Tackling sparse noise in 1-bit compressive sensing and matrix completion, we have two implementations today, in the compressive sensing case, AOP is compared to BIHT while in the Matrix Completion case, it is compared to GRASTA and SpaRCS. Here they are: Robust 1-bit compressive sensing using adaptive outlier pursuit by Ming Yan, Yi Yang, Stanley Osher. The abstract reads:
In compressive sensing (CS), the goal is to recover signals at reduced sample rate compared to the classic ShannonNyquist rate. However, the classic CS theory assumes the measurements to be real-valued and have inﬁnite bit precision. The quantization of CS measurements has been studied recently and it has been shown that accurate and stable signal acquisition is possible even when each measurement is quantized to only one single bit. There are many algorithms proposed for 1- bit compressive sensing and they work well when there is no noise in the measurements, e.g., there are no sign ﬂips, while the performance is worsened when there are a lot of sign ﬂips in the measurements. In this paper, we propose a robust method for recovering signals from 1-bit measurements using adaptive outlier pursuit. This method will detect the positions where sign ﬂips happen and recover the signals using “correct” measurements. Numerical experiments show the accuracy of sign ﬂips detection and high performance of signal recovery for our algorithms compared with other algorithms.
1-bit Compressive Sensing
1-bit compressive sensing was firstly introduced and studied by Boufounos and Baraniuk in 2008, and the framework is as follows:
where is a mapping from to the Boolean cube . We have to recover signals where is the unit hyper-sphere of dimension . See more details about 1-bit compressive sensing, please go to http://dsp.rice.edu/1bitCS.The implementations for both 1-bit compressive sensing and matrix completion can be downloaded from this page. All entries related to 1-bit compressive sensing in general are listed under thwe 1bit tag.
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.