Images are reconstructed from undersampled k-space data using a residual machine learning algorithm (e.g., a ResNet architecture) to estimate missing k-space lines from acquired k-space data with improved noise resilience. Using a residual machine learning algorithm provides for combining the advantages of both linear and nonlinear k-space reconstructions. The linear residual connection can implement a convolution that estimates most of the energy in k-space, and the multi-layer machine learning algorithm can be implemented with nonlinear activation functions to estimate imperfections, such as noise amplification due to coil geometry, that arise from the linear component.