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1. "Multipulse subspace detectors"

   Scharf, L.L.; Pakrooh, P. (October 2017, Conference record - Asilomar Conference on Signals, Systems, & Computers)

   In this paper we frame a fairly comprehensive set of spacetime detection problems, where a subspace signal modulates the mean-value vector of a multivariate normal measurement and nonstationary additive noise determines the covariance matrix. The measured spacetime data matrix consists of multiple measurements in time. As time advances, the signal component moves around in a subspace, and the noise covariance matrix changes in scale. 

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2. DeepTensor: Low-Rank Tensor Decomposition With Deep Network Priors

   https://doi.org/10.1109/TPAMI.2024.3450575  

   Saragadam, Vishwanath; Balestriero, Randall; Veeraraghavan, Ashok; Baraniuk, Richard G (December 2024, IEEE Transactions on Pattern Analysis and Machine Intelligence)

   DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors where each low-rank tensor is generated by a deep network (DN) that is trained in a self-supervised manner to minimize the mean-square approximation error. Our key observation is that the implicit regularization inherent in DNs enables them to capture nonlinear signal structures that are out of the reach of classical linear methods like the singular value decomposition (SVD) and principal components analysis (PCA). We demonstrate that the performance of DeepTensor is robust to a wide range of distributions and a computationally efficient drop-in replacement for the SVD, PCA, nonnegative matrix factorization (NMF), and similar decompositions by exploring a range of real-world applications, including hyperspectral image denoising, 3D MRI tomography, and image classification. 

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3. Covariance Matrix Estimation under Total Positivity for Portfolio Selection*

   https://doi.org/10.1093/jjfinec/nbaa018  

   Agrawal, Raj; Roy, Uma; Uhler, Caroline (September 2020, Journal of Financial Econometrics)

   null (Ed.)

   Abstract Selecting the optimal Markowitz portfolio depends on estimating the covariance matrix of the returns of N assets from T periods of historical data. Problematically, N is typically of the same order as T, which makes the sample covariance matrix estimator perform poorly, both empirically and theoretically. While various other general-purpose covariance matrix estimators have been introduced in the financial economics and statistics literature for dealing with the high dimensionality of this problem, we here propose an estimator that exploits the fact that assets are typically positively dependent. This is achieved by imposing that the joint distribution of returns be multivariate totally positive of order 2 (MTP2). This constraint on the covariance matrix not only enforces positive dependence among the assets but also regularizes the covariance matrix, leading to desirable statistical properties such as sparsity. Based on stock market data spanning 30 years, we show that estimating the covariance matrix under MTP2 outperforms previous state-of-the-art methods including shrinkage estimators and factor models. 

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4. Denoising diffusion weighted imaging data using convolutional neural networks

   https://doi.org/10.1371/journal.pone.0274396  

   Cheng, Hu; Vinci-Booher, Sophia; Wang, Jian; Caron, Bradley; Wen, Qiuting; Newman, Sharlene; Pestilli, Franco (September 2022, PLOS ONE)

   Yap, Pew-Thian (Ed.)

   Diffusion weighted imaging (DWI) with multiple, high b-values is critical for extracting tissue microstructure measurements; however, high b-value DWI images contain high noise levels that can overwhelm the signal of interest and bias microstructural measurements. Here, we propose a simple denoising method that can be applied to any dataset, provided a low-noise, single-subject dataset is acquired using the same DWI sequence. The denoising method uses a one-dimensional convolutional neural network (1D-CNN) and deep learning to learn from a low-noise dataset, voxel-by-voxel. The trained model can then be applied to high-noise datasets from other subjects. We validated the 1D-CNN denoising method by first demonstrating that 1D-CNN denoising resulted in DWI images that were more similar to the noise-free ground truth than comparable denoising methods, e.g., MP-PCA, using simulated DWI data. Using the same DWI acquisition but reconstructed with two common reconstruction methods, i.e. SENSE1 and sum-of-square, to generate a pair of low-noise and high-noise datasets, we then demonstrated that 1D-CNN denoising of high-noise DWI data collected from human subjects showed promising results in three domains: DWI images, diffusion metrics, and tractography. In particular, the denoised images were very similar to a low-noise reference image of that subject, more than the similarity between repeated low-noise images (i.e. computational reproducibility). Finally, we demonstrated the use of the 1D-CNN method in two practical examples to reduce noise from parallel imaging and simultaneous multi-slice acquisition. We conclude that the 1D-CNN denoising method is a simple, effective denoising method for DWI images that overcomes some of the limitations of current state-of-the-art denoising methods, such as the need for a large number of training subjects and the need to account for the rectified noise floor. 

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5. Accurate Cooperative Sensor Fusion by Parameterized Covariance Generation for Sensing and Localization Pipelines in CAVs

   https://doi.org/10.1109/ITSC55140.2022.9922598  

   Andert, Edward; Shrivastava, Aviral (October 2022, Accurate Cooperative Sensor Fusion by Parameterized Covariance Generation for Sensing and Localization Pipelines in CAVs)

   A major challenge in cooperative sensing is to weight the measurements taken from the various sources to get an accurate result. Ideally, the weights should be inversely proportional to the error in the sensing information. However, previous cooperative sensor fusion approaches for autonomous vehicles use a fixed error model, in which the covariance of a sensor and its recognizer pipeline is just the mean of the measured covariance for all sensing scenarios. The approach proposed in this paper estimates error using key predictor terms that have high correlation with sensing and localization accuracy for accurate covariance estimation of each sensor observation. We adopt a tiered fusion model consisting of local and global sensor fusion steps. At the local fusion level, we add in a covariance generation stage using the error model for each sensor and the measured distance to generate the expected covariance matrix for each observation. At the global sensor fusion stage we add an additional stage to generate the localization covariance matrix from the key predictor term velocity and combines that with the covariance generated from the local fusion for accurate cooperative sensing. To showcase our method, we built a set of 1/10 scale model autonomous vehicles with scale accurate sensing capabilities and classified the error characteristics against a motion capture system. Results show an average and max improvement in RMSE when detecting vehicle positions of 1.42x and 1.78x respectively in a four-vehicle cooperative fusion scenario when using our error model versus a typical fixed error model. 

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