Encoding-decoding (ED) CNNs have demonstrated state-of-the-art performance for noise reduction over the past years. This has triggered the pursuit of better understanding the inner workings of such architectures, which has led to the theory of deep convolutional framelets (TDCF), revealing important links between signal processing and CNNs. Specifically, the TDCF demonstrates that ReLU CNNs induce low-rankness, since these models often do not satisfy the necessary redundancy to achieve perfect reconstruction (PR). In contrast, this paper explores CNNs that do meet the PR conditions. We demonstrate that in these type of CNNs soft shrinkage and PR can be assumed. Furthermore, based on our explorations we propose the learned wavelet-frame shrinkage network, or LWFSN and its residual counterpart, the rLWFSN. The ED path of the (r)LWFSN complies with the PR conditions, while the shrinkage stage is based on the linear expansion of thresholds proposed Blu and Luisier. In addition, the LWFSN has only a fraction of the training parameters (<1%) of conventional CNNs, very small inference times, low memory footprint, while still achieving performance close to state-of-the-art alternatives, such as the tight frame (TF) U-Net and FBPConvNet, in low-dose CT denoising.