arXiv subjects

Samuli Siltanen

Publications and source records attributed to Samuli Siltanen.

At least 19 recordsLinked to original sources

arXiv2026

Mathematical framework for perception-driven parameter choice in image denoising

We approach image denoising from a perception-driven perspective: how can we select the parameters that are best suited for human visual perception? We combine research methods in mathematics and psychology to develop a mathematical framework for measuring perceived similarity. We construct a sample set of differently denoised photographs by using the same base image as input data and by tuning the parameter value in a total variation denoising algorithm. A comparison test is conducted with human participants to survey perceived differences between the images. Analyzing the results with psychometric scaling provides us with a HaarPSI value to use as a threshold in discretizing parameter grids. As a result, we obtain psychometrically scaled, openly available image sets that are ready to use in further experiments in perception-driven imaging, as well as a framework for ensuing experiments involving comparison tests.

eess.IV↗

arXiv2026

Complex Wavelet-Based Sinogram Segmentation for Metal Artifact Reduction in Cone-Beam CT

Metal objects pose a significant challenge in cone-beam computed tomography, as their strong and energy-dependent X-ray attenuation leads to inconsistent projections and severe streaking and shading artifacts in reconstructed images. These artifacts degrade image quality and limit the reliability of subsequent medical analysis. We propose a projection-domain metal artifact reduction method based on analytical metal segmentation in the three-dimensional sinogram using the three-dimensional Dual-Tree Complex Wavelet Transform, where directional wavelet coefficients are exploited to extract the wavefront set and singular support of metal structures. The resulting segmentation enables projection-domain inpainting and artifact-reduced reconstruction by combining metal-free and metal-only reconstructions. The proposed approach is evaluated on both simulated and clinical cone-beam computed tomography data and consistently reduces metal artifacts compared to conventional image-domain hard-thresholding methods. The results demonstrate improved visual quality and robustness in clinically realistic scenarios, highlighting the potential of analytically grounded, non-learned projection-domain segmentation for metal artifact reduction.

physics.med-ph↗

arXiv2026

Automatic regularization parameter choice for tomography using a double model approach

Image reconstruction in X-ray tomography is an ill-posed inverse problem, particularly with limited available data. Regularization is thus essential, but its effectiveness hinges on the choice of a regularization parameter that balances data fidelity against a priori information. We present a novel method for automatic parameter selection based on the use of two distinct computational discretizations of the same problem. A feedback control algorithm dynamically adjusts the regularization strength, driving an iterative reconstruction toward the smallest parameter that yields sufficient similarity between reconstructions on the two grids. The effectiveness of the proposed approach is demonstrated using real tomographic data.

cs.CV↗

arXiv2025

Recomposed realities: animating still images via patch clustering and randomness

We present a patch-based image reconstruction and animation method that uses existing image data to bring still images to life through motion. Image patches from curated datasets are grouped using k-means clustering and a new target image is reconstructed by matching and randomly sampling from these clusters. This approach emphasizes reinterpretation over replication, allowing the source and target domains to differ conceptually while sharing local structures.

cs.CV↗

arXiv2025

Learned enclosure method for experimental EIT data

Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary measurements is nonlinear and highly ill-posed, making it difficult to solve accurately. In recent years, there has been growing interest in combining analytical methods with machine learning to solve inverse problems. In this paper, we propose a method for estimating the convex hull of inclusions from boundary measurements by combining the enclosure method proposed by Ikehata with neural networks. We demonstrate its performance using experimental data. Compared to the classical enclosure method with least squares fitting, the learned convex hull achieves superior performance on both simulated and experimental data.

eess.IV↗

arXiv2025

Dual-grid parameter choice method with application to image deblurring

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice remains an open question in general. A novel approach for parameter choice is introduced, based on the use of two slightly different computational models for the same inverse problem. Small parameter values should give two very different reconstructions due to amplification of noise. Large parameter values lead to two identical but trivial reconstructions. Optimal parameter is chosen between the extremes by matching image similarity of the two reconstructions with a pre-defined value. Efficacy of the new method is demonstrated with image deblurring using measured data and two different regularizers.

math.NA↗

arXiv2025

Stroke classification using Virtual Hybrid Edge Detection from in silico electrical impedance tomography data

