Sensing tensors with Gaussian filters

Kalman Filtered Compressed Sensing

We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear "incoherent" measurements, in real-time. The signals are sparse in some transform domain referred to as the sparsity basis. For a single spatial signal, the solution is provided by Compressed Sensing (CS). The question that we address is, for a sequence of sparse signals, can we do better than CS, if (a) the sparsity pattern of the signal's transform coefficients' vector changes slowly over time, and (b) a simple prior model on t…

KF-CS: Compressive Sensing on Kalman Filtered Residual

We consider the problem of recursively reconstructing time sequences of sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear incoherent measurements with additive noise. The idea of our proposed solution, KF CS-residual (KF-CS) is to replace compressed sensing (CS) on the observation by CS on the Kalman filtered (KF) observation residual computed using the previous estimate of the support. KF-CS error stability over time is studied. Simulation comparisons with CS and LS-CS are shown.

A Bayesian Compressed Sensing Kalman Filter for Direction of Arrival Estimation

In this paper, we look to address the problem of estimating the dynamic direction of arrival (DOA) of a narrowband signal impinging on a sensor array from the far field. The initial estimate is made using a Bayesian compressive sensing (BCS) framework and then tracked using a Bayesian compressed sensing Kalman filter (BCSKF). The BCS framework splits the angular region into N potential DOAs and enforces a belief that only a few of the DOAs will have a non-zero valued signal present. A BCSKF can then be used to track the change in the DOA using the same framework. There can be an issue when the…

Decoupling multivariate functions using a nonparametric filtered tensor decomposition

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to interpret, in part because of the large number of required parameters. Decoupling techniques aim at providing an alternative representation of the nonlinearity. The so-called decoupled form is often a more efficient parameterisation of the relationship while being highly structured, favouring interpretability. In this work two new algorithms, based on filtered tenso…

Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning

We propose tensor-network compressed sensing (TNCS) by combining the ideas of compressed sensing, tensor network (TN), and machine learning, which permits novel and efficient quantum communications of realistic data. The strategy is to use the unsupervised TN machine learning algorithm to obtain the entangled state $|Ψ\rangle$ that describes the probability distribution of a huge amount of classical information considered to be communicated. To transfer a specific piece of information with $|Ψ\rangle$, our proposal is to encode such information in the separable state with the minimal distance …

基于张量分解的一致性协同过滤

Consistent Collaborative Filtering via Tensor Decomposition

本文提出切片反对称分解（SAD）协同过滤模型，通过为每个物品引入额外潜在向量，将点积扩展为一般内积以捕捉用户非线性偏好和成对比较循环，在超过100万交互的数据集上实现了最一致的个性化偏好并保持顶级推荐准确率。