Reverse Convolution and Its Applications to Image Restoration

Convolution and transposed convolution are fundamental operators widely used in neural networks. However, transposed convolution, a.k.a. deconvolution, does not truly invert convolution due to their inherent differences in formulation. To date, there is no reverse convolution operator that has been developed as a basic component in deep neural networks. In this paper, we propose a novel depthwise reverse convolution operator as a first-step exploration to effectively reverse the depthwise convolution by formulating and solving a regularized least-squares optimization problem. We thoroughly investigate its kernel initialization, padding strategies, and other critical aspects to ensure its effective implementation. Building upon this reverse convolution operator, we integrate it with layer normalization, 1$\times$1 convolution, and GELU activation to form a reverse convolution block, similar to a Transformer block. The proposed reverse convolution block can easily replace its convolution and transposed convolution counterparts in existing architectures, leading to the development of ConverseNet. By incorporating it into classical models like DnCNN, SRResNet and USRNet, we train ConverseNet to solve three typical image restoration tasks including Gaussian denoising, super-resolution and deblurring. Extensive experiments demonstrate the effectiveness of the proposed reverse convolution operator as both a fundamental building block and a novel deconvolution operator for inverse problems. We hope our work could pave the way for developing new operators in deep model design and applications.