Recovering and distinguishing different ionospheric layers and signals usually requires slow and complicated procedures. In this work, we construct and train five convolutional neural network (CNN) models: DeepLab, fully convolutional DenseNet24 (FC-DenseNet24), deep watershed transform (DWT), Mask R-CNN, and spatial attention-UNet (SA-UNet) for the recovery of ionograms. The performance of the models is evaluated by intersection over union (IoU). We collect and manually label 6131 ionograms, which are acquired from a low-latitude ionosonde in Taiwan. These ionograms are contaminated by strong quasi-static noise, with an average signal-to-noise ratio (SNR) equal to 1.4. Applying the five models to these noisy ionograms, we show that the models can recover useful signals with IoU > 0.6. The highest accuracy is achieved by SA-UNet. For signals with less than 15% of samples in the data set, they can be recovered by Mask R-CNN to some degree (IoU > 0.2). In addition to the number of samples, we identify and examine the effects of three factors: (1) SNR, (2) shape of signal, (3) overlapping of signals on the recovery accuracy of different models. Our results indicate that FC-DenseNet24, DWT, Mask R-CNN and SA-UNet are capable of identifying signals from very noisy ionograms (SNR < 1.4), overlapping signals can be well identified by DWT, Mask R-CNN and SA-UNet, and that more elongated signals are better identified by all models.