Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

image restorationhelphelp Q1: Image Restoration (12 marks) = Suppose an image f(x,y) is first blurred by a point spread function (PSF) h(x, y) and then

image text in transcribed

image restorationhelphelp

Q1: Image Restoration (12 marks) = Suppose an image f(x,y) is first blurred by a point spread function (PSF) h(x, y) and then corrupted by a noise process n(x,y). The degraded image is denoted as g(x,y) = h(x,y) * f(x,y) + n(x, y). It is known that the noise n(x, y) and image f(x,y) are uncorrelated, and n(x,y) is white Gaussian with zero mean and variance o 2. 1) Assume that h(x,y) = 8(x,y) and there are L noisy observations {g}(x,y)}}=1 of f(x,y), i.e., g(x,y) = f(x,y) + ni(x, y), l = 1,...,L, and {n(x, y)}{= are independent realizations of the white Gaussian noise process n(x, y). A denoised image is obtained as f(x,y) = {{-191(x, y). Determine the noise variance in the denoised image f (x,y). (2 marks) 2) Suppose the size of f(x, y) is 216 x 216 (i.e., x, y = 0, ---,215) and ie PSF h(x, y) is given below: h(x,y) 1 = 3 ro 0 1 0 1 0 1 0 0 a) Derive the frequency response of h(x, y). (4 marks) b) Derive the direct inverse filter in the frequency domain to restore f(x,y). Discuss whether there is any frequency where the response of the direct inverse filter is infinite. (3 marks) c) Assume the power spectral density (PSD) of the image (process) is given by Pry(u, v), u, v = 0,---,215. Derive a linear filter in the frequency domain to restore f(x,y) that achieves the minimum mean square error (MMSE). Discuss whether there is any frequency where the frequency response of the derived filter is infinite

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Exploring Public Relations Global Strategic Communication

Authors: Ralph Tench, Liz Yeomans

4th Edition

1292112182, 9781292112183

More Books

Students also viewed these Accounting questions