arXiv subjects

Arttu Arjas

Publications and source records attributed to Arttu Arjas.

7 recordsLinked to original sources

arXiv2026

ISTA-Based Joint Dictionary Learning and Channel Estimation for XL-MIMO Systems

Channel estimation in extra-large multiple-input multiple-output systems is challenging due to near-field propagation, where the array response depends on both the angle and distance of the propagation paths. Existing near-field channel estimation methods typically rely either on fixed angle-distance grids, which suffer from grid mismatch effects, or on multi-stage refinement procedures with increased computational complexity. To address these limitations, this paper proposes the \textit{dictionary-learning iterative soft-thresholding algorithm (DL-ISTA)}, a method for joint near-field dictionary learning and channel estimation based on the iterative soft-thresholding algorithm. The proposed method jointly estimates the sparse channel coefficients and the continuous angle-distance parameters through alternating optimization, thereby avoiding discretization errors associated with fixed grids. To promote robust convergence, the angle-distance parameters are initialized using Sobol sequences, which provide uniform coverage of the parameter space. Numerical results show that DL-ISTA outperforms a baseline with comparable computational complexity and attains comparable or better accuracy than a substantially more complex benchmark.

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arXiv2026

Cross-Predictive Sparse Bayesian Learning with Application to XL-MIMO Channel Estimation

Accurate channel estimation is a key requirement in extremely large-scale multiple-input multiple-output (XL-MIMO) systems. Sparse Bayesian learning (SBL) is a well-established framework for exploiting channel sparsity, but its performance depends on parametric prior assumptions and hyperparameter optimization based on marginal likelihood, which may be sensitive to noise, limited pilot observations, and model mismatch. In this work, we propose \textit{cross-predictive SBL (CP-SBL)}, a data-driven variant of SBL in which the sparsity-inducing weights are learned by minimizing a randomized cross-predictive objective rather than through likelihood maximization. The proposed method preserves the hierarchical Bayesian structure of SBL while replacing parametric prior learning with a predictive consistency criterion derived from random data splitting. Numerical results for near-field XL-MIMO channel estimation show that CP-SBL consistently achieves lower normalized mean squared error than the baseline SBL across a wide range of signal-to-noise ratios, pilot lengths, numbers of antennas, and numbers of propagation paths, with comparable complexity and without requiring manual hyperparameter tuning.

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arXiv2026

Nonlinear Sparse Bayesian Learning Methods with Application to Massive MIMO Channel Estimation with Hardware Impairments

Accurate channel estimation is critical for realizing the performance gains of massive multiple-input multiple-output (MIMO) systems. Traditional approaches to channel estimation typically assume ideal receiver hardware and linear signal models. However, practical receivers suffer from impairments such as nonlinearities in the low-noise amplifiers and quantization errors, which invalidate standard model assumptions and degrade the estimation accuracy. In this work, we propose a nonlinear channel estimation framework that models the distortion function arising from hardware impairments using Gaussian process (GP) regression while leveraging the inherent sparsity of massive MIMO channels. First, we form a GP-based surrogate of the distortion function, employing pseudo-inputs to reduce the computational complexity. Then, we integrate the GP-based surrogate of the distortion function into newly developed enhanced sparse Bayesian learning (SBL) methods, enabling distortion-aware sparse channel estimation. Specifically, we propose two nonlinear SBL methods based on distinct optimization objectives, each offering a different trade-off between estimation accuracy and computational complexity. Numerical results demonstrate significant gains over the Bussgang linear minimum mean squared error estimator and linear SBL, particularly under strong distortion and at high signal-to-noise ratio.

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arXiv2025

Enhanced Sparse Bayesian Learning Methods with Application to Massive MIMO Channel Estimation

We consider the problem of sparse channel estimation in massive multiple-input multiple-output systems. In this context, we propose an enhanced version of the sparse Bayesian learning (SBL) framework, referred to as enhanced SBL (E-SBL), which is based on a reparameterization of the original SBL model. Specifically, we introduce a scale vector that brings extra flexibility to the model, which is estimated along with the other unknowns. Moreover, we introduce a variant of E-SBL, referred to as modified E-SBL (M-E-SBL), which is based on a computationally more efficient parameter estimation. We compare the proposed E-SBL and M-E-SBL with the baseline SBL and with a method based on variational message passing (VMP) in terms of computational complexity and performance. Numerical results show that the proposed E-SBL and M-E-SBL outperform the baseline SBL and VMP in terms of mean squared error of the channel estimation in all the considered scenarios. Furthermore, we show that M-E-SBL produces results comparable with E-SBL with considerably cheaper computations.

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arXiv2023

Sequential model correction for nonlinear inverse problems

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to second-order methods that are computationally more expensive. In this work we aim to approximate a nonlinear model with a linear one and correct the resulting approximation error. We develop a sequential method that iteratively solves a linear inverse problem and updates the approximation error by evaluating it at the new solution. This treatment convexifies the problem and allows us to benefit from established convex optimization methods. We separately consider cases where the approximation is fixed over iterations and where the approximation is adaptive. In the fixed case we show theoretically under what assumptions the sequence converges. In the adaptive case, particularly considering the special case of approximation by first-order Taylor expansion, we show that with certain assumptions the sequence converges to a critical point of the original nonconvex functional. Furthermore, we show that with quadratic objective functions the sequence corresponds to the Gauss-Newton method. Finally, we showcase numerical results superior to the conventional model correction method. We also show, that a fixed approximation can provide competitive results with considerable computational speed-up.

math.NA↗

arXiv2022

Neural Network Kalman filtering for 3D object tracking from linear array ultrasound data

Many interventional surgical procedures rely on medical imaging to visualise and track instruments. Such imaging methods not only need to be real-time capable, but also provide accurate and robust positional information. In ultrasound applications, typically only two-dimensional data from a linear array are available, and as such obtaining accurate positional estimation in three dimensions is non-trivial. In this work, we first train a neural network, using realistic synthetic training data, to estimate the out-of-plane offset of an object with the associated axial aberration in the reconstructed ultrasound image. The obtained estimate is then combined with a Kalman filtering approach that utilises positioning estimates obtained in previous time-frames to improve localisation robustness and reduce the impact of measurement noise. The accuracy of the proposed method is evaluated using simulations, and its practical applicability is demonstrated on experimental data obtained using a novel optical ultrasound imaging setup. Accurate and robust positional information is provided in real-time. Axial and lateral coordinates for out-of-plane objects are estimated with a mean error of 0.1mm for simulated data and a mean error of 0.2mm for experimental data. Three-dimensional localisation is most accurate for elevational distances larger than 1mm, with a maximum distance of 6mm considered for a 25mm aperture.

stat.AP↗

arXiv2020

Blind hierarchical deconvolution

Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the convolution kernel to recover an accurate reconstruction and additionally prior assumptions on the regularity of the signal are needed. To overcome these limitations, we parametrise the convolution kernel and prior length-scales, which are then jointly estimated in the inversion procedure. The proposed framework of blind hierarchical deconvolution enables accurate reconstructions of functions with varying regularity and unknown kernel size and can be solved efficiently with an empirical Bayes two-step procedure, where hyperparameters are first estimated by optimisation and other unknowns then by an analytical formula.

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