Diffusion magnetic resonance imaging （dMRI） is an important medical imaging tool for the non-invasive detection of microstructures in biological tissues. Among others， intravoxel incoherent motion （IVIM） is a widely used dMRI model to separate diffusion and microvascular perfusion. Conventional methods to resolve IVIM parameters rely on fitting a biexponential model from multi-b-value dMRI data （typically ≥10 b-values）， which requires a relatively long acquisition time. Such an acquisition is challenging for IVIM imaging of the body， such as placental IVIM， which is strongly influenced by both fetal and maternal motions. Deep learning models can accelerate the dMRI acquisition using a subset of the q-space data. However， common deep learning based on convolutional neural networks is not relevant to biophysical models and， therefore， the outputs of the network are difficult to interpret. Here， this work combines sparse coding with deep learning to develop a sparse coding based deep neural network for the IVIM parameter estimation that takes advantage of the feature representation of deep networks while incorporating a potential bi-exponential model to estimate the microcirculation parameters of the placenta. Compared with other algorithms， the proposed algorithm demonstrates advantages in accuracy and generalizability.