Image denoising via wavelet transform-based compressive sampling
We utilized compressive sampling (CS) in the wavelet transform domain to compress and improve the signal-to-noise ratio (SNR) of optical images degraded by additive Gaussian white and 1/f noise and multiplicative speckle noise. The wavelet transforms of the raw image were first computed then their corresponding Fourier transforms were compressively sampled at below the prescribed Nyquist rate using a radial mask consisting of m lines, centered at frequency f = 0. The missing high frequency components were recovered through total variational minimization and then inverse discrete wavelet transformation to obtain image reconstructions with higher SNRs. The effects of different wavelet decomposition levels and compression rates were analyzed by measuring the SNR and fidelity gains of the image reconstruction. The technique yielded positive SNR and fidelity gains for heavily degraded raw images for a given compression rate. The gain is minimal when the raw image becomes relatively noise-free.