gnn-with-sub-fourier-paper
Science Score: 26.0%
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Low similarity (4.8%) to scientific vocabulary
Repository
Basic Info
- Host: GitHub
- Owner: babhrujoshi
- Language: Jupyter Notebook
- Default Branch: main
- Size: 635 MB
Statistics
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
Code for paper: A coherence parameter for characterizing generative compressed sensing with Fourier measurements
Authors: 1. Aaron Berk 2. Simone Brugiapaglia 3. Babhru Joshi 4. Yaniv Plan 5. Matthew Scott 6. Ozgur Yilmaz
File Structure
1. scr contains notebooks used to generate figures
2. figures contains figures in the paper
3. trained_GNN contains trained decoder
4. saved_data contains saved experiments in jld format
Problem
Consider the compressed sensing problem of recovering $x\in\mathbb{R}^n$ from noisy measurements of the form
$$y = A x_{0} + \epsilon, $$
where $\epsilon\in\mathbb{R}^n$ is noise and $A$ is a sub-sampled Fourier matrix (or general isometry). We assume the unknown signal $x0$ lives in the range of known generative model $G:\mathbb{R}^k \rightarrow \mathbb{R}^n$, i.e. $x{0} = G(z0)$ for some $z0 \in \mathbb{R}^k$. We assume the generative model $G$ is fully-connected feedforward network of the form
$$ G(x) = Ad\sigma(A{d-1} \cdots \sigma(A_1 z)\cdots),$$
where $Ai \in \mathbb{R}^{ni \times n{i-1}}$ is the weight matrix and $\sigma(\cdot)$ is the activation function. We determine the conditions (on $A, G, x{0}$, \etc) under which it is possible to (approximately) recover $x_{0}$ from noisy linear measurements $y$ by (approximately) solving an optimization problem of the form
$$\min{z \in \mathbb{R}^{k}} ||b - A G(z) ||{2}. $$
Owner
- Name: Babhru Joshi
- Login: babhrujoshi
- Kind: user
- Website: https://babhrujoshi.github.io/
- Repositories: 3
- Profile: https://github.com/babhrujoshi
Postdoctoral Fellow at The University of British Columbia