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From Exact to Approximate Solutions

In: Sparse and Redundant Representations

Author

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  • Michael Elad

    (The Technion – Israel Institute of Technology, Computer Science Department)

Abstract

The exact constraint A x = b is often relaxed, with an approximated equality measured using the quadratic penalty function $$Q\left(\mathbf{X}\right)=\parallel \mathbf{A}\mathbf{x}-\mathbf{b}{\parallel^{2}_{2}}.$$ Such relaxation allows us to (i) define a quasi-solution in case no exact solution exists (even in cases where A has more rows than columns); (ii) exploit ideas from optimization theory; (iii) measure the quality of a candidate solution; and more.

Suggested Citation

  • Michael Elad, 2010. "From Exact to Approximate Solutions," Springer Books, in: Sparse and Redundant Representations, chapter 0, pages 79-109, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-7011-4_5
    DOI: 10.1007/978-1-4419-7011-4_5
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