Satellite image segmentation is crucial in various fields, but acquiring a large amount of labeled data can be challenging. Often, remote sensing images are unlabeled due to the high cost of manual labeling, which hampers training effectiveness and generalization. To address this issue, we propose a spatially and temporally informed graph-based semi-supervised learning approach for satellite image segmentation based on Poisson learning. The main difference to traditional Poisson learning is that our distance function that we use to compute similarity between pixels considers spectral, spatial, and temporal information. Experimental results on the Sentinel-2 time series demonstrate that our approach outperforms other traditional approaches, achieving robust performance in remote sensing image segmentation, especially at a very low label rate.

Multiresolution deep learning approaches, such as the U-Net architecture, have achieved high performance in classifying and segmenting images. Most traditional convolutional neural network (CNNs) architectures commonly use pooling to enlarge the receptive field, which usually results in irreversible information loss. The U-Net architecture avoids this information loss by introducing skip-connections that allow to reconstruct lost information. Leveraging this property of the U-Net, this study proposes to include a Riesz-Quincunx (RQ) wavelet transform, which combines 1) higher-order Riesz wavelet transform and 2) orthogonal Quincunx wavelets (commonly used to reduce blur in medical images) inside the U-Net to reduce noise in satellite images and their time-series. Combining both approaches, we introduce a hybrid Riesz-Quincunx-UNet Variational Auto-Encoder (RQUNet-VAE) scheme for image and time series decomposition used to reduce noise in satellite imagery. By including denoising capabilities directly inside the UNet architecture, we hypothesize that our RQUNet-VAE may improve downstream image processing tasks that use the traditional U-Net architecture. We present qualitative and quantitative experimental results that demonstrate that our proposed RQUNet-VAE is effective at reducing noise in satellite imagery yielding results similar to other state-of-the-art noise reduction methods. We further show that our RQUNet-VAE outperforms the U-Net architecture specifically in cases where images exhibit high levels of noise. We show this result in two down-stream applications for multi-band satellite images, including image time-series decomposition and image segmentation.

In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that algorithms derived from such minimization problems can be used to construct (deep) learning architectures has spurred the development of algorithms that can be trained for a specifically desired image decomposition, e.g., into cartoon and texture. While many such methods are very successful, theoretical guarantees are only scarcely available. To this end, in this contribution, we formalize a general class of intersection point problems encompassing a wide range of (learned) image decomposition models, and we give an existence result for a large subclass of such problems, i.e., giving the existence of a fixed point of the corresponding algorithm. This class generalizes classical model-based variational problems, such as the TV-$\ell^2$-model or the more general TV-Hilbert model. To illustrate the potential for learned algorithms, novel (nonlearned) choices within our class show comparable results in denoising and texture removal.

Kernel mixture models are routinely used for density estimation. However, in multivariate settings, issues arise in efficiently approximating lower-dimensional structure in the data. For example, it is common to suppose that the density is concentrated near a lower-dimensional non-linear subspace or manifold. Typical kernels used to locally approximate such subspaces are inflexible, so that a large number of components are often needed. We propose a novel class of LOcally COnvex (LOCO) kernels that are flexible in adapting to nonlinear local structure. LOCO kernels are induced by introducing random knots within local neighborhoods, and generating data as a random convex combination of these knots with adaptive weights and an additive noise. For identifiability, we constrain all observations from a particular component to have the same mean. For Bayesian inference subject to this constraint, we develop a hybrid Gibbs sampler and optimization algorithm that incorporates a Lagrange multiplier within a splitting method. The resulting LOCO algorithm is shown to dramatically outperform typical Gaussian mixture models in challenging examples.

Automated biometric identification systems are inherently challenged to optimize false (non-)match rates. This can be addressed either by directly improving comparison subsystems, or indirectly by allowing only “good quality” biometric queries to be compared. We are interested in the latter, where the challenge lies in relating the “good quality” of a query to its utility with respect to a comparison subsystem. First, we propose a new general robust biometric quality validation scheme (RBQ VS) that, mimicking the use-case, robustly quantifies comparison improvement obtained by employing a specific quality estimator. For this purpose, we robustify an existing validation scheme by repeated random subsampling cross-validation. Second, specifically for the task of fingerprint comparison, we propose a novel biometric feature for quality estimation. Since comparison subsystems based on fingerprint minutiae, which are ridge endings and bifurcations, appear to miss minutiae or detect spurious minutiae, especially in the presence of smudge noise, we propose an algorithm aiming at measuring corruption by smudge. To this end, we employ a recently developed three parts image-decomposition and link our new smudge noise quality estimator (SNoQE) to the structure of the texture part found. At last, using the FVC databases and an NIST database, we compare the SNoQE with the popular NFIQ 2.0 estimator, and its predecessor. Experimental results show that the single-feature SNoQE can compete with the multi-feature NFIQ 2.0 and, in fact, adds new information not sufficiently reproduced by the NFIQ 2.0. Indeed, a simple combination of SNoQE and NFIQ 2.0 tends to outperform on all databases included in the comparison study. An implementation of the RBQ VS and the SNoQE can be found online.