Denoising diffusion models have emerged as the go-to generative framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution tasks, which remains an under-explored challenge. Using a diffusion model on an out-of-distribution dataset, realistic reconstructions can be generated, but with hallucinating image features that are uniquely present in the training dataset. To address this discrepancy and improve reconstruction accuracy, we introduce a novel test-time adaptation sampling framework called Steerable Conditional Diffusion. Specifically, this framework adapts the diffusion model, concurrently with image reconstruction, based solely on the information provided by the available measurement. Utilising the proposed method, we achieve substantial enhancements in out-of-distribution performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.

Despite their prevalence in neural networks, we still lack a thorough theoretical characterization of rectified linear unit (ReLU) layers. This article aims to further our understanding of ReLU layers by studying how the activation function ReLU interacts with the linear component of the layer and what role this interaction plays in the success of the neural network in achieving its intended task. To this end, we introduce two new tools: ReLU singular values of operators and the Gaussian mean width of operators. By presenting, on the one hand, theoretical justifications, results, and interpretations of these two concepts and, on the other hand, numerical experiments and results of the ReLU singular values and the Gaussian mean width being applied to trained neural networks, we hope to give a comprehensive, singular-value-centric view of ReLU layers. We find that ReLU singular values and the Gaussian mean width do not only enable theoretical insights but also provide one with metrics that seem promising for practical applications. In particular, these measures can be used to distinguish correctly and incorrectly classified data as it traverses the network. We conclude by introducing two tools based on our findings: double layers and harmonic pruning.

Recent studies on the adversarial vulnerability of neural networks have shown that models trained to be more robust to adversarial attacks exhibit more interpretable saliency maps than their non-robust counterparts. We aim to quantify this behaviour by considering the alignment between input image and saliency map. We hypothesize that as the distance to the decision boundary grows, so does the alignment. This connection is strictly true in the case of linear models. We confirm these theoretical findings with experiments based on models trained with a local Lipschitz regularization and identify where the nonlinear nature of neural networks weakens the relation.

MOTIVATION: Non-negative matrix factorization (NMF) is a common tool for obtaining low-rank approximations of non-negative data matrices and has been widely used in machine learning, e.g. for supporting feature extraction in high-dimensional classification tasks. In its classical form, NMF is an unsupervised method, i.e. the class labels of the training data are not used when computing the NMF. However, incorporating the classification labels into the NMF algorithms allows to specifically guide them toward the extraction of data patterns relevant for discriminating the respective classes. This approach is particularly suited for the analysis of mass spectrometry imaging (MSI) data in clinical applications, such as tumor typing and classification, which are among the most challenging tasks in pathology. Thus, we investigate algorithms for extracting tumor-specific spectral patterns from MSI data by NMF methods. RESULTS: In this article, we incorporate a priori class labels into the NMF cost functional by adding appropriate supervised penalty terms. Numerical experiments on a MALDI imaging dataset confirm that the novel supervised NMF methods lead to significantly better classification accuracy and stability as compared with other standard approaches. AVAILABILITY AND IMPLEMENTATON: https://gitlab.informatik.uni-bremen.de/digipath/Supervised_NMF_Methods_for_MALDI.git. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivation: Tumor classification using imaging mass spectrometry (IMS) data has a high potential for future applications in pathology. Due to the complexity and size of the data, automated feature extraction and classification steps are required to fully process the data. Since mass spectra exhibit certain structural similarities to image data, deep learning may offer a promising strategy for classification of IMS data as it has been successfully applied to image classification. Results: Methodologically, we propose an adapted architecture based on deep convolutional networks to handle the characteristics of mass spectrometry data, as well as a strategy to interpret the learned model in the spectral domain based on a sensitivity analysis. The proposed methods are evaluated on two algorithmically challenging tumor classification tasks and compared to a baseline approach. Competitiveness of the proposed methods is shown on both tasks by studying the performance via cross-validation. Moreover, the learned models are analyzed by the proposed sensitivity analysis revealing biologically plausible effects as well as confounding factors of the considered tasks. Thus, this study may serve as a starting point for further development of deep learning approaches in IMS classification tasks. Availability and implementation: https://gitlab.informatik.uni-bremen.de/digipath/Deep_Learning_for_Tumor_Classification_in_IMS. Contact: [email protected] or [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

X-ray computed tomography is an important technique for clinical diagnose and nondestructive testing. In many applications a number of image processing steps are needed before the image information becomes useful. Image segmentation is one of such processing steps and has important applications. The conventional flow is to first reconstruct the image and then obtain image segmentation afterwards. In contrast, an iterative method for simultaneous reconstruction and segmentation (SRS) with Mumford-Shah model has been proposed, which not only regularizes the ill-posedness of the tomographic reconstruction problem, but also produces the image segmentation at the same time. The Mumford-Shah model is both mathematically and computationally difficult. In this paper, we propose a data-decomposed algorithm of the SRS method, accelerate it using FPGA devices. The proposed algorithm has a structure that invokes a single kernel many times without involving other computational tasks. Though this structure seems best fit on GPU-like devices, experimental results show that a 73X, 11X, and 1.4X speedup can be achieved by the FPGA acceleration over the CPU implementation of the original SRS algorithm and ray-parallel SRS algorithm, and the GPU implementation of the ray-parallel SRS.

