This paper presents a novel approach based on the direct use of deep neural networks to approximate wavelet sub-bands for remote sensing (RS) image scene classification in the JPEG 2000 compressed domain. The proposed approach consists of two main steps. The first step aims to approximate the finer level wavelet sub-bands. To this end, we introduce a novel Deep Neural Network approach that utilizes the coarser level binary decoded wavelet sub-bands to approximate the finer level wavelet sub-bands (the image itself) through a series of deconvolutional layers. The second step aims to describe the high-level semantic content of the approximated wavelet sub- bands and to perform scene classification based on the learnt descriptors. This is achieved by: i) a series of convolutional layers for the extraction of descriptors which models the approximated sub-bands; and ii) fully connected layers for the RS image scene classification. Then, we introduce a loss function that allows to learn the parameters of both steps in an end-to-end trainable and unified neural network. The proposed approach requires only the coarser level wavelet sub-bands as input and thus minimizes the amount of decompression applied to the compressed RS images. Experimental results show the effectiveness of the proposed approach in terms of classification accuracy and reduced computational time when compared to the conventional use of Convolutional Neural Networks within the JPEG 2000 compressed domain.