ECE558 — Digital Imaging

Tuesday and Thursday, 12:30–2:00pm, 2013 ECEB

Instructor

• Ivan Dokmanić, dokmanic at illinois dot edu

• Office hours:

Teaching assistant

• Konik Kothari, kkothar3 at illinois dot edu

• Office hours: Thursday, 5pm–6pm

• Location: CSL 469b

Course description

In the first part of the course we will introduce the major imaging modalities. We will start with the 2D Fourier transform as it repeatedly turns out to play a central role in understanding how images come about, and then use it to study optical imaging, tomography, and interferometric as well as diffraction-based techniques. We will then move to a study of the abstract notion of an ill-posed inverse problem, where we'll talk about the issues of uniqueness and stability, introduce regularization techniques and apply them to a selection of problems introduced in the first part. In addition to classical techniques we will touch upon sparsity, compressive sensing, and phase retrieval.

Syllabus

• 2D Fourier transform

  • Definition and existence

  • Properties: Parseval identity, Plancherel identity, inverse transform

  • Linear operators on images, convolution

  • Uncertainty principle

• Physics of image formation / remote imaging for different modalities

  • Optical imaging

  • X-ray tomography

  • Diffraction crystallography

  • Interferometric Radio Astronomy

• Ill-posed inverse problems

  • Direct and inverse problems

  • Well-posed problems and ill-posed problems

  • Regularization techniques

    • Tikhonov

    • Landweber iteration

    • SVD truncation

    • (all special cases of) SVD windowing

  • Sparsity-promoting regularization

  • Applications in deblurring and tomography

• Phase retrieval

  • Charge flipping

  • Lifting

  • First-order methods

Week by week

Grading

All submissions will happen over Compass.

• 50% homeworks

• 50% final project (25% journal review + proposal, 50% report and code, 25% presentation)