2.2.2 | Rigrsure
Rigrsure is a soft threshold method evaluator of unbiased risk. It’s
calculated as follows:
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ }\lambda_{i}=\sigma_{i}\sqrt{\omega_{\text{b\ }}}\text{\ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ }\left(3\right)\)
\(\omega_{b}\ \)represents the square of thebth wavelet coefficient (coefficient at minimal
risk) selected from the vector W = [\(\omega_{1}\),\(\omega_{2}\),…, \(\omega_{N}\)]. This vector comprises the squared
values of the wavelet coefficients, arranged in ascending order. Here,\(\sigma_{i}\) denotes the standard deviation of the noisy signal at\(i_{t}\) scale.