  2D convolution (Conv2d), which is responsible for extracting features from
the input image, is one of the key modules of a convolutional neural network
(CNN). However, Conv2d is vulnerable to image corruptions and adversarial
samples. It is an important yet rarely investigated problem that whether we can
design a more robust alternative of Conv2d for more reliable feature
extraction. In this paper, inspired by the recently developed learnable sparse
transform that learns to convert the CNN features into a compact and sparse
latent space, we design a novel building block, denoted by RConv-MK, to
strengthen the robustness of extracted convolutional features. Our method
leverages a set of learnable kernels of different sizes to extract features at
different frequencies and employs a normalized soft thresholding operator to
adaptively remove noises and trivial features at different corruption levels.
Extensive experiments on clean images, corrupted images as well as adversarial
samples validate the effectiveness of the proposed robust module for reliable
visual recognition. The source codes are enclosed in the submission.