Electrical impedance tomography (EIT) is a non-invasive imaging method for recovering the internal conductivity of a physical body from electric boundary measurements. EIT combined with machine learning has shown promise for the classification of strokes. However, most previous works have used raw EIT voltage data as network inputs. We build upon a recent development which suggested the use of special noise-robust Virtual Hybrid Edge Detection (VHED) functions as network inputs, although that work used only highly simplified and mathematically ideal models. In this work we strengthen the case for the use of EIT, and VHED functions especially, for stroke classification. We design models with high detail and mathematical realism to test the use of VHED functions as inputs. Virtual patients are created using a physically detailed 2D head model which includes features known to create challenges in real-world imaging scenarios. Conductivity values are drawn from statistically realistic distributions, and phantoms are afflicted with either hemorrhagic or ischemic strokes of various shapes and sizes. Simulated noisy EIT electrode data, generated using the realistic Complete Electrode Model (CEM) as opposed to the mathematically ideal continuum model, is processed to obtain VHED functions. We compare the use of VHED functions as inputs against the alternative paradigm of using raw EIT voltages. Our results show that (i) stroke classification can be performed with high accuracy using 2D EIT data from physically detailed and mathematically realistic models, and (ii) in the presence of noise, VHED functions outperform raw data as network inputs.

math.AP↗

arXiv2024

Image Reconstruction in Cone Beam Computed Tomography Using Controlled Gradient Sparsity

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray tomography (CBCT) has been limited so far, mainly due to heavy computational loads at clinically relevant 3D resolutions and the difficulty in choosing the regularization parameter. Here an efficient minimization algorithm is presented, combined with a dynamic parameter adjustment based on control theory. The result is a fully automatic 3D reconstruction method running in clinically acceptable time. The input on top of projection data and system geometry is desired degree of sparsity of the reconstruction. This can be determined from an atlas of CT scans, or alternatively used as an easily adjustable parameter with straightforward interpretation.

physics.med-ph↗

arXiv2024

CT scans without X-rays: parallel-beam imaging from nonlinear current flows

Parallel-beam X-ray computed tomography (CT) and electrical impedance tomography (EIT) are two imaging modalities which stem from completely different underlying physics, and for decades have been thought to have little in common either practically or mathematically. CT is only mildly ill-posed and uses straight X-rays as measurement energy, which admits simple linear mathematics. However, CT relies on exposing targets to ionizing radiation and requires cumbersome setups with expensive equipment. In contrast, EIT uses harmless electrical currents as measurement energy and can be implemented using simple low-cost portable setups. But EIT is burdened by nonlinearity stemming from the curved paths of electrical currents, as well as extreme ill-posedness which causes characteristic low spatial resolution. In practical EIT reconstruction methods, nonlinearity and ill-posedness have been considered intertwined in a complicated fashion. In this work we demonstrate a surprising connection between CT and EIT which partly unravels the main problems of EIT and leads directly to a proposed imaging modality which we call virtual hybrid parallel-beam tomography (VHPT). We show that hidden deep within EIT data is information which possesses the same linear geometry as parallel-beam CT data. This admits a fundamental restructuring of EIT, separating ill-posedness and nonlinearity into simple modular sub-problems, and yields ''virtual radiographs'' and CT-like images which reveal previously concealed information. Furthermore, as proof of concept we present VHPT images of real-world objects.

math.AP↗

arXiv2024

Helsinki Speech Challenge 2024

The Helsinki Speech Challenge 2024 (HSC2024) invites researchers to enhance and deconvolve speech audio recordings. We recorded a dataset that challenges participants to apply speech enhancement and inverse problems techniques to recorded speech data. This dataset includes paired samples of AI-generated clean speech and corresponding recordings, which feature varying levels of corruption, including frequency attenuation and reverberation. The challenge focuses on developing innovative deconvolution methods to accurately recover the original audio. The effectiveness of these methods will be quantitatively assessed using a speech recognition model, providing a relevant metric for evaluating enhancements in real-world scenarios.

eess.AS↗

arXiv2023

TILT: topological interface recovery in limited-angle tomography

A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown target, while some oriented singularities remain invisible in the data. Topological Interface recovery for Limited-angle Tomography, or TILT, is based on lifting the visible part of the wavefront set under a universal covering map. In the space provided, it is possible to connect the appropriate pieces of the lifted wavefront set correctly using dual-tree complex wavelets, a dedicated metric, and persistent homology. The result is not only a suggested invisible boundary but also a computational representation for all interfaces in the target.

eess.IV↗

arXiv2023

Inner product regularized multi-energy X-ray tomography for material decomposition

