Transformed denoising autoencoder prior for image restoration

Image restoration problem is generally ill-posed, which can be alleviated by learning image prior. Inspired by the considerable performance of utilizing priors in pixel domain and wavelet domain jointly, we propose a novel transformed denoising autoencoder as prior (TDAEP). The core idea behind TDAEP is to enhance the classical denoising autoencoder (DAE) via transform domain, which captures complementary information from multiple views. Specifically, 1-level nonorthogonal wavelet coefficients are used to form 4-channel feature images. Moreover, a 5-channel tensor is obtained by stacking the original image under the pixel domain and 4-channel feature images under the wavelet domain. Then we train the transformed DAE (TDAE) with the 5-channel tensor as the network input. The optimized image prior is obtained based on the trained autoencoder, and it is incorporated into an iterative restoration procedure with the aid of the auxiliary variable technique. The resulting model is affiliationed by proximal gradient descent technique. Numerous experiments demonstrated that the TDAEP outperforms a set of image restoration benchmark algorithms.