Table of contents

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

Project Description

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

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,

   • 
     • 
   • 
     • 

Project Setup

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

How To Restore Images In This Project

python src/main.py

Reference

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).