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The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a…
We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of…
This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to…
In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational…
The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is…
Filtered backprojection (FBP) is an efficient and popular class of tomographic image reconstruction methods. In photoacoustic tomography, these algorithms are based on theoretically exact analytic inversion formulas which results in…
With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…
The Hough transform (HT) is a fundamental tool across various domains, from classical image analysis to neural networks and tomography. Two key aspects of the algorithms for computing the HT are their computational complexity and accuracy -…
A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability…
Photoacoustic microscopy (PAM) is a novel implementation of photoacoustic imaging (PAI) for visualizing the 3D bio-structure, which is realized by raster scanning of the tissue. However, as three involved critical imaging parameters,…
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
Topological maps are favorable for their small storage compared to geometric map. However, they are limited in relocalization and path planning capabilities. To solve this problem, a feature-based hierarchical topological map (FHT-Map) is…
In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart…
Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two…
A new algorithmic framework is presented for holographic phase retrieval via maximum likelihood optimization, which allows for practical and robust image reconstruction. This framework is especially well-suited for holographic coherent…