1. A method for determining a high resolution image comprising: (a) receiving a low resolution image; (b) determining a vector for a patch of said low resolution image based upon a total number of non-zero dictionary elements of a low resolution dictionary that are used to said determine said vector, where said total number is modified using a parameter that balances the sparsity of a solution by adjusting the number of said elements used to determine said vector, said parameter inversely varied over said image relative to a standard deviation of a localized patch of said low resolution image; (c) determining a high resolution patch based upon a high resolution dictionary and said vector; (d) determining said high resolution image based upon said high resolution patch in a manner suitable to enhance the visual appearance of the high resolution image compared to said low resolution image and free from a constraint of reconstructing an original high resolution image corresponding to said low resolution image.