In sparse coding it is common to tile an image into nonoverlapping patches, and then use a dictionary to create a sparse representation of each tile independently. In this situation, the overcompleteness of the dictionary is the number of dictionary elements divided by the patch size. In deconvolutional neural networks (DCNs), dictionaries learned on nonoverlapping tiles are replaced by a family of convolution kernels. Hence adjacent points in the feature maps (V1 layers) have receptive fields in the image that are translations of each other. The translational distance is determined by the dimensions of V1 in comparison to the dimensions of the image space. We refer to this translational distance as the stride. We implement a type of DCN using a modified Locally Competitive Algorithm (LCA) to investigate the relationship between the number of kernels, the stride, the receptive field size, and the quality of reconstruction. We find, for example, that for 16x16-pixel receptive fields, using eight kernels and a stride of 2 leads to sparse reconstructions of comparable quality as using 512 kernels and a stride of 16 (the nonoverlapping case). We also find that for a given stride and number of kernels, the patch size does not significantly affect reconstruction quality. Instead, the learned convolution kernels have a natural support radius independent of the patch size.

本文研究了使用改进的LCA算法的一种DCN类型，探讨了卷积核数量、步长、感受野大小对重建质量的影响，发现使用八个卷积核和步长为2的情况下可以产生与512个卷积核、步长为16的情况下相当的稀疏重建质量，此外发现在给定的步长和卷积核数量下，路径大小不显著影响重建质量。

使用短步长复制卷积核，实现较少独立卷积核的稀疏重建