Multi-energy X-ray tomography is studied for decomposing three materials using three X-ray energies and a classical energy-integrating detector. A novel regularization term comprises inner products between the material distribution functions, penalizing any overlap of different materials. The method is tested on real data measured of a phantom embedded with Na$_2$SeO$_3$, Na$_2$SeO$_4$, and elemental selenium. It is found that the two-dimensional distributions of selenium in different oxidation states can be mapped and distinguished from each other with the new algorithm. The results have applications in material science, chemistry, biology and medicine.

cond-mat.mtrl-sci↗

arXiv2022

Learning a microlocal prior for limited-angle tomography

Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along the central direction of projections, leading to poor separation between slices perpendicular to the central direction. A new method is introduced, based on machine learning and geometry, producing an estimate for interfaces between regions of different X-ray attenuation. The estimate can be presented on top of the reconstruction, indicating more reliably the true form and extent of features. The method uses directional edge detection, implemented using complex wavelets and enhanced with morphological operations. By using machine learning, the visible part of the wavefront set is first extracted and then extended to the full domain, filling in the parts of the wavefront set that would otherwise be hidden due to the lack of measurement directions.

eess.IV↗

arXiv2021

Anatomical atlas of the upper part of the human head for electroencephalography and bioimpedance applications

Volume conductor problems in cerebral electrophysiology and bioimpedance do not have analytical solutions for nontrivial geometries and require a 3D model of the head and its electrical properties for solving the associated PDEs numerically. Ideally, the model should be made with patient-specific information. In clinical practice, this is not always the case and an average head model is often used. Also, the electrical properties of the tissues might not be completely known due to natural variability. The objective of this work is to develop a 4D (3D+T) statistical anatomical atlas of the electrical properties of the upper part of the human head for cerebral electrophysiology and bioimpedance applications. The atlas is an important tool for in silico studies on cerebral circulation and electrophysiology that require statistically consistent data, e.g., machine learning, sensitivity analyses, and as a benchmark to test inverse problem solvers. The atlas was constructed based on MRI images of human individuals and comprises the electrical properties of the main internal structures and can be adjusted for specific electrical frequencies. The proposed atlas also comprises a time-varying model of arterial brain circulation, based on the solution of the Navier-Stokes equation in the main arteries and their vascular territories. The atlas was successfully used to simulate electrical impedance tomography measurements indicating the necessity of signal-to-noise between 100 and 125dB to identify vascular changes due to the cardiac cycle, corroborating previous studies.

physics.med-ph↗

arXiv2021

Material-separating regularizer for multi-energy X-ray tomography

Dual-energy X-ray tomography is considered in a context where the target under imaging consists of two distinct materials. The materials are assumed to be possibly intertwined in space, but at any given location there is only one material present. Further, two X-ray energies are chosen so that there is a clear difference in the spectral dependence of the attenuation coefficients of the two materials. A novel regularizer is presented for the inverse problem of reconstructing separate tomographic images for the two materials. A combination of two things, (a) non-negativity constraint, and (b) penalty term containing the inner product between the two material images, promotes the presence of at most one material in a given pixel. A preconditioned interior point method is derived for the minimization of the regularization functional. Numerical tests with digital phantoms suggest that the new algorithm outperforms the baseline method, Joint Total Variation regularization, in terms of correctly material-characterized pixels. While the method is tested only in a two-dimensional setting with two materials and two energies, the approach readily generalizes to three dimensions and more materials. The number of materials just needs to match the number of energies used in imaging.

math.NA↗

arXiv2021

Helsinki Deblur Challenge 2021: description of photographic data

The photographic dataset collected for the Helsinki Deblur Challenge 2021 (HDC2021) contains pairs of images taken by two identical cameras of the same target but with different conditions. One camera is always in focus and produces sharp and low-noise images the other camera produces blurred and noisy images as it is gradually more and more out of focus and has a higher ISO setting. Even though the dataset was designed and captured with the HDC2021 in mind it can be used for any testing and benchmarking of image deblurring algorithms. The data is available here: https://doi.org/10.5281/zenodo.477228

eess.IV↗

arXiv2021

Synergistic Multi-spectral CT Reconstruction with Directional Total Variation

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel, we propose to fuse this available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise-ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyze the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed.

math.OC↗

arXiv2021

4D Dual-Tree Complex Wavelets for Time-Dependent Data

The dual-tree complex wavelet transform (DT-$\mathbb{C}$WT) is extended to the 4D setting. Key properties of 4D DT-$\mathbb{C}$WT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic three-dimensional target from X-ray projection measurements can be formulated as 4D space-time tomography. The results suggest that 4D DT-$\mathbb{C}$WT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.

math.NA↗