Convolutional neural networks (CNNs) have recently achieved impressive performances in image processing tasks such as image classification and object recognition. However, CNNs typically have a large number of parameters, leading to their requirement of a large number of training samples to extract spatial features. To address these limitations, we propose a lightweight ScatterNet with the learnable weight matrix and sparse transformation such as scale transformation and translation to learn sparse filters. This filter based on ScatterNet uses He initialization algorithm and learns from input images which are viewed as two-directional sequential data in the initial stage of model training. A Strip-Recurrent module sweeps both horizontally and vertically across the image to compress feature matrices. Then, ScatterNet decomposes the above feature matrices as a learned mixture of different harmonic functions to integrate the spectral analysis into CNNs. Finally, we combine the sequential and spectral features to build our hybrid architectures to complete image classification and segmentation. These architectures can obtain good classification accuracy on both small and large training datasets. Our proposed method is evaluated at both layer and network levels on five widely-used benchmark datasets: MNIST, CIFAR-10, CIFAR-100, Small NORB and Tiny ImageNet. We also study other small sample problems such as medical image segmentation and image classification based on few-shot learning. Experiments show that our proposed layer and hybrid model achieves better accuracy for small sample training.