Restoration of Colour Images Using Backward Stochastic Differential Equations with Reflection

Implementation of Image Denoising based on Backward Stochastic Differential Equations

“…t ) from pixel A to B: (I) -using the scheme (10) and large dt, (II) -using the scheme (11) and large dt, (III) -using the scheme (10) and small dt than the cardinality of the smoothing times set {t 0 , t 1 , . .…”

“…A terminal time τ j provides that the numerical simulation of the diffusion trajectory gives at least j values of X x (ω) which differ from the value in the previous step. Figure 2 illustrates a difference between the scheme (10) and the scheme (11). There are shown three examples of trajectories (G γ * u 0 )(X x t ) from the pixel A to the pixel B.…”

“…Trajectories (I) and (III) were generated using the scheme (10) for large and small value of the parameter dt, respectively. Trajectory (II) was generated using the scheme (11) for large dt. It is easy to see, that at locations where the image is constant, trajectory (II) diffuses as trajectory (I).…”

“…In image processing one can find theoretical results [1] and some practical aspects [4,6,10,11,13,16] of BSDE-based applications. In [4] the problem of reconstruction of the noisy chromaticity is considered.…”

“…The model of forward anisotropic filtering in a direction perpendicular to the gradient and inverse anisotropic filtering in the gradient direction in terms of BSDEs was presented in [10] and [16] for grayscale and color images respectively. An interesting work using BSDE with reflection to reconstruct images in spaces other than R n was presented in [11].…”