Table 2.

Different performance indicators used for evaluating the reconstruction quality.

Journal	Indicator	Equation and Description
Measurement	the absolute mean error	$Error=\left[\frac{1}{X\ast Z}{\displaystyle \sum _{i=1}^X{\displaystyle \sum _{j=1}^Z\left|I(x,j)-U(x,j)\right|}}\right]\ast 100[\%]$ The absolute mean error is a quantitative evaluation [7]. It considers eventual image transforms, such as rotation, translation, and zoom transform [45]. Therefore, it is fairer.
IEEE Transactions on Medical Imaging	NRMSE	$NRMSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^X{\displaystyle \sum _{j=1}^Z{\left[I(x,j)-U(x,j)\right]}^2}}}{{\displaystyle \sum _{i=1}^X{\displaystyle \sum _{j=1}^Z{\left[I(x,j)\right]}^2}}}}$ The NRMSE is an objective evaluation index of image quality based on pixel error. It reflects the degree of difference between the reconstructed image and the original image [45]. The smaller the NRMSE, the better the reconstruction quality.
IEEE Transactions on Medical Imaging	SSIM	SSIM (I, U) = L(I,U) × C(I,U) × S(I,U) $L\left(I,U\right)=\frac{2u_I{u}_Y+C_1}{u_I^2+u_U^2+C_1}$ $C\left(I,U\right)=\frac{2{\sigma }_I{\sigma }_U+C_2}{{\sigma }_I^2+{\sigma }_U^2+C_2}$ $S\left(I,U\right)=\frac{{\sigma }_{IU}+C_3}{{\sigma }_I{\sigma }_U+C_3}$ where uI and uU represent the mean values of images I and U, respectively. σI and σI represent the standard deviations of image I and U. σIU represents the image I and U covariance. C1, C2, and C3 are constants to prevent the denominator from being 0 and maintain stability. SSIM takes the similarity of local structures into account [45], therefore, it is more suitable for perceiving visual quality. The SSIM is limited by 1, and a higher SSIM means a better reconstruction result [79].
Physics in Medicine & Biology	The reconstruction time t	The reconstruction time represents the solution time of equation $\widehat{\mathit{u}}=\widehat{\mathit{S}}\mathit{c}$, where $\widehat{\mathit{S}}$ and $\widehat{\mathit{u}}$ represent the truncated system matrix and truncated measurement, respectively. The shorter t is, the better the reconstruction performance. The reconstruction time is always the mean of the execution time for 100 times [56].