JPEG2000 (j2k) is a highly popular format for image and video compression.With the rapidly growing applications of cloud based image classification, most existing j2k-compatible schemes would stream compressed color images from the source before reconstruction at the processing center as inputs to deep CNNs. We propose to remove the computationally costly reconstruction step by training a deep CNN image classifier using the CDF 9/7 Discrete Wavelet Transformed (DWT) coefficients directly extracted from j2k-compressed images. We demonstrate additional computation savings by utilizing shallower CNN to achieve classification of good accuracy in the DWT domain. Furthermore, we show that traditional augmentation transforms such as flipping/shifting are ineffective in the DWT domain and present different augmentation transformations to achieve more accurate classification without any additional cost. This way, faster and more accurate classification is possible for j2k encoded images without image reconstruction. Through experiments on CIFAR-10 and Tiny ImageNet data sets, we show that the performance of the proposed solution is consistent for image transmission over limited channel bandwidth.