DD-DCSR: Image Denoising for Low-Dose CT via Dual-Dictionary Deep Convolutional Sparse Representation

Most of the existing low-dose computed tomography (LDCT) denoising algorithms, based on convolutional neural networks, are not interpretable enough due to a lack of mathematical basis. In the process of image denoising, the sparse representation based on a single dictionary cannot restore the texture details of the image perfectly. To solve these problems, we propose a Dual-Dictionary Convolutional Sparse Representation (DD-CSR) method and construct a Dual-Dictionary Deep Convolutional Sparse Representation network (DD-DCSR) to unfold the model iteratively. The modules in the network correspond to the model one by one. In the proposed DD-CSR, the high-frequency information is extracted by Local Total Variation (LTV), and then two different learnable convolutional dictionaries are used to sparsely represent the LDCT image and its high-frequency map. To improve the robustness of the model, the adaptive coefficient is introduced into the convolutional dictionary of LDCT images, which allows the image to be represented by fewer convolutional dictionary atoms and reduces the number of parameters of the model. Considering that the sparse degree of convolutional sparse feature maps is closely related to noise, the model introduces learnable weight coefficients into the penalty items of processing LDCT high-frequency maps. The experimental results show that the interpretable DD-DCSR network can well restore the texture details of the image when removing noise/artifacts.