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• Project Description
  • ADMM-ADAM workflow
• Project Setup
• How To Restore Images In this Project
• Reference

ADMM-ADAM is a powerful hyperspectral image (HSI) restoration framework designed by Dr. Chia-Hsiang in 2021 (Journal Link). It's based on "convex optimization", "feature extractor" and "ADMM optimizer" to make a high reducibility image.

ADMM-ADAM workflow as follows:

1. Train a Deep Learning model with ADAM optimizer (GAN in here), and get a Deep Learning olution (image)

2. Extract the most important information of Deep Learning solution by PCA (or some other feature extractor)

3. design a convex optimization problem with ADMM optimizer as follows:

   

   where,

   • X:
     • be an M-band hyperspectral (target) image with L pixels
   • Y:
     • be the observed image, meaning that some of its entries are missing
   • Ω:
     • denote the index set of those available data.
   • X_{DL}:
     • can be obtained using ADAM optimizer (GAN model with ADAM optimizer in here, you can get it by darkfanxing/GAN)
   • λ:
     • is called regularization parameter empirically set as 0.01 in this work
   • Q:
     • Q-qudratic norm, which extracts useful features from for effective regularization
     • feature extractor is PCA in here

   Assume we have N materials, each pixel can be modeled as a linear combination of N spectral signature vectors in R^{M}. In other words, all the hyperspectral pixel vectors belong to a N-dimensional subspace if we ignore some non-linearity or noise effects, so the target image X can be represented as follows:

   

   where,

   • : the most important N component (eigenvector), i.e. N material
   • : some coefficient matrix and we can simplify the objective function:

   

   so convex optimization problem can be represented as follows:

   

   the meaning of F-norm is:

   

   Once is available, it can be used to reconstruct the complete hyperspectral image as Hehe... it is happy time for reformulating convex optimization problem into the standard ADMM form:

   

   and give a augmented Lagrangian term :

   

   where,

   • :
     • is the scaled dual variable
   • 
     • is the penalty parameter, empirically set as 0.001

   Then, ADMM optimizer solves the problem as detailed as follows:

   

   where,

   • 
   • 
   • 

   where,

   • 
     • 
   • 
     • 

To avoid Python package version conflicts, the project use pipenv (Python vitural environment) to install Python packages.

rm Pipfile
pip install pipenv
pipenv shell
pipenv install

python src/main.py

Lin, Chia-Hsiang, Yen-Cheng Lin, and Po-Wei Tang. "ADMM-ADAM: A New Inverse Imaging Framework Blending the Advantages of Convex Optimization and Deep Learning." IEEE Transactions on Geoscience and Remote Sensing (2021).