Name
Abstract | ||
|---|---|---|
We consider the problem of jointly recovering the vector
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{b}$</tex-math></inline-formula>
and the matrix
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{C}$</tex-math></inline-formula>
from noisy measurements
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{Y} = \boldsymbol{A}(\boldsymbol{b})\boldsymbol{C} + \boldsymbol{W}$</tex-math></inline-formula>
, where
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{A}(\cdot)$</tex-math></inline-formula>
is a known affine linear function of
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{b}$</tex-math></inline-formula>
(i.e.,
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{A}(\boldsymbol{b})=\boldsymbol{A}_0+\sum _{i=1}^Q b_i \boldsymbol{A}_i$</tex-math></inline-formula>
with known matrices
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{A}_i$</tex-math></inline-formula>
). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks. To solve this bilinear recovery problem, we propose the Bilinear Adaptive Vector Approximate Message Passing (VAMP) algorithm. We demonstrate numerically that the proposed approach is competitive with other state-of-the-art approaches to bilinear recovery, including lifted VAMP and Bilinear Generalized Approximate Message Passing. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1109/tsp.2019.2916100 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
Noise measurement,Machine learning,Signal processing algorithms,Sparse matrices,Uncertainty,Maximum likelihood estimation,Deconvolution | Affine transformation,Blind deconvolution,Matrix completion,Matrix (mathematics),Control theory,Algorithm,Linear function,Compressed sensing,Mathematics,Message passing,Bilinear interpolation | Journal |
Volume | Issue | ISSN |
abs/1809.00024 | 13 | 1053-587X |
Citations | PageRank | References |
1 | 0.35 | 43 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Subrata Sarkar | 1 | 7 | 2.78 |
| Alyson K. Fletcher | 2 | 552 | 41.10 |
| Sundeep Rangan | 3 | 3101 | 163.90 |
| Philip Schniter | 4 | 1620 | 93.74 |