Applied Mathematics

We compare several methods to zoom an image that is decimated and had a blur operator applied. Results are shown for various amounts of pre knowledge concerning the blur and contrasted with a new method of digital zoom with a projection matrix trained on another measured image. Results show that the new technique is superior in the manner it uses available information.

We show that in creating the projection matrix we need not necessarily use the actual image, but can use some perturbed version of it to move the solution in the direction we desire. In this example we show how we can increase the sharpness of the resulting digital zoom operator by adding a small amount of a Sobel operator to the original training image. This leaves the possibility of applying various operators to the training image to produce a solution closer toward our desired solution. Our example is again done for a 5X zoom with blur.

We continue our application of underdetermined linear systems with image processing and digital zoom. We contrast our technique to conventional image restoration algorithms followed by Spline interpolation. This section contains increased blur and discusses the use of a priori knowledge and demonstrates that our digital-zoom technique makes better use of knowledge or lack thereof than conventional applications.

We apply our technique to basic imaging where an image is sampled at a lower resolution and a higher resolution (size) image is desired. We represent the imaging system as a typical focal plane array or CCD and show how we train a projection matrix to perform a 5x digital zoom. Results are compared with conventional Spline.

We address an approximation method for solving underdetermined matrix problems; that is problems with more unknowns than equations. We show that applying some prior knowledge or assumed property of the solution can reduce solution space and significantly improve on the solution estimation. In part 1 we present the concept and show several one dimensional examples.