# Difference between revisions of "ℓ1 Norm Minimization Task"

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* ([[2013_FastMinimizationAlgorithmsforRo|Yang et al., 2013]]) ⇒ [[Allen Y Yang]], [[Zihan Zhou]], [[Arvind Ganesh Balasubramanian]], [[S Shankar Sastry]], and [[Yi Ma]]. ([[2013]]). “[http://arxiv.org/pdf/1007.3753 Fast-minimization Algorithms for Robust Face Recognition].” In: Image Processing, IEEE Transactions on, 22(8). | * ([[2013_FastMinimizationAlgorithmsforRo|Yang et al., 2013]]) ⇒ [[Allen Y Yang]], [[Zihan Zhou]], [[Arvind Ganesh Balasubramanian]], [[S Shankar Sastry]], and [[Yi Ma]]. ([[2013]]). “[http://arxiv.org/pdf/1007.3753 Fast-minimization Algorithms for Robust Face Recognition].” In: Image Processing, IEEE Transactions on, 22(8). | ||

− | ** QUOTE: [[ | + | ** QUOTE: [[ℓ1 Norm Minimization Task|<i>l</i>1-minimization]] refers to [[finding the minimum]] [[l1-norm solution]] to an [[underdetermined linear system]] </math>b=Ax</math>. </s> Under certain conditions as described in [[compressive sensing theory]], the [[minimum solution|minimum]] [[l1-norm solution]] is also the [[sparsest solution]]. </s> |

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[[Category:Concept]] | [[Category:Concept]] |

## Latest revision as of 20:45, 23 December 2019

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.

## 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:
*l*1-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.

- QUOTE: