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Multiresolution deep learning approaches, such as the U-Net architecture, have achieved high performance in classifying and segmenting images. However, these approaches do not provide a latent image representation and cannot be used to decompose, denoise, and reconstruct image data. The U-Net and other convolutional neural network (CNNs) architectures commonly use pooling to enlarge the receptive field, which usually results in irreversible information loss. This study proposes to include a Riesz-Quincunx (RQ) wavelet transform, which combines 1) higher-order Riesz wavelet transform and 2) orthogonal Quincunx wavelets (which have both been used to reduce blur in medical images) inside the U-net architecture, to reduce noise in satellite images and their time-series. In the transformed feature space, we propose a variational approach to understand how random perturbations of the features affect the image to further reduce noise. Combining both approaches, we introduce a hybrid RQUNet-VAE scheme for image and time series decomposition used to reduce noise in satellite imagery. We present qualitative and quantitative experimental results that demonstrate that our proposed RQUNet-VAE was more effective at reducing noise in satellite imagery compared to other state-of-the-art methods. We also apply our scheme to several applications for multi-band satellite images, including: image denoising, image and time-series decomposition by diffusion and image segmentation.