Conditions of use of LASSO and AMP about amptutorial

[zqy754093810]

The OAMP algorithm is based on the LASSO problem, but because of the existence of the 1 norm in LASSO, the solution is sparse, so if the signal itself is not sparse or not sparse through the Fourier transform to the frequency domain, can it still be used under such conditions

The OAMP algorithm can be used for the standard linear regression y=Hx+w with H being a unitarily-invariant matrix. Even if the signal of interest is not sparse, the OAMP also works, such as the QPSK symbol in wireless communications.

[xb1176989662]

Thanks for the answer, but why, after all, OAMP is also the solution to the LASSO problem

[zqy754093810]

Thanks for the answer, but why, after all, OAMP is also the solution to the LASSO problem

The LASSO problem can be regarded as the postulated MMSE estimator with Laplace prior, and the AMP family algorithm is an approximator to the postulated MMSE estimator. Thus, the AMP family algorithm can be used for the LASSO problem. More details please find in eq (11) of "A concise tutorial on AMP".

[xb1176989662]

Thanks for the reply and good luck in research

[xb1176989662]

Hello, I tried the EXP1 code in your document "A Concise Tutorial on Approximate MessagePassing" and changed the sparse x to not sparse, but the estimated hatx obtained in this way is still sparse, and according to this result, it is impossible to solve the LASSO problem through AMP, why is that