Can I use L1-Optimization to estimate a linear set of equations?

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Benson Gou le 28 Mai 2017

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I have a linear equation Bx=P. Where B is an overdetermined matrix (M x N, M > N), x is a variable column vector, and P is the measurement vector but P has a number of bad data. My question is: can I use L1-optimization to estimate x? Are there multiple solutions? Thanks a lot.