Recovering Images from Noise: Mathematical Modeling, Optimization, and Uncertainty (Spring 2027)
Images captured by cameras, medical imaging devices, and scientific instruments are often corrupted by noise, blur, or incomplete measurements. Recovering the original image from imperfect observations is an important mathematical problem with applications in medical imaging, astronomy, and computer vision.
In this project, students will explore how mathematical modeling, linear algebra, and optimization can be used to restore degraded images. We will begin by understanding how noise and blur affect digital images, then implement and compare several image restoration techniques, including filtering, regularization, and iterative optimization methods. Students will investigate how different algorithms balance reconstruction quality, preservation of important image features, and computational efficiency.
The project will emphasize hands-on numerical experiments using Python, where students can visualize their results and explore questions such as: How much noise can be removed without losing important details? How does the amount of blur affect reconstruction accuracy? Which methods perform best when the available data are limited or highly corrupted?
Depending on students' interests and progress, we may further investigate uncertainty and robustness in reconstructed images and develop improved computational strategies.
For more information contact Rafiq Islam (mri@iastate.edu)
People:
Rafiq Islam (Postdoc)
TBD
Pre-requisites:
Minimum Prerequisites
Calculus II or equivalent.
Introductory linear algebra, completed or in progress.
Interest in applied mathematics and computational problem-solving.
Preferred (Not Required)
Some experience with Python or another programming language.
Multivariable calculus.
Basic probability or statistics.
Familiarity with numerical methods.
No prior experience in image processing, optimization, or Bayesian statistics is required.