Spectral imaging is a fundamental diagnostic technique in physical sciences with widespread application. Conventionally, spectral imaging techniques rely on a scanning process, which renders them unsuitable for dynamic scenes. Here we study the problem of estimating the physical parameters of interest from the measurements of a non-scanning spectral imager based on a parametric model. This inverse problem, which can be viewed as a multi-frame deblurring problem, is formulated as a maximum a posteriori (MAP) estimation problem. The global optimum of the nonlinear MAP problem is found using an efficient dynamic programming algorithm. Lastly, the method is illustrated for an application in solar spectral imaging. Numerical results suggest that estimation accuracy is comparable to the conventional slit spectroscopy, but with the added benefit of a two-dimensional fleld-of-view.