Flexible Multi-layer Sparse Approximations of Matrices and Applications

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems

Learning computationally efficient dictionaries and their implementation as fast transforms

Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. In this paper, inspired by usual fast transforms, we consider a general dictionary structure that allows cheaper manipulation, and propose an algorithm to learn such dictionaries --and their fast implementation-- over training data. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments

Parametric channel estimation for massive MIMO

Channel state information is crucial to achieving the capacity of multi-antenna (MIMO) wireless communication systems. It requires estimating the channel matrix. This estimation task is studied, considering a sparse channel model particularly suited to millimeter wave propagation, as well as a general measurement model taking into account hybrid architectures. The contribution is twofold. First, the Cram{\'e}r-Rao bound in this context is derived. Second, interpretation of the Fisher Information Matrix structure allows to assess the role of system parameters, as well as to propose asymptotically optimal and computationally efficient estimation algorithms

Text-informed audio source separation. Example-based approach using non-negative matrix partial co-factorization

International audienceThe so-called informed audio source separation, where the separation process is guided by some auxiliary information, has recently attracted a lot of research interest since classical blind or non-informed approaches often do not lead to satisfactory performances in many practical applications. In this paper we present a novel text-informed framework in which a target speech source can be separated from the background in the mixture using the corresponding textual information. First, given the text, we propose to produce a speech example via either a speech synthesizer or a human. We then use this example to guide source separation and, for that purpose, we introduce a new variant of the non-negative matrix partial co-factorization (NMPCF) model based on a so-called excitation-filter-channel speech model. Such a modeling allows sharing the linguistic information between the speech example and the speech in the mixture. The corresponding multiplicative update (MU) rules are eventually derived for the parameters estimation and several extensions of the model are proposed and investigated. We perform extensive experiments to assess the effectiveness of the proposed approach in terms of source separation and alignment performance

Channel charting based beamforming

Channel charting (CC) is an unsupervised learning method allowing to locate users relative to each other without reference. From a broader perspective, it can be viewed as a way to discover a low-dimensional latent space charting the channel manifold. In this paper, this latent modeling vision is leveraged together with a recently proposed location-based beamforming (LBB) method to show that channel charting can be used for mapping channels in space or frequency. Combining CC and LBB yields a neural network resembling an autoencoder. The proposed method is empirically assessed on a channel mapping task whose objective is to predict downlink channels from uplink channels.Comment: Asilomar Conference on Signals, Systems, and Computers, Oct 2022, Pacific Grove, United State