mean weighted support set error (Section \[sec:weightedSupportSet\]) and mean absolute error (Section \[sec:MAE\]).

Mean weighted support set error (MWSE) {#sec:weightedSupportSet}
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[**MWSE-optimal estimator:**]{} In support set estimation, the goal is to estimate the support of the signal, which is 1 if the corresponding entry in the signal is non-zero and 0 if it is zero. There are two types of errors in support set estimation: false alarms (support is 0, but estimated to be 1) and misses (support is 1, but estimated to be 0). In some applications such as medical imaging and radar detection, a miss may mean that the doctor misses an illness of the patient, or the radar misses an incoming missile. Hence, the cost paid for a miss could be tremendous compared to a false alarm. There are other applications where a false alarm is more costly than a miss. For example, in court, if an innocent person is mistakenly judged guilty, he/she will likely suffer a great deal. Therefore, we should weight these two errors differently in different applications. Let $b_n$ and $\widehat{b}_n$ be the true support and the estimated support of the $n$-th entry of the signal, respectively, and $\beta\in[0,1]$ is an application-dependent weight, 