The conventional approach of computed tomography (CT) is to solve each image processing task individually in sequence. An obvious drawback is that the measured data is only used once at the first step, and the possible errors, from noises in the measured data, inappropriate modeling, or inappropriate parameters, are not easy to be corrected and will be propagated into the later steps. As a consequence, approaches that combine the reconstruction and the specific processing task have become popular. This work adopts an iterative algorithm with simultaneous reconstruction and segmentation using the Mumford-Shah model, which can be applied not only to regularize the ill-posedness of the tomographic reconstruction problem, but also to compute segmentation directly from the measured data. The Mumford-Shah model is both mathematically and computationally difficult. In this paper, we accelerated this computation and data intensive application by FPGA devices and achieved 9.24X speedup over the conventional CPU implementation.

Image segmentation aims at partitioning an image into multiple segments. The application of this procedure produces a label map (also referred to as segmentation map) that classifies the pixels of the original image. In contrast to "natural" images, label maps are nominal-scale images, typically represented as integer-valued images. Nominal-scaled label maps can also appear as a representation of the raw data in areas, such as in geostatistics. In some applications, the original resolution of a label map does not suffice and a larger size map has to be generated. In this paper, we present a magnification algorithm for label maps and nominal images. The main property of our method is that it preserves the topology during the magnification process, which means that no isolated pixel vanishes. To the best of our knowledge, apart from nearest-neighbor interpolation, the problem of label map magnification has not previously been addressed in the literature. The main idea of the proposed method is to accomplish a boundary refinement by smoothing the regions' boundaries on a finer grid. The method relies on well known methods, namely, the fundamental operations of morphological image processing-erosion and dilation-and the level-set method. The level-set method is well suited for our purposes since it does not depend on a parametrization and it is numerically stable. The topological flexibility of the level-set method-often found to be an advantage in applications-is a drawback here, since the topology of the original label map should be preserved. However, using the so-called simple point criterion from digital topology, one can adapt the conventional level-set method so that the topology will not be modified throughout the magnification procedure.

MOTIVATION: Automatic classification of high-resolution mass spectrometry proteomic data has increasing potential in the early diagnosis of cancer. We propose a new procedure of biomarker discovery in serum protein profiles based on: (i) discrete wavelet transformation of the spectra; (ii) selection of discriminative wavelet coefficients by a statistical test and (iii) building and evaluating a support vector machine classifier by double cross-validation with attention to the generalizability of the results. In addition to the evaluation results (total recognition rate, sensitivity and specificity), the procedure provides the biomarker patterns, i.e. the parts of spectra which discriminate cancer and control individuals. The evaluation was performed on matrix-assisted laser desorption ionization time-of-flight (MALDI-TOF) serum protein profiles of 66 colorectal cancer patients and 50 controls. RESULTS: Our procedure provided a high recognition rate (97.3%), sensitivity (98.4%) and specificity (95.8%). The extracted biomarker patterns mostly represent the peaks expressing mean differences between the cancer and control spectra. However, we showed that the discriminative power of a peak is not simply expressed by its mean height and cannot be derived by comparison of the mean spectra. The obtained classifiers have high generalization power as measured by the number of support vectors. This prevents overfitting and contributes to the reproducibility of the results, which is required to find biomarkers differentiating cancer patients from healthy individuals. AVAILABILITY: The data and scripts used in this study are available at http://www.math.uni-bremen.de/~theodore/MALDIDWT.

In this paper, we propose a wavelet-based image-coding scheme allowing lossless and lossy compression, simultaneously. Our two-layered approach utilizes the best of two worlds: it uses a highly performing wavelet-based or wavelet packet-based coding technique for lossy compression in the low bit range as a first stage. For the second (optional) stage, we extend the concept of reversible integer wavelet transforms to the more flexible class of adaptive reversible integer wavelet packet transforms which are based on the generation of a whole library of bases, from which the best representation for a given residue between the reconstructed lossy compressed image and the original image is chosen using a fast-search algorithm. We present experimental results demonstrating that our compression algorithm yields a rate-distortion performance similar or superior to the best currently published pure lossy still image-coding methods. At the same time, the lossless compression performance of our two-layered scheme is comparable to that of state-of-the-art pure lossless image-coding schemes. Compared to other combined lossy/lossless coding schemes such as the emerging JPEG-2000 still image-coding standard PSNR improvements up to 3 dB are achieved for a set of standard test images.

The authors derives an algorithm for reconstructing contours of an object from 3D cone beam X-ray data. By reducing the amount of the searched-for information, contours, or density jumps instead of the densities themselves, the authors are able to develop fast algorithms for data incomplete with respect to both the movement of the X-ray source and the detector reading. The method is related to local or Lambda tomography. Numerical simulations show the efficiency of the algorithm.