@InProceedings{8902559,
  author = {L. Bergerhoff and J. Weickert and Y. Dar},
  booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},
  title = {Algorithms for Piecewise Constant Signal Approximations},
  year = {2019},
  pages = {1-5},
  abstract = {We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original signal. We formalise this goal as a discrete nonconvex optimisation problem, for which we study two algorithms. First we reformulate a recent adaptive sampling method by Dar and Bruckstein in a compact and transparent way. This allows us to analyse its limitations when it comes to violations of its three key assumptions: signal smoothness, local linearity, and error balancing. As a remedy, we propose a direct optimisation approach which does not rely on any of these assumptions and employs a particle swarm optimisation algorithm. Our experiments show that for nonsmooth signals or low sample numbers, the direct optimisation approach offers substantial qualitative advantages over the Dar-Bruckstein method. As a more general contribution, we disprove the optimality of the principle of error balancing for optimising data in the ℓ2 norm.},
  keywords = {concave programming;mean square error methods;particle swarm optimisation;piecewise constant techniques;signal sampling;piecewise constant signal approximations;one-dimensional signals;mean squared error;discrete nonconvex optimisation problem;signal smoothness;error balancing;direct optimisation approach;particle swarm optimisation algorithm;nonsmooth signals;Dar-Bruckstein method;adaptive sampling method;local linearity;Optimization;Linearity;Signal processing algorithms;Europe;Signal processing;Approximation algorithms;Particle swarm optimization;Adaptive Signal Processing;Nonuniform Sampling;Nonconvex optimisation;Particle Swarm optimisation;Segmentation},
  doi = {10.23919/EUSIPCO.2019.8902559},
  issn = {2076-1465},
  month = {Sep.},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570529555.pdf},
}

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We formalise this goal as a discrete nonconvex optimisation problem, for which we study two algorithms. First we reformulate a recent adaptive sampling method by Dar and Bruckstein in a compact and transparent way. This allows us to analyse its limitations when it comes to violations of its three key assumptions: signal smoothness, local linearity, and error balancing. As a remedy, we propose a direct optimisation approach which does not rely on any of these assumptions and employs a particle swarm optimisation algorithm. Our experiments show that for nonsmooth signals or low sample numbers, the direct optimisation approach offers substantial qualitative advantages over the Dar-Bruckstein method. As a more general contribution, we disprove the optimality of the principle of error balancing for optimising data in the ℓ2 norm.","keywords":"concave programming;mean square error methods;particle swarm optimisation;piecewise constant techniques;signal sampling;piecewise constant signal approximations;one-dimensional signals;mean squared error;discrete nonconvex optimisation problem;signal smoothness;error balancing;direct optimisation approach;particle swarm optimisation algorithm;nonsmooth signals;Dar-Bruckstein method;adaptive sampling method;local linearity;Optimization;Linearity;Signal processing algorithms;Europe;Signal processing;Approximation algorithms;Particle swarm optimization;Adaptive Signal Processing;Nonuniform Sampling;Nonconvex optimisation;Particle Swarm optimisation;Segmentation","doi":"10.23919/EUSIPCO.2019.8902559","issn":"2076-1465","month":"Sep.","url":"https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570529555.pdf","bibtex":"@InProceedings{8902559,\n author = {L. Bergerhoff and J. Weickert and Y. Dar},\n booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},\n title = {Algorithms for Piecewise Constant Signal Approximations},\n year = {2019},\n pages = {1-5},\n abstract = {We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original signal. We formalise this goal as a discrete nonconvex optimisation problem, for which we study two algorithms. First we reformulate a recent adaptive sampling method by Dar and Bruckstein in a compact and transparent way. This allows us to analyse its limitations when it comes to violations of its three key assumptions: signal smoothness, local linearity, and error balancing. As a remedy, we propose a direct optimisation approach which does not rely on any of these assumptions and employs a particle swarm optimisation algorithm. Our experiments show that for nonsmooth signals or low sample numbers, the direct optimisation approach offers substantial qualitative advantages over the Dar-Bruckstein method. As a more general contribution, we disprove the optimality of the principle of error balancing for optimising data in the ℓ2 norm.},\n keywords = {concave programming;mean square error methods;particle swarm optimisation;piecewise constant techniques;signal sampling;piecewise constant signal approximations;one-dimensional signals;mean squared error;discrete nonconvex optimisation problem;signal smoothness;error balancing;direct optimisation approach;particle swarm optimisation algorithm;nonsmooth signals;Dar-Bruckstein method;adaptive sampling method;local linearity;Optimization;Linearity;Signal processing algorithms;Europe;Signal processing;Approximation algorithms;Particle swarm optimization;Adaptive Signal Processing;Nonuniform Sampling;Nonconvex optimisation;Particle Swarm optimisation;Segmentation},\n doi = {10.23919/EUSIPCO.2019.8902559},\n issn = {2076-1465},\n month = {Sep.},\n url = {https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570529555.pdf},\n}\n\n","author_short":["Bergerhoff, L.","Weickert, J.","Dar, Y."],"key":"8902559","id":"8902559","bibbaseid":"bergerhoff-weickert-dar-algorithmsforpiecewiseconstantsignalapproximations-2019","role":"author","urls":{"Paper":"https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570529555.pdf"},"keyword":["concave programming;mean square error methods;particle swarm optimisation;piecewise constant techniques;signal sampling;piecewise constant signal approximations;one-dimensional signals;mean squared error;discrete nonconvex optimisation problem;signal smoothness;error balancing;direct optimisation approach;particle swarm optimisation algorithm;nonsmooth signals;Dar-Bruckstein method;adaptive sampling method;local linearity;Optimization;Linearity;Signal processing algorithms;Europe;Signal processing;Approximation algorithms;Particle swarm optimization;Adaptive Signal Processing;Nonuniform Sampling;Nonconvex optimisation;Particle Swarm optimisation;Segmentation"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"inproceedings","biburl":"https://raw.githubusercontent.com/Roznn/EUSIPCO/main/eusipco2019url.bib","creationDate":"2021-02-11T19:15:21.907Z","downloads":0,"keywords":["concave programming;mean square error methods;particle swarm optimisation;piecewise constant techniques;signal sampling;piecewise constant signal approximations;one-dimensional signals;mean squared error;discrete nonconvex optimisation problem;signal smoothness;error balancing;direct optimisation approach;particle swarm optimisation algorithm;nonsmooth signals;dar-bruckstein method;adaptive sampling method;local linearity;optimization;linearity;signal processing algorithms;europe;signal processing;approximation algorithms;particle swarm optimization;adaptive signal processing;nonuniform sampling;nonconvex optimisation;particle swarm optimisation;segmentation"],"search_terms":["algorithms","piecewise","constant","signal","approximations","bergerhoff","weickert","dar"],"title":"Algorithms for Piecewise Constant Signal Approximations","year":2019,"dataSources":["NqWTiMfRR56v86wRs","r6oz3cMyC99QfiuHW"]}