arXiv subjects

Joakim Andén

Publications and source records attributed to Joakim Andén.

At least 19 recordsLinked to original sources

arXiv2026

Multiscale reconstruction of protein conformations from cryo-EM images

We present a novel multiscale algorithm for directly recovering the atomic model structure of a protein from single-particle cryo-EM data. Our algorithm is able to estimate protein structures to state-of-the-art accuracy for high-noise and low-contrast data. It is also robust to misspecifications in the TEM image formation model. These desirable properties are primarily due to the use of an explicit representation of the protein backbone in terms of bonds, torsion angles and bond angles, which supplies rich prior information to the structure recovery process. We apply our method on three protein cryo-EM datasets, generated using an electron microscope digital twin, and show that using a multiscale approach yields an improvement of the root-mean-square deviation (RMSD) and template modelling (TM) scores with respect to the ground truth. Furthermore, there is evidence that larger-scale structures are being prioritised with the multiscale algorithm, which reduces the possibility of convergence to bad local minima.

eess.IV↗

arXiv2026

Protein Graph Neural Networks for Heterogeneous Cryo-EM Reconstruction

We present a geometry-aware method for heterogeneous single-particle cryogenic electron microscopy (cryo-EM) reconstruction that predicts atomic backbone conformations. To incorporate protein-structure priors, we represent the backbone as a graph and use a graph neural network (GNN) autodecoder that maps per-image latent variables to 3D displacements of a template conformation. The objective combines a data-discrepancy term based on a differentiable cryo-EM forward model with geometric regularization, and it supports unknown orientations via ellipsoidal support lifting (ESL) pose estimation. On synthetic datasets derived from molecular dynamics trajectories, the proposed GNN achieves higher accuracy compared to a multilayer perceptron (MLP) of comparable size, highlighting the benefits of a geometry-informed inductive bias.

cs.CV↗

arXiv2025

Joint Denoising of Cryo-EM Projection Images using Polar Transformers

Many imaging modalities involve reconstruction of unknown objects from collections of noisy projections related by random rotations. In one of these modalities, cryogenic electron microscopy (cryo-EM), the extremely low signal-to-noise ratio (SNR) makes integration of information from multiple images crucial. Existing approaches to cryo-EM processing, however, either rely on handcrafted priors or apply deep learning only on select portions of the pipeline, such as particle picking, micrograph denoising, or refinement. A fully end-to-end reconstruction approach requires a neural network architecture that integrates information from multiple images while respecting the rotational symmetry of the measurement process. In this work, we introduce the polar transformer, a new neural network architecture that combines polar representations and transformers along with a convolutional attention mechanism that preserves the rotational symmetry of the problem. We apply it to the particle-level denoising problem, where it is able to learn discriminative features in the images, enabling optimal clustering, alignment, and denoising. On simulated datasets, this achieves up to a $2\times$ reduction in mean squared error (MSE) at a signal-to-noise ratio (SNR) of $0.02$, suggesting new opportunities for data-driven approaches to reconstruction in cryo-EM and related tomographic modalities.

eess.IV↗

arXiv2025

Moment-based Posterior Sampling for Multi-reference Alignment

We propose a Bayesian approach to the problem of multi-reference alignment -- the recovery of signals from noisy, randomly shifted observations. While existing frequentist methods accurately recover the signal at arbitrarily low signal-to-noise ratios, they require a large number of samples to do so. In contrast, our proposed method leverages diffusion models as data-driven plug-and-play priors, conditioning these on the sample power spectrum (a shift-invariant statistic) enabling both accurate posterior sampling and uncertainty quantification. The use of an appropriate prior significantly reduces the required number of samples, as illustrated in simulation experiments with comparisons to state-of-the-art methods such as expectation--maximization and bispectrum inversion. These findings establish our approach as a promising framework for other orbit recovery problems, such as cryogenic electron microscopy (cryo-EM).

eess.SP↗

arXiv2025

Moment Constraints and Phase Recovery for Multireference Alignment

Multireference alignment (MRA) refers to the problem of recovering a signal from noisy samples subject to random circular shifts. Expectation--maximization (EM) and variational approaches use statistical modeling to achieve high accuracy at the cost of solving computationally expensive optimization problems. The method of moments, instead, achieves fast reconstructions by utilizing the power spectrum and bispectrum to determine the signal up to shift. Our approach combines the two philosophies by viewing the power spectrum as a manifold on which to constrain the signal. We then maximize the data likelihood function on this manifold with a gradient-based approach to estimate the true signal. Algorithmically, our method involves iterating between template alignment and projections onto the manifold. The method offers increased speed compared to EM and demonstrates improved accuracy over bispectrum-based methods.

