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This work offers an approach to aerial image classification for use in remote sensing object recognition, image processing and computer vision. Sparse coding (SC) is used to classify unmanned-aerial-vehicle (UAV) and satellite images because SC representation can generalize a large dataset and improve the detection of distinctive features by reducing calculation time for feature matching and classification. Features from images are extracted based on the following descriptors: (a) Scale Invariant Feature Transform; (b) Histogram of Oriented Gradients; and (c) Local Binary Patterns. SC representation and local image features are combined to represent global features for classification. Features are deployed in a sparse model to store descriptor features using extant dictionaries such as (a) the Discrete Cosine Transform and (b) the Discrete Wavelet Transform. An additional two dictionaries are proposed as developed for the present work: (c) the Discrete Ridgelet Transform (DRT) and (d) the Discrete Tchebichef Transform. The DRT dictionary is constructed by using the Ricker wavelet function to generate finite Ridgelet transforms as basis elements for a hybrid dictionary. Different pooling methods have also been employed to convert sparse-coded features into a feature matrix. Various machine learning algorithms are then applied to the feature matrix to classify objects contained in UAV and satellite imagery data. Experimental results show that the SC model secured better accuracy rates for extracted discriminative features contained in remote sensing images. The authors concluded that the proposed SC technique and proposed dictionaries provided feasible solutions for image classification and object recognition.