Advances in Signal Processing and Tensor Reconstruction

The field of signal processing and tensor reconstruction is rapidly evolving, with a focus on developing efficient and accurate methods for handling high-dimensional data. Recent research has emphasized the importance of adaptive sensing, compressive sampling, and sparse tensor models in achieving these goals. Notably, innovations in algorithms such as alternating least squares and power methods have improved the convergence rates and accuracy of tensor decomposition and eigenvalue computation. Furthermore, the integration of deep learning techniques, such as convolutional neural networks and state space models, has enabled the reconstruction of complex physical fields and time-series data with high accuracy. Overall, the field is moving towards the development of more efficient, scalable, and interpretable methods for signal processing and tensor reconstruction. Noteworthy papers include: Fourier Low-rank and Sparse Tensor for Efficient Tensor Completion, which proposes a novel tensor model that captures low-frequency and high-frequency components separately, and FR-Mamba, which introduces a state space model-based framework for time-series physical field reconstruction. Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution also presents a scalable Bayesian CPD algorithm that leverages generalized approximate message passing to avoid matrix inversions.

Sources

Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation

Fourier Low-rank and Sparse Tensor for Efficient Tensor Completion

Convergence of the alternating least squares algorithm for CP tensor decompositions

Sequential Interval Passing for Compressed Sensing

Convolutional Long Short-Term Memory Neural Networks Based Numerical Simulation of Flow Field

Improved power methods for computing eigenvalues of dual quaternion Hermitian matrices

FR-Mamba: Time-Series Physical Field Reconstruction Based on State Space Model

Large-Scale Bayesian Tensor Reconstruction: An Approximate Message Passing Solution

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