  A new statistical model designed for regression analysis with a sparse design
matrix is proposed. This new model utilizes the positions of the limited
non-zero elements in the design matrix to decompose the regression model into
sub-regression models. Statistical inferences are further made on the values of
these limited non-zero elements to provide a reference for synthesizing these
sub-regression models. With this concept of the regression decomposition and
synthesis, the information on the structure of the design matrix can be
incorporated into the regression analysis to provide a more reliable
estimation. The proposed model is then applied to resolve the spatial
resolution enhancement problem for spatially oversampled images. To
systematically evaluate the performance of the proposed model in enhancing the
spatial resolution, the proposed approach is applied to the oversampled images
that are reproduced via random field simulations. These application results
based on different generated scenarios then conclude the effectiveness and the
feasibility of the proposed approach in enhancing the spatial resolution of
spatially oversampled images.
