the nodes of $G$ in such a way that for every node $v$ in $G$, at least one mobile agent visits $v$ and no two agents are in the same node in any round and stop. The agents know the size of the graph but do not know its topology. If an agent arrives in the one-hop neighborhood of the other agent, both agents can detect the presence of the other agent but have no idea at which neighboring node the other agent resides. The agents may wake up in different rounds An agent, after waking up, has no knowledge about the wake-up time of the other agent. We study the problem of collision-free exploration where some pebbles are placed by an Oracle at the nodes of the graph to assist the agents in achieving collision-free exploration. The Oracle knows the graph, the starting positions of the agents, and their wake-up schedule, and it places some pebbles that may be of different colors, at most one at each node. The number of different colors of the pebbles placed by the Oracle is called the {\it color index} of the corresponding pebble placement algorithm. The central question we study is as follows: "What is the minimum number $z$ such that there exists a collision-free exploration of a given graph with pebble placement of color index $z$?" For general graphs, we show that it is impossible to design an algorithm that achieves collision-free exploration with color index 1. We propose an exploration algorithm with color index 3. We also proposed a polynomial exploration algorithm for bipartite graphs with color index 2.

Kernel-based nonlinear dictionary learning methods operate in a feature space obtained by an implicit feature map, and they are not independent of computationally expensive operations like Singular Value Decomposition (SVD). This paper presents an SVD-free lightweight approach to learning a nonlinear dictionary using a randomized functional link called a Random Vector Functional Link (RVFL). The proposed RVFL-based nonlinear Dictionary Learning (RVFLDL) learns a dictionary as a sparse-to-dense feature map from nonlinear sparse coefficients to the dense input features. Sparse coefficients w.r.t an initial random dictionary are derived by assuming Horseshoe prior are used as inputs making it a lightweight network. Training the RVFL-based dictionary is free from SVD computation as RVFL generates weights from the input to the output layer analytically. Higher-order dependencies between the input sparse coefficients and the dictionary atoms are incorporated into the training process by nonlinearly transforming the sparse coefficients and adding them as enhanced features. Thus the method projects sparse coefficients to a higher dimensional space while inducing nonlinearities into the dictionary. For classification using RVFL-net, a classifier matrix is learned as a transform that maps nonlinear sparse coefficients to the labels. The empirical evidence of the method illustrated in image classification and reconstruction applications shows that RVFLDL is scalable and provides a solution better than those obtained using other nonlinear dictionary learning methods.

X-ray computed tomography (CT) based on photon counting detectors (PCD) extends standard CT by counting detected photons in multiple energy bins. PCD data can be used to increase the contrast-to-noise ratio (CNR), increase spatial resolution, reduce radiation dose, reduce injected contrast dose, and compute a material decomposition using a specified set of basis materials. Current commercial and prototype clinical photon counting CT systems utilize PCD-CT reconstruction methods that either reconstruct from each spectral bin separately, or first create an estimate of a material sinogram using a specified set of basis materials and then reconstruct from these material sinograms. However, existing methods are not able to utilize simultaneously and in a modular fashion both the measured spectral information and advanced prior models in order to produce a material decomposition. We describe an efficient, modular framework for PCD-based CT reconstruction and material decomposition using on Multi-Agent Consensus Equilibrium (MACE). Our method employs a detector proximal map or agent that uses PCD measurements to update an estimate of the pathlength sinogram. We also create a prior agent in the form of a sinogram denoiser that enforces both physical and empirical knowledge about the material-decomposed sinogram. The sinogram reconstruction is computed using the MACE algorithm, which finds an equilibrium solution between the two agents, and the final image is reconstructed from the estimated sinogram. Importantly, the modularity of our method allows the two agents to be designed, implemented, and optimized independently. Our results on simulated data show a substantial (450%) CNR boost vs conventional maximum likelihood reconstruction when applied to a phantom used to evaluate low contrast detectability., Comment: 11 pages, 10 figures, submitted to SPIE Medical Imaging 2024

Deep neural networks (DNN) are commonly used to denoise and sharpen X-ray computed tomography (CT) images with the goal of reducing patient X-ray dosage while maintaining reconstruction quality. However, naive application of DNN-based methods can result in image texture that is undesirable in clinical applications. Alternatively, generative adversarial network (GAN) based methods can produce appropriate texture, but naive application of GANs can introduce inaccurate or even unreal image detail. In this paper, we propose a texture matching generative adversarial network (TMGAN) that enhances CT images while generating an image texture that can be matched to a target texture. We use parallel generators to separate anatomical features from the generated texture, which allows the GAN to be trained to match the desired texture without directly affecting the underlying CT image. We demonstrate that TMGAN generates enhanced image quality while also producing image texture that is desirable for clinical application., Comment: Submitted to IEEE Transactions on Medical Imaging

Image-based crop growth modeling can substantially contribute to precision agriculture by revealing spatial crop development over time, which allows an early and location-specific estimation of relevant future plant traits, such as leaf area or biomass. A prerequisite for realistic and sharp crop image generation is the integration of multiple growth-influencing conditions in a model, such as an image of an initial growth stage, the associated growth time, and further information about the field treatment. We present a two-stage framework consisting first of an image prediction model and second of a growth estimation model, which both are independently trained. The image prediction model is a conditional Wasserstein generative adversarial network (CWGAN). In the generator of this model, conditional batch normalization (CBN) is used to integrate different conditions along with the input image. This allows the model to generate time-varying artificial images dependent on multiple influencing factors of different kinds. These images are used by the second part of the framework for plant phenotyping by deriving plant-specific traits and comparing them with those of non-artificial (real) reference images. For various crop datasets, the framework allows realistic, sharp image predictions with a slight loss of quality from short-term to long-term predictions. Simulations of varying growth-influencing conditions performed with the trained framework provide valuable insights into how such factors relate to crop appearances, which is particularly useful in complex, less explored crop mixture systems. Further results show that adding process-based simulated biomass as a condition increases the accuracy of the derived phenotypic traits from the predicted images. This demonstrates the potential of our framework to serve as an interface between an image- and process-based crop growth model., Comment: 26 pages, 16 figures, code available at https://github.com/luked12/crop-growth-cgan

Deep learning (DL) shows promise of advantages over conventional signal processing techniques in a variety of imaging applications. The networks' being trained from examples of data rather than explicitly designed allows them to learn signal and noise characteristics to most effectively construct a mapping from corrupted data to higher quality representations. In inverse problems, one has options of applying DL in the domain of the originally captured data, in the transformed domain of the desired final representation, or both. X-ray computed tomography (CT), one of the most valuable tools in medical diagnostics, is already being improved by DL methods. Whether for removal of common quantum noise resulting from the Poisson-distributed photon counts, or for reduction of the ill effects of metal implants on image quality, researchers have begun employing DL widely in CT. The selection of training data is driven quite directly by the corruption on which the focus lies. However, the way in which differences between the target signal and measured data is penalized in training generally follows conventional, pointwise loss functions. This work introduces a creative technique for favoring reconstruction characteristics that are not well described by norms such as mean-squared or mean-absolute error. Particularly in a field such as X-ray CT, where radiologists' subjective preferences in image characteristics are key to acceptance, it may be desirable to penalize differences in DL more creatively. This penalty may be applied in the data domain, here the CT sinogram, or in the reconstructed image. We design loss functions for both shaping and selectively preserving frequency content of the signal.