Recurrent Inference Machines for Inverse Problems
Berkeley Statistics and Machine Learning Forum
From Compressed Sensing to Deep Learning
Inverse Problems
Denoising
Deconvolution
Inpainting
The Bayesian Approach
 p(y  x) is the likelihood function, contains the physical modeling of the problem:

p(x) is the prior, contains our assumptions about the solution
 Typically, people look for a point estimate of the solution, the Maximum A Posteriori solution:
Where does my prior come from ?
Wavelet Sparsity
Total Variation
Gaussian
Classical Image Priors
Image Restauration by Convex Optimization
 Simple differentiable priors: gradient descent
 Non differentiable priors: proximal algorithms
Unrolling Inference
Interpreting optimization algorithms as Deep Neural Networks
Example in MRI: Deep ADMMNet for Compressive Sensing MRI
Compressive Sensing for MRI
Credit: Lustig et al. 2008
Solving by ADMM
Advantages of the approach
 Automatically tune optimization parameters for faster convergence
 Automatically learns optimal representation dictionary
 Automatically learns optimal proximal operators
This is great, but can we do better?
Learning the Inference
Recurrent Inference Machines for Solving Inverse Problems
Putzky & Welling, 2017
Reinterpreting MAP inference as a RNN
Why not write this iteration as:
 Update strategy and step size become implicit
 Prior becomes implicit
To match the RNN framework, an additional variable s is introduced to store an optimization memory state.
We trained three models on these tasks: (1) a Recurrent Inference Machine (RIM) as described in 2, (2) a gradientdescent network (GDN) which does not use the current estimate as an input (compare Andrychowicz et al. [15]), and (3) a feedforward network (FFN) which uses the same inputs as the RIM but where we replaced the GRU unit with a ReLu layer in order to remove hidden state dependence.
Superresolution example with factor 3
Applications in the Wild 1/2
Recurrent Inference Machines
for Accelerated MRI Reconstruction
Lønning et al. 2018
All models in this paper were trained on acceleration factors that were randomly sampled from the uniform distribution U (1.5, 5.2). Subsampling patterns were then generated using a Gaussian distribution.
Applications in the wild 2/2
DataDriven Reconstruction of Gravitationally Lensed Galaxies using Recurrent Inference Machines
Morningstar et al. 2019
Inverting Strong Gravitational Lensing
Recurrent Inferrence Machines
By eiffl
Recurrent Inferrence Machines
Session on RIMs for the Berkeley Statistics and Machine Learning Forum
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