The recent prosperity of learning-based image rain and noise removal is mainly due to the well-designed neural network architectures and large labeled datasets. However, we find that current image rain and noise removal methods result in low utilization of images. To alleviate the reliance on large labeled datasets, we propose the task-driven image rain and noise removal (TRNR) based on the introduced patch analysis strategy. The patch analysis strategy provides image patches with various spatial and statistical properties for training and has been verified to increase the utilization of images. Further, the patch analysis strategy motivates us to consider learning image rain and noise removal task-driven instead of data-driven. Therefore we introduce the N-frequency-K-shot learning task for TRNR. Each N-frequency-K-shot learning task is based on a tiny dataset containing NK image patches sampled by the patch analysis strategy. TRNR enables neural networks to learn from abundant N-frequency-K-shot learning tasks other than from adequate data. To verify the effectiveness of TRNR, we build a light Multi-Scale Residual Network (MSResNet) with about 0.9M parameters to learn image rain removal and use a simple ResNet with about 1.2M parameters dubbed DNNet for blind gaussian noise removal with a few images (for example, 20.0% train-set of Rain100H). Experimental results demonstrate that TRNR enables MSResNet to learn better from fewer images. In addition, MSResNet and DNNet utilizing TRNR have obtained better performance than most recent deep learning methods trained data-driven on large labeled datasets. These experimental results have confirmed the effectiveness and superiority of the proposed TRNR. The codes of TRNR will be public soon.