Projection Set Algorithms
- Proximal gradient methods are a powerful technique to solve non-convex inverse problems
- Problem: find the intersection of two sets, only operating on one set a time
- Two Convex Sets
- Two Non-Convex Sets
- Multiple Non-Convex Sets
- Higher-Dimensional Sets: Sudoku
- Sudoku is a constraint satisfaction problem:
- Each row contains only one of each of the numbers 1-9
- Each column contains only one of each of the numbers 1-9
- Each 3x3 block contains only one of each of the numbers 1-9
- Solution must be consistent with a (minimum) set of pre-defined clues
- Each constraint can be interpreted as a projection to a non-convex set
- This can be solved using iterative proximal gradient algorithms
- iteration 01
- iteration 02
- iteration 03
- iteration 04
- iteration 05
- animated solution