cs.IT↗

arXiv2025

A boostlet transform for wave-based acoustic signal processing in space-time

Sparse representation systems that encode signal architecture have had a profound impact on sampling and compression paradigms. Remarkable examples are multi-scale directional systems, which, similar to our vision system, encode the underlying architecture of natural images with sparse features. Inspired by this philosophy, we introduce a representation system for wave-based acoustic signal processing in 2D space--time, referred to as the \emph{boostlet transform}, which encodes sparse features of natural acoustic fields using the Poincaré group and isotropic dilations. Boostlets are spatiotemporal functions parametrized with dilations, Lorentz boosts, and translations in space--time. Physically speaking, boostlets are supported away from the acoustic radiation cone, i.e., having broadband frequency with phase velocities other than the speed of sound, resulting in a peculiar scaling function. We formulate a discrete boostlet frame using Meyer wavelets and bump functions and examine its sparsity properties. An analysis with experimentally measured fields indicates that discrete boostlet coefficients decay significantly faster and attain superior reconstruction performance than wavelets, curvelets, shearlets, and wave atoms. The results demonstrate that boostlets provide a natural, compact representation system for acoustic waves in space-time.

physics.flu-dyn↗

arXiv2025

Sparse wavefield reconstruction and denoising with boostlets

Boostlets are spatiotemporal functions that decompose nondispersive wavefields into a collection of localized waveforms parametrized by dilations, hyperbolic rotations, and translations. We study the sparsity properties of boostlets and find that the resulting decompositions are significantly sparser than those of other state-of-the-art representation systems, such as wavelets and shearlets. This translates into improved denoising performance when hard-thresholding the boostlet coefficients. The results suggest that boostlets offer a natural framework for sparsely decomposing wavefields in unified space-time.

eess.AS↗

arXiv2024

Mean-Field Microcanonical Gradient Descent

Microcanonical gradient descent is a sampling procedure for energy-based models allowing for efficient sampling of distributions in high dimension. It works by transporting samples from a high-entropy distribution, such as Gaussian white noise, to a low-energy region using gradient descent. We put this model in the framework of normalizing flows, showing how it can often overfit by losing an unnecessary amount of entropy in the descent. As a remedy, we propose a mean-field microcanonical gradient descent that samples several weakly coupled data points simultaneously, allowing for better control of the entropy loss while paying little in terms of likelihood fit. We study these models in the context of financial time series, illustrating the improvements on both synthetic and real data.

stat.ML↗

arXiv2022

Wavelet Moments for Cosmological Parameter Estimation

Extracting non-Gaussian information from the non-linear regime of structure formation is key to fully exploiting the rich data from upcoming cosmological surveys probing the large-scale structure of the universe. However, due to theoretical and computational complexities, this remains one of the main challenges in analyzing observational data. We present a set of summary statistics for cosmological matter fields based on 3D wavelets to tackle this challenge. These statistics are computed as the spatial average of the complex modulus of the 3D wavelet transform raised to a power $q$ and are therefore known as invariant wavelet moments. The 3D wavelets are constructed to be radially band-limited and separable on a spherical polar grid and come in three types: isotropic, oriented, and harmonic. In the Fisher forecast framework, we evaluate the performance of these summary statistics on matter fields from the Quijote suite, where they are shown to reach state-of-the-art parameter constraints on the base $Λ$CDM parameters, as well as the sum of neutrino masses. We show that we can improve constraints by a factor 5 to 10 in all parameters with respect to the power spectrum baseline.

