Motivation

• Image inpainting is a technique to reconstruct the missing information in an image 

• It has multiple astronomical applications including restoring images corrupted by instrument artifacts, removing undesirable objects like cosmic ray hits and bright star halos 

• Allows scientists to obtain a more complete and accurate representation of the target object

Project Goals

My project aims to explore algorithms for the noisy matrix completion (a.k.a. image inpainting) problem using optimization methods:

1. Formulate a cost function for the optimization problem

2. Solve the optimization problem using an image prior based on low-rank matrix completion (LRMC) and the sparse coefficients of pre-designed dictionaries/transformations, e.g., Discrete Cosine Transform (DCT) and Orthogonal Discrete Wavelet Transform (ODWT) 

3. Compare the results to the pre-existing deep learning-based algorithm from a research paper (Yu et al., 2018)

4. Analyze the performance of the reconstructed images using different algorithms with Peak Signal-to-Noise Ratio (PSNR)

By comparing the traditional and modern DSP techniques, I hope to determine whether the newer technique offers sufficient improvements and understand the evolution of DSP technology. 

What I learned:

• Using optimization methods to define the problem

• Performing complex linear algebra methods

• Implementing the algorithms in code and getting more familiar with Python, OpenCV, and PyTorch programming

• Optimizing the time complexity of the algorithms

• Understanding the machine learning methods in image processing

• Analyzing the performance of different algorithms and results using evaluation metrics such as PSNR