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I am trying to reconstruct a signal using basis pursuit denoising of the compressed sensing framework (which is basically lasso), $\min\limits_{x} \frac{1}{2} || y − Ax||_2^2 + \lambda ||x||_1$. Here, $x$ is sparse.

I am trying to tune the parameter $\lambda$.

Assuming $y_\text{true}$ is a 10000 length signal, I am trying to tune the $\lambda$ using the first 2000 elements.

It seems that if $\lambda$ is decreased the reconstruction error is decreased but the sparsity is increased. I am told that we can use AIC or BIC in this case. But I don't know what should be the proper expression for AIC or BIC, also I don't know which one is better.

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  • $\begingroup$ Have a look here $\endgroup$ – havakok May 1 at 12:37

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