  Deep convolutional networks often append additive constant ("bias") terms to
their convolution operations, enabling a richer repertoire of functional
mappings. Biases are also used to facilitate training, by subtracting mean
response over batches of training images (a component of "batch
normalization"). Recent state-of-the-art blind denoising methods (e.g., DnCNN)
seem to require these terms for their success. Here, however, we show that
these networks systematically overfit the noise levels for which they are
trained: when deployed at noise levels outside the training range, performance
degrades dramatically. In contrast, a bias-free architecture -- obtained by
removing the constant terms in every layer of the network, including those used
for batch normalization-- generalizes robustly across noise levels, while
preserving state-of-the-art performance within the training range. Locally, the
bias-free network acts linearly on the noisy image, enabling direct analysis of
network behavior via standard linear-algebraic tools. These analyses provide
interpretations of network functionality in terms of nonlinear adaptive
filtering, and projection onto a union of low-dimensional subspaces, connecting
the learning-based method to more traditional denoising methodology.
