Zhenghan Fang*, Sam Buchanan*, Jeremias Sulam
IMSI Computational Imaging Workshop
Wed, 7 Aug, 2024
*Equal contribution.
What's in a Prior?
Learned Proximal Networks for Inverse Problems
Inverse Problems
x
y
- Computational imaging
Measure
Inversion
y=Ax+v
Inverse Problems
MAP estimate
\min_x \tfrac{1}{2}\|y - Ax \|_2^2 + {\color{darkorange} R}(x)
{\color{darkorange} R} = -\log p_x
Prox. Grad. Desc.
x_{k+1} = {\color{darkorange}\mathrm{prox}_{\eta R}}(x_k - \eta A^H(A x_k - y))
Deep neural networks
{\color{darkorange}\mathrm{prox}_{R}} (z) = \argmin_u \tfrac{1}{2} \|u-z\|_2^2 + R(u)
Proximal Operator
x_{k+1} = \quad {\color{red}f_{\theta}} \quad \ (x_k - \eta A^H(A x_k - y))
Plug-n-Play
Questions and Contributions
1. When is a neural network \(f_\theta\) a proximal operator?
2. What's the prior \(R\) learned by the neural network \(f_\theta\)?
3. How can we learn the prox of the true prior?
4. Convergence guarantees for PnP
Prior Landscape
Proximal Matching Loss
Learned proximal networks (LPN)
neural networks for prox. operators
Questions and Contributions
1. When is a neural network \(f_\theta\) a proximal operator?
2. What's the prior \(R\) learned by the neural network \(f_\theta\)?
3. How can we learn the prox of the true prior?
4. Convergence guarantees for PnP
Prior Landscape
Proximal Matching Loss
Learned proximal networks (LPN)
neural networks for prox. operators
Compressed Sensing
Acknowledgements and References
Fang, Buchanan, Sulam. What's in a Prior? Learned Proximal Networks for Inverse Problems. ICLR 2024.
Sam Buchanan
TTIC
Jeremias Sulam
JHU
IMSI Computational Imaging Workshop 2024 3min
By Zhenghan Fang
