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The performance of the proposed method is compared with the following existing methods: nearest neighbor interpolation (NN), bicubic interpolation, zero-padding in the Fourier space (ZP) [56], the Gerchberg algorithm [7], TV regularized super-resolution [22], and LRTV [23].
The proposed method as well as TV and LRTV needs to tune the hyperparameters by the input image.
The number of iterations until the convergence of the proposed method was larger than that of LRTV and TV.
In this section, we show the reconstruction accuracy of the proposed method compared to the existing methods: NN, bicubic interpolation, ZP, the Gerchberg algorithm, TV regularized super-resolution, and LRTV super-resolution.
Although the TV-based approaches preserved their edges clearly, the results of TV and LRTV lack high-frequency components in the Fourier space.
Therefore 0([N.sup.4.sub.c]) for the proximal operator of rank is the worst computational cost for each iteration, which is the same as that of LRTV.
The convergence speed/number of iterations of the proposed method are slower/larger than that of LRTV. As mentioned in Section 3.2, this would be because the additional two Lagrange multipliers, [alpha] and [gamma], are necessary for the optimization.
The experimental results showed that our superresolution technique dramatically reduced noise and ringing caused by the Gerchberg method and it also performed better than LRTV super-resolution and the other methods considered.