1. A method of adaptive motion estimation and deblurring of acquired digital images, comprising: acquiring multiple digital images with a moving digital image acquisition device that includes an image sensor, including a relatively sharp, underexposed reference image and a blurred image; estimating an initial approximate point spread function (PSF) based on a first DC offset point corresponding to the moving of the device during the acquiring of the multiple digital images; choosing multiple crops from the blurred image and the reference image or an interpolated version of the reference image, or both, and equalizing a brightness between these crops; computing a second PSF for a pair of horizontal and vertical offsets; calculating a Cepstrum and refining the second PSF to generate a third PSF based on the Cepstrum; precisely determining a position of a first PSF point; and deblurring at least one of the digital images using a best found PSF based on the third PSF and first PSF point.