Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image

Figure 4

Denoising for integrated one-dimensional signal comprising rectangle wave, sine wave, and sawtooth wave. (a) Original clean signal and noisy signal (adds white Gaussian noise to the original clean signal, peak signal-to-noise ratio (PSNR) = 25.2486), (b) Gaussian denoising, (c) fourth-order TV denoising [71–73], (d) bilateral filtering denoising [86–88], (e) contourlet denoising [89, 90], (f) wavelet denoising [88, 91], (g) nonlocal means noise filtering (NLMF) denoising [92, 93], (h) fractional-order anisotropic diffusion denoising [82], and (i) FDM denoising (𝑣₁=1.025, 𝑣₂=2.25, 𝑣₃=1.05, Δ𝑡=0.0296).

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