High resolution sparse estimation of exponentially decaying N-dimensional signals
| Autor: | Andreas Jakobsson, Johan Sward, Stefan Ingi Adalbjörnsson |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Optimization problem
Computer science 02 engineering and technology Machine learning computer.software_genre symbols.namesake Matrix (mathematics) Kronecker delta Frequency grid 0202 electrical engineering electronic engineering information engineering Electrical and Electronic Engineering Signal processing K-SVD Estimation theory business.industry 020206 networking & telecommunications Grid Fourier transform Control and Systems Engineering Signal Processing symbols 020201 artificial intelligence & image processing Computer Vision and Pattern Recognition Artificial intelligence business computer Algorithm Software |
| Zdroj: | Signal Processing. 128:309-317 |
| ISSN: | 0165-1684 |
| DOI: | 10.1016/j.sigpro.2016.04.002 |
| Popis: | In this work, we consider the problem of high-resolution estimation of the parameters detailing an N-dimensional (N-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Since such signals are not sparse in an oversampled Fourier matrix, earlier approaches typically exploit large dictionary matrices that include not only a finely spaced frequency grid, but also a grid over the considered damping factors. Even in the 2-D case, the resulting dictionary is typically very large, resulting in a computationally cumbersome optimization problem. Here, we introduce a sparse modeling framework for N-dimensional exponentially damped sinusoids using the Kronecker structure inherent in the model. Furthermore, we introduce a novel dictionary learning approach that iteratively refines the estimate of the candidate frequency and damping coefficients for each component, thus allowing for smaller dictionaries, and for frequency and damping parameters that are not restricted to a grid. The performance of the proposed method is illustrated using simulated data, clearly showing the improved performance as compared to previous techniques. HighlightsA novel gridless sparsity-based parameter estimation method for damped, possibly nonuniformly sampled, multidimensional sinusoids.Statistically efficient performance is illustrated in the numerical section.Efficient implementation using the ADMM framework, as well as exploiting the Kronecker structure of resulting dictionaries. |
| Databáze: | OpenAIRE |
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