89 research outputs found
Plug-and-Play Algorithms for Video Snapshot Compressive Imaging
We consider the reconstruction problem of video snapshot compressive imaging
(SCI), which captures high-speed videos using a low-speed 2D sensor (detector).
The underlying principle of SCI is to modulate sequential high-speed frames
with different masks and then these encoded frames are integrated into a
snapshot on the sensor and thus the sensor can be of low-speed. On one hand,
video SCI enjoys the advantages of low-bandwidth, low-power and low-cost. On
the other hand, applying SCI to large-scale problems (HD or UHD videos) in our
daily life is still challenging and one of the bottlenecks lies in the
reconstruction algorithm. Exiting algorithms are either too slow (iterative
optimization algorithms) or not flexible to the encoding process (deep learning
based end-to-end networks). In this paper, we develop fast and flexible
algorithms for SCI based on the plug-and-play (PnP) framework. In addition to
the PnP-ADMM method, we further propose the PnP-GAP (generalized alternating
projection) algorithm with a lower computational workload. We first employ the
image deep denoising priors to show that PnP can recover a UHD color video with
30 frames from a snapshot measurement. Since videos have strong temporal
correlation, by employing the video deep denoising priors, we achieve a
significant improvement in the results. Furthermore, we extend the proposed PnP
algorithms to the color SCI system using mosaic sensors, where each pixel only
captures the red, green or blue channels. A joint reconstruction and
demosaicing paradigm is developed for flexible and high quality reconstruction
of color video SCI systems. Extensive results on both simulation and real
datasets verify the superiority of our proposed algorithm.Comment: 18 pages, 12 figures and 4 tables. Journal extension of
arXiv:2003.13654. Code available at
https://github.com/liuyang12/PnP-SCI_pytho
Completing Low-Rank Matrices with Corrupted Samples from Few Coefficients in General Basis
Subspace recovery from corrupted and missing data is crucial for various
applications in signal processing and information theory. To complete missing
values and detect column corruptions, existing robust Matrix Completion (MC)
methods mostly concentrate on recovering a low-rank matrix from few corrupted
coefficients w.r.t. standard basis, which, however, does not apply to more
general basis, e.g., Fourier basis. In this paper, we prove that the range
space of an matrix with rank can be exactly recovered from few
coefficients w.r.t. general basis, though and the number of corrupted
samples are both as high as . Our model covers
previous ones as special cases, and robust MC can recover the intrinsic matrix
with a higher rank. Moreover, we suggest a universal choice of the
regularization parameter, which is . By our
filtering algorithm, which has theoretical guarantees, we can
further reduce the computational cost of our model. As an application, we also
find that the solutions to extended robust Low-Rank Representation and to our
extended robust MC are mutually expressible, so both our theory and algorithm
can be applied to the subspace clustering problem with missing values under
certain conditions. Experiments verify our theories.Comment: To appear in IEEE Transactions on Information Theor
1-Bit Matrix Completion
In this paper we develop a theory of matrix completion for the extreme case
of noisy 1-bit observations. Instead of observing a subset of the real-valued
entries of a matrix M, we obtain a small number of binary (1-bit) measurements
generated according to a probability distribution determined by the real-valued
entries of M. The central question we ask is whether or not it is possible to
obtain an accurate estimate of M from this data. In general this would seem
impossible, but we show that the maximum likelihood estimate under a suitable
constraint returns an accurate estimate of M when ||M||_{\infty} <= \alpha, and
rank(M) <= r. If the log-likelihood is a concave function (e.g., the logistic
or probit observation models), then we can obtain this maximum likelihood
estimate by optimizing a convex program. In addition, we also show that if
instead of recovering M we simply wish to obtain an estimate of the
distribution generating the 1-bit measurements, then we can eliminate the
requirement that ||M||_{\infty} <= \alpha. For both cases, we provide lower
bounds showing that these estimates are near-optimal. We conclude with a suite
of experiments that both verify the implications of our theorems as well as
illustrate some of the practical applications of 1-bit matrix completion. In
particular, we compare our program to standard matrix completion methods on
movie rating data in which users submit ratings from 1 to 5. In order to use
our program, we quantize this data to a single bit, but we allow the standard
matrix completion program to have access to the original ratings (from 1 to 5).
Surprisingly, the approach based on binary data performs significantly better
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