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Precise error analysis of the LASSO

C. Thrampoulidis ; Ashkan Panahi (Institutionen för data- och informationsteknik, Datavetenskap (Chalmers)) ; D. Guo ; B. Hassibi
40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015; Brisbane Convention and Exhibition CentreBrisbane; Australia; 19 April 2014 through 24 April 2014 (1520-6149). Vol. 2015-August (2015), p. 3467-3471.
[Konferensbidrag, refereegranskat]

A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, k-sparse signal x0 ∈ n from underdetermined, noisy, linear measurements y = Ax0 + z ∈ m. One standard approach is to solve the following convex program x = arg minx y -Ax2+λx1, which is known as the ℓ2-LASSO. We assume that the entries of the sensing matrix A and of the noise vector z are i.i.d Gaussian with variances 1/m and σ2. In the large system limit when the problem dimensions grow to infinity, but in constant rates, we precisely characterize the limiting behavior of the normalized squared error x -x0 2 2/σ2. Our numerical illustrations validate our theoretical predictions.

Nyckelord: Gaussian min-max theorem , LASSO , normalized squared error , sparse recovery , square-root LASSO



Denna post skapades 2016-05-11. Senast ändrad 2016-08-17.
CPL Pubid: 236232

 

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Institutioner (Chalmers)

Institutionen för data- och informationsteknik, Datavetenskap (Chalmers)

Ämnesområden

Elektroteknik och elektronik

Chalmers infrastruktur