# How to choose $\lambda$ is compressed sensing

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.

• Have a look here – havakok May 1 '19 at 12:37