ℓ1 Norm Minimization Task

An ℓ1 Norm Minimization Task is a minimization task that is required to find an l1-norm solution to an underdetermined linear system </math>b=Ax</math>.

• Context:
  • It can be solved by an ℓ1 Minimization System (that implements an ℓ1 Minimization Algorithm).
  • It can range from being a Constrained ℓ1 Minimization Task to being an Unconstrained ℓ1 Minimization Task.
• See: Covariance Matrix, ℓ2 Minimization, ℓ1 Norm.

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References

2013

• (Yang et al., 2013) ⇒ Allen Y Yang, Zihan Zhou, Arvind Ganesh Balasubramanian, S Shankar Sastry, and Yi Ma. (2013). “Fast-minimization Algorithms for Robust Face Recognition.” In: Image Processing, IEEE Transactions on, 22(8).
  • QUOTE: l1-minimization refers to finding the minimum l1-norm solution to an underdetermined linear system </math>b=Ax</math>. Under certain conditions as described in compressive sensing theory, the minimum l1-norm solution is also the sparsest solution.

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