astro-ph.CO↗

arXiv2021

cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs

Nonuniform fast Fourier transforms dominate the computational cost in many applications including image reconstruction and signal processing. We thus present a general-purpose GPU-based CUDA library for type 1 (nonuniform to uniform) and type 2 (uniform to nonuniform) transforms in dimensions 2 and 3, in single or double precision. It achieves high performance for a given user-requested accuracy, regardless of the distribution of nonuniform points, via cache-aware point reordering, and load-balanced blocked spreading in shared memory. At low accuracies, this gives on-GPU throughputs around $10^9$ nonuniform points per second, and (even including host-device transfer) is typically 4-10$\times$ faster than the latest parallel CPU code FINUFFT (at 28 threads). It is competitive with two established GPU codes, being up to 90$\times$ faster at high accuracy and/or type 1 clustered point distributions. Finally we demonstrate a 5-12$\times$ speedup versus CPU in an X-ray diffraction 3D iterative reconstruction task at $10^{-12}$ accuracy, observing excellent multi-GPU weak scaling up to one rank per GPU.

cs.DC↗

arXiv2020

Time-Frequency Scattering Accurately Models Auditory Similarities Between Instrumental Playing Techniques

Instrumental playing techniques such as vibratos, glissandos, and trills often denote musical expressivity, both in classical and folk contexts. However, most existing approaches to music similarity retrieval fail to describe timbre beyond the so-called "ordinary" technique, use instrument identity as a proxy for timbre quality, and do not allow for customization to the perceptual idiosyncrasies of a new subject. In this article, we ask 31 human subjects to organize 78 isolated notes into a set of timbre clusters. Analyzing their responses suggests that timbre perception operates within a more flexible taxonomy than those provided by instruments or playing techniques alone. In addition, we propose a machine listening model to recover the cluster graph of auditory similarities across instruments, mutes, and techniques. Our model relies on joint time--frequency scattering features to extract spectrotemporal modulations as acoustic features. Furthermore, it minimizes triplet loss in the cluster graph by means of the large-margin nearest neighbor (LMNN) metric learning algorithm. Over a dataset of 9346 isolated notes, we report a state-of-the-art average precision at rank five (AP@5) of $99.0\%\pm1$. An ablation study demonstrates that removing either the joint time--frequency scattering transform or the metric learning algorithm noticeably degrades performance.

cs.SD↗

arXiv2020

Multitaper estimation on arbitrary domains

Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian tapers is only tractable for certain symmetric domains, such as rectangles or disks. In addition, no performance bounds are currently available for the mean squared error of the spectral density estimate. This situation is inadequate for applications such as cryo-electron microscopy, where noise models must be estimated from irregular domains with small sample sizes. We show that the multitaper estimator only depends on the linear space spanned by the tapers. As a result, Slepian tapers may be replaced by proxy tapers spanning the same subspace (validating the common practice of using partially converged solutions to the Slepian eigenproblem as tapers). These proxies may consequently be calculated using standard numerical algorithms for block diagonalization. We also prove a set of performance bounds for multitaper estimators on arbitrary domains. The method is demonstrated on synthetic and experimental datasets from cryo-electron microscopy, where it reduces mean squared error by a factor of two or more compared to traditional methods.

math.ST↗

arXiv2020

Bias and variance reduction and denoising for CTF Estimation

When using an electron microscope for imaging of particles embedded in vitreous ice, the objective lens will inevitably corrupt the projection images. This corruption manifests as a band-pass filter on the micrograph. In addition, it causes the phase of several frequency bands to be flipped and distorts frequency bands. As a precursor to compensating for this distortion, the corrupting point spread function, which is termed the contrast transfer function (CTF) in reciprocal space, must be estimated. In this paper, we will present a novel method for CTF estimation. Our method is based on the multi-taper method for power spectral density estimation, which aims to reduce the bias and variance of the estimator. Furthermore, we use known properties of the CTF and of the background of the power spectrum to increase the accuracy of our estimation. We will show that the resulting estimates capture the zero-crossings of the CTF in the low-mid frequency range.

eess.IV↗

arXiv2019

Factorization of the translation kernel for fast rigid image alignment

An important component of many image alignment methods is the calculation of inner products (correlations) between an image of $n\times n$ pixels and another image translated by some shift and rotated by some angle. For robust alignment of an image pair, the number of considered shifts and angles is typically high, thus the inner product calculation becomes a bottleneck. Existing methods, based on fast Fourier transforms (FFTs), compute all such inner products with computational complexity $\mathcal{O}(n^3 \log n)$ per image pair, which is reduced to $\mathcal{O}(N n^2)$ if only $N$ distinct shifts are needed. We propose to use a factorization of the translation kernel (FTK), an optimal interpolation method which represents images in a Fourier--Bessel basis and uses a rank-$H$ approximation of the translation kernel via an operator singular value decomposition (SVD). Its complexity is $\mathcal{O}(Hn(n + N))$ per image pair. We prove that $H = \mathcal{O}((W + \log(1/ε))^2)$, where $2W$ is the magnitude of the maximum desired shift in pixels and $ε$ is the desired accuracy. For fixed $W$ this leads to an acceleration when $N$ is large, such as when sub-pixel shift grids are considered. Finally, we present numerical results in an electron cryomicroscopy application showing speedup factors of $3$-$10$ with respect to the state of the art.

