We recast the multilayered sparse inversion problem as a multilayered neural network problem. Unlike standard least squares migration (LSM) which finds the optimal reflectivity image, neural network least squares migration (NNLSM) finds both the optimal reflectivity image and the quasi-migration-Green’s functions. These quasi-migration-Green’s functions are also denoted as the convolutional filters in a convolutional neural network (CNN) and are similar to migration Green’s functions. We show that the CNN filters and feature maps are directly related to the migration Green’s functions and reflectivity distributions. Thus, we provide for the first time a physical interpretation of the filters and feature maps in deep CNN in terms of the operators for seismic imaging. The advantage of NNLSM over standard LSM is that its computational cost is significantly less and it can be used for denoising coherent and incoherent noise in migration images. Its disadvantage is that the NNLSM reflectivity image is only an approximation to the actual reflectivity distribution.