High resolution sparse estimation of exponentially decaying two-dimensional signals. Adalbjörnsson, S. I., Swärd, J., & Jakobsson, A. In *2014 22nd European Signal Processing Conference (EUSIPCO)*, pages 491-495, Sep., 2014.

Paper abstract bibtex

Paper abstract bibtex

In this work, we consider the problem of high-resolution estimation of the parameters detailing a two-dimensional (2-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Interpreting the estimation problem as a block (or group) sparse representation problem allows the decoupling of the 2-D data structure into a sum of outer-products of 1-D damped sinusoidal signals with unknown damping and frequency. The resulting non-zero blocks will represent each of the 1-D damped sinusoids, which may then be used as non-parametric estimates of the corresponding 1-D signals; this implies that the sought 2-D modes may be estimated using a sequence of 1-D optimization problems. The resulting sparse representation problem is solved using an iterative ADMM-based algorithm, after which the damping and frequency parameter can be estimated by a sequence of simple 1-D optimization problems.

@InProceedings{6952137, author = {S. I. Adalbjörnsson and J. Swärd and A. Jakobsson}, booktitle = {2014 22nd European Signal Processing Conference (EUSIPCO)}, title = {High resolution sparse estimation of exponentially decaying two-dimensional signals}, year = {2014}, pages = {491-495}, abstract = {In this work, we consider the problem of high-resolution estimation of the parameters detailing a two-dimensional (2-D) signal consisting of an unknown number of exponentially decaying sinusoidal components. Interpreting the estimation problem as a block (or group) sparse representation problem allows the decoupling of the 2-D data structure into a sum of outer-products of 1-D damped sinusoidal signals with unknown damping and frequency. The resulting non-zero blocks will represent each of the 1-D damped sinusoids, which may then be used as non-parametric estimates of the corresponding 1-D signals; this implies that the sought 2-D modes may be estimated using a sequence of 1-D optimization problems. The resulting sparse representation problem is solved using an iterative ADMM-based algorithm, after which the damping and frequency parameter can be estimated by a sequence of simple 1-D optimization problems.}, keywords = {optimisation;parameter estimation;signal representation;signal resolution;high resolution sparse estimation;exponentially decaying two-dimensional signals;2D signal;block sparse representation problem;outer-products;1D damped sinusoidal signals;unknown damping;nonzero blocks;nonparametric estimates;1D optimization problems;iterative ADMM-based algorithm;frequency parameter;2D data structure decoupling;parameter estimation;Damping;Estimation;Frequency estimation;Signal to noise ratio;Nuclear magnetic resonance;Minimization;Dictionaries;Sparse signal modeling;Spectral analysis;Sparse reconstruction;Parameter estimation;ADMM}, issn = {2076-1465}, month = {Sep.}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569925345.pdf}, }

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