Reference-based compressed sensing: A sample complexity approach
João F. C. Mota, Lior Weizman, Nikos Deligiannis, Yonina C. Eldar, Miguel R. D. Rodrigues
Abstract
We address the problem of reference-based compressed sensing: reconstruct a sparse signal from few linear measurements using as prior information a reference signal, a signal similar to the signal we want to reconstruct. Access to reference signals arises in applications such as medical imaging, e.g., through prior images of the same patient, and compressive video, where previously reconstructed frames can be used as reference. Our goal is to use the reference signal to reduce the number of required measurements for reconstruction. We achieve this via a reweighted ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> minimization scheme that updates its weights based on a sample complexity bound. The scheme is simple, intuitive and, as our experiments show, outperforms prior algorithms, including reweighted ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> minimization, ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> minimization, and modified CS.
BibTeX
@inproceedings{icassp2016_referencebasedco,
title = {Reference-based compressed sensing: A sample complexity approach},
author = {João F. C. Mota and Lior Weizman and Nikos Deligiannis and Yonina C. Eldar and Miguel R. D. Rodrigues},
booktitle = {ICASSP 2016},
year = {2016}
}