Abstract: A method is provided for decompressing an image originally compressed using a known compression technique. An original compressed image file is defined by a plurality of locations that correspond to image data. A set of smooth test images is created by iteratively applying a plurality of different size PIXON® kernels to each location of a starting image beginning with a smallest size kernel. Each smooth test image is compressed using the known compression technique, then compared against the original compressed image at each location of the image to determine a goodness-of-fit of the compressed smooth test image to each location of the original compressed image file. For each location, the smooth test image that has the largest size kernel that passes a pre-determined goodness-of-fit criterion is selected for a given location of the decompressed image. A compression method utilizes the PIXON® method for optimization of knot points within an image.