Recently, nonconvex and nonsmooth models such as those using 0 'norm' have drawn much attention in the area of image restoration. This work investigates the local and global minimizers of the 0 gradient regularized model with box constraints. There are four major ingredients. Firstly, we show that the set of local minimizers can be represented by solutions to some quadratic problems, which are independent of the fidelity parameter α. Based on this, every point satisfying the first-order necessary condition is a local minimizer. Secondly, any two local minimizers have different energy values under certain assumptions, implying the uniqueness of the global minimizer. Thirdly, there exists a uniform lower bound for nonzero gradients of the restored images. Finally, we show that the global minimizer set is piecewise constant in terms of α, and when A is of full column rank and α is large enough, the distance between the true image and the restored images is bounded by the noise level.The numerical examples perfectly demonstrate our theoretical analysis.
The seeking of resonator with high Q and low insertion loss is attractive for critical sensing scenes based on the surface acoustic wave (SAW). In this work, 128° YX LiNbO3-based SAW resonators were utilized to optimize the output performance through IDT structure parameters. Once the pairs of IDTs, the acoustic aperture, the reflecting grid logarithm, and the gap between IDT and reflector are changed, a better resonance frequency of 224.85 MHz and a high Q of 1364.5 were obtained. All the results demonstrate the structure parameters design is helpful for the performance enhancement with regard to SAW resonators, especially for designing and fabricating high-Q devices.
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