Evaluation of reconstruction algorithms
Introduction of reconstruction algorithms
For comparison purpose, five different algorithms are selected to test their performance in terms of accuracy and efficiency. Involved algorithms includes L1 Magic - Primal Dual Interior Point, ADMM - Basis Pursuit, ADMM - Lasso, Matlab - Lasso, NESTA.
Introduction of figure of merits
Two merits are selected to evaluate reconstruction quality. The first is reconstructed frequency error that calculate the fraction of discrepancy of reconstructed frequencies and actual frequencies, which contains the structure information of target profile. The second merit is root mean square error of false frequencies.
reconstruction accuracy
Reconstructed signals was compared with actual signal in frequency domain. Two merits are selected to evaluate reconstruction quality: reconstructed frequency error (RFE) and root mean square error (RMSE). Reconstructed frequency error is defined as
\(\begin{matrix} RFE = \frac{\sum(S_i - \bar{S}_i)}{\sum(S_i)} & & i=1,2,...,N \end{matrix}\)
where \(S\) is reconditioned signal and \(\overline{S}\) is actual signal. N is signal length. The RFE reflects the total amount of discrepancy in terms of signal energy between reconstructed frequencies and actual frequencies, which contains the structure information of target profile. The root mean square error is defined as
\(RMSE = {\sqrt {\frac{1} {N}{\sum\limits_{i = 1}^N {(S_{i} - \bar{S}_{i} } })^{2} } }\)
\(RMSE = {\sqrt {\frac{1} {N}{\sum\limits_{i = 1}^N {(S_{i} - \bar{S}_{i} } })^{2} } }\)