Image Restoration - Electrical and Computer （图像恢复电子和计算机）.pdf

Image Restoration EE 528 Digital Image Processing All images taken from Gonzalez and Woods online slides /DIP/dip _faculty/classroom_presentations_downloads .htm Material mostly based on A.K. Jain’s book Some topics taken from Gonzalez Woods Intuition images on slides, math details will be covered in class or is in the book Image Enhancement or Restoration Most of what we learnt in Image Enhancement chapter can also be classified as Image Restoration techniques. Specifically Linear filtering (low pass for noise reduction, high pass for edge sharpening, band-pass for both) Median filtering (for salt and pepper noise), Log-domain filtering and other nonlinear techniques Inverse Pseudo-inverse Filters Inverse Filter Assumes no noise, only blurring. Blurring filter known In case of noise If blurring filter has zeros at some frequencies (which it will since it is a low-pass filter), those frequencies will be amplified in the noise Pseudo-inverse filter: removes the problem at zero (or near zero) frequencies, but still amplifies noise at other frequencies where the blurring filter response is not zero but small Image blurred by atmospheric turbulence with additive noise Inverse v/s Pseudo-inverse filtering Wiener Smoother Assumes image is blurred and has additive noise (independent of image) Need to know Blurring filter Noise covariance True image autocorrelation Mean of noise of true image (or assume zero mean) Gives “linear MMSE” estimate: linear filter with least expected value of MSE w.r.t. the true image Truly MMSE when the observed and true image are jointly Gaussian Motion blurred image Pseudo-inverse v/s Wiener Column 2: Pseudo-inverse Column 3: Wiener Maximum noise in row 1, least in row 3 Wiener smoother Observed: v. True: u, convo