Performance of the Delsarte-Goethals Frame on Clustered Sparse Vectors
| العنوان: | Performance of the Delsarte-Goethals Frame on Clustered Sparse Vectors |
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| المؤلفون: | A. R. Calderbank, Sina Jafarpour, Marco F. Duarte |
| المصدر: | IEEE Transactions on Signal Processing. 61:1998-2008 |
| بيانات النشر: | Institute of Electrical and Electronics Engineers (IEEE), 2013. |
| سنة النشر: | 2013 |
| مصطلحات موضوعية: | Discrete wavelet transform, Theoretical computer science, Sparse approximation, computer.file_format, Compressive imaging, Compressed sensing, Signal Processing, Recovery procedure, Partition (number theory), Electrical and Electronic Engineering, Recovery performance, Raster graphics, Algorithm, computer, Mathematics |
| الوصف: | The Delsarte-Goethals frame (DGF) has been proposed for deterministic compressive sensing of sparse and compressible signals. Results in compressive sensing theory show that the DGF enables successful recovery of an overwhelming majority of sufficiently sparse signals. However, these results do not give a characterization of the sparse vectors for which the recovery procedure fails. In this paper, we present a formal analysis of the DGF that highlights the presence of clustered sparse vectors within its null space. This in turn implies that sparse recovery performance is diminished for sparse vectors that have their nonzero entries clustered together. Such clustered structure is present in compressive imaging applications, where commonly-used raster scannings of 2-D discrete wavelet transform representations yield clustered sparse representations for natural images. Prior work leverages this structure by proposing specially tailored sparse recovery algorithms that partition the recovery of the input vector into known clustered and unclustered portions. Alternatively, we propose new randomized and deterministic raster scannings for clustered coefficient vectors that improve recovery performance. Experimental results verify the aforementioned analysis and confirm the predicted improvements for both noiseless and noisy measurement regimes. |
| تدمد: | 1941-0476 1053-587X |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_________::55e9d14158eb86e836a1a61f2989d5e5Test https://doi.org/10.1109/tsp.2013.2242064Test |
| حقوق: | CLOSED |
| رقم الانضمام: | edsair.doi...........55e9d14158eb86e836a1a61f2989d5e5 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 19410476 1053587X |
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