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Start Over Search Limiters Full Text Topic signal processing and analysis Topic matrix decomposition Publication Year Range Last 50 years
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1. Thiran Filters for Wideband DSP-Based Multi-Beam True Time Delay RF Sensing Applications.

Author

Perera, Sirani M., Rathnasekara, Gayani, and Madanayake, Arjuna

Subjects
APPLICATION-specific integrated circuits, CIRCUIT complexity, RADIO frequency, VANDERMONDE matrices, IMPULSE response, DIGITAL signal processing, MATRIX decomposition, FREQUENCY modulation transmitters
Abstract

The ability to sense propagating electromagnetic plane waves based on their directions of arrival (DOAs) is fundamental to a range of radio frequency (RF) sensing, communications, and imaging applications. This paper introduces an algorithm for the wideband true time delay digital delay Vandermonde matrix (DVM), utilizing Thiran fractional delays that are useful for realizing RF sensors having multiple look DOA support. The digital DVM algorithm leverages sparse matrix factorization to yield multiple simultaneous RF beams for low-complexity sensing applications. Consequently, the proposed algorithm offers a reduction in circuit complexity for multi-beam digital wideband beamforming systems employing Thiran fractional delays. Unlike finite impulse response filter-based approaches which are wideband but of a high filter order, the Thiran filters trade usable bandwidth in favor of low-complexity circuits. The phase and group delay responses of Thiran filters with delays of a fractional sampling period will be demonstrated. Thiran filters show favorable results for sample delay blocks with a temporal oversampling factor of three. Thiran fractional delays of orders three and four are mapped to Xilinx FPGA RF-SoC technologies for evaluation. The preliminary results of the APF-based Thiran fractional delays on FPGA can potentially be used to realize DVM factorizations using application-specific integrated circuit (ASIC) technology. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Non-negative Tensor Factorization with missing data for the modeling of gene expressions in the Human Brain

Author

Søren Føns Vind Nielsen, Morten Mørup, Mboup, Mamadou, Adali , Tü lay, Moreau, Éric, and Larsen, Jan

Subjects
Pure mathematics, Non-negative Tensor Factorization, Computing and Processing, Bioengineering, Non-negative Matrix Factorization, Non-negative matrix factorization, Matrix decomposition, Combinatorics, Abstracts, medicine, Genetics, Training, Marginalization, Gene, Tensile stress, Mathematics, Engineering Profession, Tensor factorization, Engineering profession, Missing Values, Loading, Human brain, Cande-Comp/PARAFAC, Vectors, Missing data, Communication, Networking and Broadcast Technologies, medicine.anatomical_structure, CP, Signal Processing and Analysis, Noise
Abstract

Non-negative Tensor Factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures; multiplicative updates, column-wise, and row-wise updating of the component matrices. We examine three gene expression prediction scenarios based on data missing at random, whole genes missing and whole areas missing within a subject. We find that the column-wise updating approach also known as HALS performs the most efficient when fitting the model. We further observe that the non-negativity constrained CP model is able to predict gene expressions better than predicting by the subject average when data is missing at random. When whole genes and whole areas are missing it is in general better to predict by subject averages. However, we find that when whole genes are missing from all subjects the model based predictions are useful. When analyzing the structure of the components derived for one of the best predicting model orders the components identified in general constitute localized regions of the brain. Non-negative tensor factorization based on marginalization thus forms a promising framework for imputing missing values and characterizing gene expression in the human brain. However, care also has to be taken in particular when predicting the genetic expression levels at a whole region of the brain missing as our analysis indicates that this requires a substantial amount of subjects with data for this region in order for the model predictions to be reliable.

Published
2014