
Main idea:
We study the problem of
recursively recovering a sequence of sparse vectors from highly corrupted
observations. At each time, we have
observed measurement = sparse signal + dense
noise
(1)
The dense noise can has much larger energy than the sparse signals. However,
the noise sequence is highly correlated over time and therefore lying in a
slowly changing low dimensional subspace.
Suppose an initial estimate of the noise subspace is available (i.e.,
estimate initial noise subspace from training sequence). The original noise
can be approximately nullify by computing an orthogonal projection of the
observed measurement onto the noise null subspace and get
projected measurement = projection matrix * sparse signal + projected
noise
(2)
The original problem (1) is transformed into a standard compressive sensing /
sparse recovery problem (2) with the projected noise being much smaller. The
sparse signal can be recovered from the projected measurements via any
standard L1 minimization approaches. With an estimate of the sparse signal,
we get an estimate of the noise and hence update the noise subspace
everysooften.
Applications:
A key application is in video
surveillance where the goal is to separate a slowly changing background from
moving foreground objects onthefly. The background sequence is well modeled
as lying in a low dimensional subspace, that can
gradually change over time, while the moving foreground objects constitute
the correlated sparse signals.
Other possible applications include online fMRI based organ active region
detection problem or sensor networks based detection and tracking of abnormal
events such as forest fires or oil spills, etc.
Some experiment results can be
found here and here
(old).
Papers:
 Chenlu Qiu and Namrata Vaswani, Automated
Recursive Projected CS (ReProCS) for Realtime
Video Layering.
 Chenlu Qiu and Namrata
Vaswani, ReProCS: A
Missing Link between Recursive Robust PCA and Recursive Sparse Recovery
in Large but Correlated Noise, arXiV: 1106.3286.
 Chenlu Qiu and Namrata Vaswani, Recursive Sparse Recovery in Large but Low
Dimensional Noise, 48th Allerton
Conference on Communication Control and Computing,
2011.
 Chenlu Qiu and Namrata
Vaswani, Support
Predicted ModifiedCS for Recursive Robust Principal Components' Pursuit, ISIT 2011.
 Chenlu Qiu and Namrata
Vaswani, Realtime
Robust Principal Components' Pursuit, Allerton, 2010.
Matlab
code: ReProCS_code.zip (
Please cite above papers if
you use this code. )
