Initial state reconstruction on graphs

The presence of noise is an intrinsic problem in acquisition processes for digital images. One way to enhance images combine the forward and backward diffusion equations. However, latter well known be exponentially unstable with respect any small perturbations on final data. In this scenario, data can regarded as a blurred image obtained from process, that pixelated network. Therefore, we study work regularization framework equation graphs. Our aim construct spectral graph-based solution based upon cut-off projection. Stability convergence results are provided together some numerical experiments.