math.NA↗

arXiv2019

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.

eess.IV↗

arXiv2019

Joint Time-Frequency Scattering

In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required to be time-shift invariant. We introduce the joint time-frequency scattering transform, a time-shift invariant representation which characterizes the multiscale energy distribution of a signal in time and frequency. It is computed through wavelet convolutions and modulus non-linearities and may therefore be implemented as a deep convolutional neural network whose filters are not learned but calculated from wavelets. We consider the progression from mel-spectrograms to time scattering and joint time-frequency scattering transforms, illustrating the relationship between increased discriminability and refinements of convolutional network architectures. The suitability of the joint time-frequency scattering transform for time-shift invariant characterization of time series is demonstrated through applications to chirp signals and audio synthesis experiments. The proposed transform also obtains state-of-the-art results on several audio classification tasks, outperforming time scattering transforms and achieving accuracies comparable to those of fully learned networks.

cs.SD↗

arXiv2019

Hyper-Molecules: on the Representation and Recovery of Dynamical Structures, with Application to Flexible Macro-Molecular Structures in Cryo-EM

Cryo-electron microscopy (cryo-EM), the subject of the 2017 Nobel Prize in Chemistry, is a technology for determining the 3-D structure of macromolecules from many noisy 2-D projections of instances of these macromolecules, whose orientations and positions are unknown. The molecular structures are not rigid objects, but flexible objects involved in dynamical processes. The different conformations are exhibited by different instances of the macromolecule observed in a cryo-EM experiment, each of which is recorded as a particle image. The range of conformations and the conformation of each particle are not known a priori; one of the great promises of cryo-EM is to map this conformation space. Remarkable progress has been made in determining rigid structures from homogeneous samples of molecules in spite of the unknown orientation of each particle image and significant progress has been made in recovering a few distinct states from mixtures of rather distinct conformations, but more complex heterogeneous samples remain a major challenge. We introduce the ``hyper-molecule'' framework for modeling structures across different states of heterogeneous molecules, including continuums of states. The key idea behind this framework is representing heterogeneous macromolecules as high-dimensional objects, with the additional dimensions representing the conformation space. This idea is then refined to model properties such as localized heterogeneity. In addition, we introduce an algorithmic framework for recovering such maps of heterogeneous objects from experimental data using a Bayesian formulation of the problem and Markov chain Monte Carlo (MCMC) algorithms to address the computational challenges in recovering these high dimensional hyper-molecules. We demonstrate these ideas in a prototype applied to synthetic data.

cs.CV↗

arXiv2018

Extended playing techniques: The next milestone in musical instrument recognition

The expressive variability in producing a musical note conveys information essential to the modeling of orchestration and style. As such, it plays a crucial role in computer-assisted browsing of massive digital music corpora. Yet, although the automatic recognition of a musical instrument from the recording of a single "ordinary" note is considered a solved problem, automatic identification of instrumental playing technique (IPT) remains largely underdeveloped. We benchmark machine listening systems for query-by-example browsing among 143 extended IPTs for 16 instruments, amounting to 469 triplets of instrument, mute, and technique. We identify and discuss three necessary conditions for significantly outperforming the traditional mel-frequency cepstral coefficient (MFCC) baseline: the addition of second-order scattering coefficients to account for amplitude modulation, the incorporation of long-range temporal dependencies, and metric learning using large-margin nearest neighbors (LMNN) to reduce intra-class variability. Evaluating on the Studio On Line (SOL) dataset, we obtain a precision at rank 5 of 99.7% for instrument recognition (baseline at 89.0%) and of 61.0% for IPT recognition (baseline at 44.5%). We interpret this gain through a qualitative assessment of practical usability and visualization using nonlinear dimensionality reduction.

cs.SD↗