Improving Imprecise Compressive Sensing Models

Dongeun Lee UNIST, Rafael de Lima, Jaesik Choi
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:168-177, 2016.

Abstract

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a few components. However, the theory of CS framework including random sampling has been focused on exact recovery of signal; impreciseness in signal recovery has been neglected. This can be problematic when there is uncertainty in the number of sparse components such as signal sparsity in dynamic systems that can change over time. We present a new theoretical framework that handles uncertainty in signal recovery from the perspective of recovery success and quality. We show that the signal recovery success in our model is more accurate than the success probability analysis in the CS framework. Our model is then extended to the case where the success or failure of signal recovery can be relaxed. We represent the number of components included in signal recovery with a right-tailed distribution and focus on recovery quality. Experimental results confirm the accuracy of our model in dynamic systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-unist16a, title = {Improving Imprecise Compressive Sensing Models}, author = {UNIST, Dongeun Lee and de Lima, Rafael and Choi, Jaesik}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {168--177}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/unist16a/unist16a.pdf}, url = {https://proceedings.mlr.press/r14/unist16a.html}, abstract = {Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a few components. However, the theory of CS framework including random sampling has been focused on exact recovery of signal; impreciseness in signal recovery has been neglected. This can be problematic when there is uncertainty in the number of sparse components such as signal sparsity in dynamic systems that can change over time. We present a new theoretical framework that handles uncertainty in signal recovery from the perspective of recovery success and quality. We show that the signal recovery success in our model is more accurate than the success probability analysis in the CS framework. Our model is then extended to the case where the success or failure of signal recovery can be relaxed. We represent the number of components included in signal recovery with a right-tailed distribution and focus on recovery quality. Experimental results confirm the accuracy of our model in dynamic systems.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Improving Imprecise Compressive Sensing Models %A Dongeun Lee UNIST %A Rafael de Lima %A Jaesik Choi %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-unist16a %I PMLR %P 168--177 %U https://proceedings.mlr.press/r14/unist16a.html %V R14 %X Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a few components. However, the theory of CS framework including random sampling has been focused on exact recovery of signal; impreciseness in signal recovery has been neglected. This can be problematic when there is uncertainty in the number of sparse components such as signal sparsity in dynamic systems that can change over time. We present a new theoretical framework that handles uncertainty in signal recovery from the perspective of recovery success and quality. We show that the signal recovery success in our model is more accurate than the success probability analysis in the CS framework. Our model is then extended to the case where the success or failure of signal recovery can be relaxed. We represent the number of components included in signal recovery with a right-tailed distribution and focus on recovery quality. Experimental results confirm the accuracy of our model in dynamic systems. %Z Reissued by PMLR on 04 October 2026.
APA
UNIST, D.L., de Lima, R. & Choi, J.. (2016). Improving Imprecise Compressive Sensing Models. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:168-177 Available from https://proceedings.mlr.press/r14/unist16a.html. Reissued by PMLR on 04 October 2026.

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