ADMM for Imaging

Interactive Explorer 3

Explore key concepts interactively

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Quick Check

Key concept question for section 3?

Option A

Option B

Option C

Correction:
Option B

This is the correct answer because it captures the core concept.

Common Mistake: Common Mistake in Section 3

Mistake:

Overlooking a critical implementation detail.

Correction:

Always verify results against known benchmarks and theoretical predictions.

Key Term 3

Core concept from section 3 of chapter 41.

Definition:

Total Variation Regularization

TV promotes piecewise-constant reconstructions:

TV(x)=∑i,j∣xi+1,j−xi,j∣2+∣xi,j+1−xi,j∣2\text{TV}(\mathbf{x}) = \sum_{i,j} \sqrt{|x_{i+1,j}-x_{i,j}|^2 + |x_{i,j+1}-x_{i,j}|^2}

Definition:

Orthogonal Matching Pursuit (OMP)

OMP greedily selects columns of A\mathbf{A}:

  1. Find j∗=arg⁡max⁡j∣⟨aj,r⟩∣j^* = \arg\max_j |\langle \mathbf{a}_j, \mathbf{r}\rangle|
  2. Add j∗j^* to support, solve least squares
  3. Update residual r\mathbf{r}
  4. Repeat until stopping criterion
LASSO / ISTA / FISTATotal Variation Reconstruction