By dropping the perfect reconstruction constraint of Eq. (2), it is often possible to achieve improved performance.
In fact, one may be able to use this sparsity as an a priori reconstruction constraint to interpolate missing k-space data.
The solution of (3) demands the proximity between the noisy image, Y, and the output image X, thus enforcing the global reconstruction constraint.
The estimation of X ^ by formula (4) is a ill-posed inverse problem, since for a given low-resolution input Y, infinitely many high-resolution images X satisfy the reconstruction constraint.
In [27, 28], Huang et al. proposed to jointly optimize the deep learning models (deep neural networks and recurrent neural networks) with an extra masking layer to enforce a reconstruction constraint.
While (hat {mathbf {X}}) may not satisfy the reconstruction constraint (2) exactly, it should be projected onto the solution space of (1), computing mathbf{X} = underset{mathbf{X}}{text{argmin}},|SHmathbf{X} - mathbf{Y}|^{2}_{2} + lambda|mathbf{X} - hat{mathbf{X}}|_{2}^{2} (9).
The program provides a user-friendly environment for model reconstruction, constraint-based model analysis, and interactive visualization of the simulation results.
Other kinds of image prior, e.g., local smoothing and nonlocal self-similarity, are also well studied as the regularization term in the reconstruction-constraint-based single-image SR methods.
Firstly, the desired q s is fixed according to the reconstruction quality constraints.
Furthermore, if there is no limitation of the cost function utilized for the reconstruction, some constraints must be also adopted.
