Hyperspectral images

which span the visible to infrared spectrum with hundreds of contiguous and narrow spectral bands

are advantageous because of their subtle discriminative spectral characteristics. Owing to the fine spectral differences between various materials of interest

hyperspectral images support improved interpretation capabilities

and they perform important functions in various fields

such as the military

precision agriculture

and mineralogy. The sparsity of signals is a powerful and promising statistical signal modeling tool for hyperspectral image processing and analysis because signals can be compactly represented by only a few coefficients that carry the most important information in a certain basis or dictionary.A full diagram of Sparse Representation（SR） consists of sparse coding（regression） and dictionary learning. A brief review about this basic theory from the perspective of hyperspectral remote sensing is presented in the second section. With various forms of complex degradation and the demand for resolution enhancement considered

basic theories as well as recent studies in the area of hyperspectral image processing

including denoising

unmixing

super-resolution

and spectral-spatial image fusion in an SR manner

are presented in the third section. Dimensional reduction

classification

target detection

and anomaly detection

which are aimed at mining subtle diagnostic information on hyperspectral images in an SR manner

are also reviewed in the hyperspectral image analysis section. This review is followed by some suggestions and remarks on SR-based hyperspectral image processing and analysis. Processing literature considers denoising as the most fundamental task

single image super-resolution as problematic

and hyperspectral unmixing and spectral-spatial fusion as necessary subjects. In the hyperspectral analysis area

classification and detection are the most important tasks

and feature extraction/dimensional reduction works as a meaningful pre-processing step. The research on SR-based hyperspectral processing and analysis has recently attained some achievements. However

the obstacles mentioned in this paper still require further study. This review also presents several important remarks and outlines the future directions in this field. First

despite the increasing research on hyperspectral signal recovery and reconstruction

single image super-resolution and multi-resolution image fusion remain a problem area

mainly because of the limited availability of prior information within the remote sensing data and because of unstable sparse inverse optimization. Thus

the method for qualified over-completed dictionary design for specific hyperspectral image processing and delicate inverse optimization is an important study area. Second

the most important issue for hyperspectral image information extraction comes in the form of a discriminative dictionary. Most research ideas on hyperspectral target detection involve multiple sparse representation classification-based model simplification

whereas the anomaly detection method relies on the quality of the local ambient dictionary. Thus

the detection area should be studied further. In addition

reasonable approximated sparse coding combined with specific dictionary learning and some unique characteristics of hyperspectral images

such as manifold structure

multi-modality

and low rank property

should be regarded as useful tools for future research.