Application of regression analysis in K-SVD dictionary learning

Recent past has witnessed the use of sparse coding of images using learned dictionaries for image compression, denoising and deblurring applications. Though, few of the works reported in literature have addressed the issue of determining the optimum size of the dictionary to be learned and the extent of learning required and largely depends on trial and error approach for finding it. This paper analyses the dictionary learning process and models it using multiple regression analysis, a mathematical tool for determining the statistical relationship among variables. The model can be used as a reference for learning dictionaries from the same training set for different applications. Though the analysis returns a fit model, it lacks generality due to the specific training image set used. However, while using a larger or content specific image set for learning a dictionary, such an analysis is extremely useful.