Resolution of  Images By Filter Coefficients and Sparsity 

Hyperspectral images (HSIs) have high spectral resolution, but they suffer from low spatial resolution. In this paper, a new learning-based approach for super-resolution (SR) using the discrete wavelet transform (DWT) is proposed. The novelty of our approach lies in designing application-specific wavelet basis (filter coefficients). An initial estimate of SR is obtained by using these filter coefficients while learning the high-frequency details in the wavelet domain.

The final solution is obtained using a sparsity-based regularization framework, in which imagedegradation and the sparseness of SR are estimated using the estimated wavelet filter coefficients (EWFCs) and the initial SR estimate, respectively. The advantage of the proposed algorithm lies in 1) the use of EWFCs to represent an optimal point spread function to model imageacquisition process; 2) use of sparsity prior to preserve neighborhood dependencies in SR image; and 3) avoiding the use of registered imageswhile learning the initial estimate. Experiments are conducted on three different kinds of images. Visual and quantitative comparisons confirm the effectiveness of the proposed method.