ECE563 Image Processing Chapter 6 Project Wiener Filter Image Restoration Implemented with FFTs 1. The problem During image acquisition images are invariable corrupted by blurring processes and noise. Here we will explore the restoration of an image corrupted by the degradations modeled in the midterm exam project. In particular, we will consider diffraction limited blur, detector integration effects, and atmospheric turbulence. Use the exact same parameters from the midterm project for the degradation here. Assume a single Fried parameter of 0 0.05r meters. In addition to that blurring, here you are to also model additive Gaussian noise with standard deviation of 1 digital unit (DU). Use the same “ideal” image as you used for the midterm project. In this project, you are to create a custom user-defined function in MATLAB called ‘wiener_filter_2d.m’ that will restore an image like our observed image given some relevant information. This function should work for the current project, but be general purpose, so it can be used for any similar restoration problem where the blurring PSF is known. The Wiener filter should be the FFT-based IIR Wiener filter discussed in class with the simple constant noise-to-signal ratio model. The Wiener filter design and image processing are to be done using FFTs. Apply the DC gain adjustment as shown in the examples in class so that the DC gain of the Wiener filter is 1. Your Wiener filter function should follow the function template provided at the end of this project statement. You may include additional optional inputs and/or outputs if you choose. In addition to the Wiener filter function, prepare a script file called ‘run_wiener_filter_2d.m’. The script file will load the input image, generate the artificially degraded image as described above (blur and noise). Next, the script file should call your new restoration function ‘wiener_filter_2d.m’ to generate a restored version of the image. Use ‘dif.m’ to quantitatively compare the ideal image with the restored image (or sue your own code). Also, compute the SSIM metric using the built-in ssim() function. Also, compute the error for the observed image relative to the ideal image for reference. Make note of the mean absolute error (MAE), mean squared error (MSE), and structural similarity image metric (SSIM) for all of your results. A tuning parameter required by the Wiener filter is the noise-to-signal (NSR) ratio. In practice this will not be known in advance. It is usually selected in a real application based on subjective evaluation of the restored image using trial and error. In this case, however, we know the ideal image so we can explore the sensitivity of the Wiener filter to this parameter by quantitatively by computing the restoration error as a function of the NSR used in the Wiener filter. Put your Wiener filter in a loop (yes, it is OK to use a loop here) and evaluate the MSE for a suitable range of NSR values. What is a suitable range you ask That is for you to determine. Find the NSR that provides approximately the lowest MSE and show the restored image for that one NSR. Graph the error on the vertical axis versus the NSR found using your loop, showing where the minimum lies. Use semilogy instead of plot to make the range of MSE values easier to display. As always, be sure to fully title and label all images and plots and include correct units. Compute and display the MAE, MSE and SSIM for a restored image using this optimum Wiener NSR. You do not need to optimize the NSR for each metric (use MSE only for choosing NSR). 2. What to turn in Once complete,
publish your script file run_wiener_filter_2d.m, to a .pdf file. Upload the output .pdf file and your wiener_filter_2d.m function file. The script file should generate the outputs enumerated below in order, properly titled, and with all axes fully labeled. Each plot must be on its own figure so they can all be inspected after execution (no overwriting figures). Your script file should: 1. Show the ideal input image. 2. Show a mesh plot of the degradation frequency response as 1 2| ( , ) |H f f . Label axes with units of cycles/sample. Plot this from -0.5 to 0.5 cyc/sample on each axis. This can be accomplished using the midterm project code (or you can use different code). 3. Show the artificially degraded image with blur and noise. The degraded image can be generated using the midterm project code (or you can use different code). 4. Graph the MSE versus the NSR used by your Wiener filter function. Use semilogy and fully and properly label the graph. 5. Show a mesh plot of the magnitude Wiener filter frequency response 1 2| ( , ) |WH f f similar to that above in Item 2. Show only the Wiener filter frequency response corresponding to the filter that gives the lowest MSE found in Part 4. Use abs() to get the magnitude and be sure to zero-center your frequency response samples. 6. Show the Wiener filtered image (restored). Show only the Wiener filter output corresponding to the filter that gives the lowest error found in Part 4. 7. Display the MAE, MSE, and SSIM for the Wiener filter with NSR that gives the lowest error found in Part 4 (you don’t need to optimize for each metric). You can use fprintf( ) to make a nice output statement for each error metric. Your plots should be clearly and correctly labeled and presented in order. Make sure all plots are have properly labeled axes with units and appropriate titles. Your MATLAB code should be well commented and clearly presented. You must use cells to organize your script file. A cell is a block of code separated using %%. Experiment for how the comments come out after publishing and make it look nice. Your function should be formatted like the template at the end of this document. Look at the code provided in chp6/run_wiener_filter.m and the slides in chp6/Wiener_filters.pdf for helpful information. You do not need to prepare a written report (just submit the published script file and your function file wiener_filter_2d.m). This project is to be done independently and the submitted code must be uniquely your own. function out = wiener_filter_2d( in, psf, NSR, pad ) % % out = wiener_filter_2d( in, psf, NSR, pad ) % % 2D IIR Wiener filter implemented with FFTs. Uses the constant noise to % signal PSD ratio approximation. % % Prepared for ECE 563 Image Processing with Dr. Hardie % % REQUIRED INPUTS % % in Input image (2D array) % psf Degradation point spread function % NSR Noise to signal PSD ratio (constant) % pad Padding size for the FFT processing to minimize border effects % % OPTIONAL INPUTS % % OUTPUTS % % out.img Output image (restored), same size as in (and aligned) % out.HW Wiener filter frequency response % out.f1 Frequency axis in x for out.HW in cyc/sample % out.f2 Frequency axis in y for out.HW in cyc/sample % % Author: —————- % Date: —————- % % COPYRIGHT 2021 ————. ALL RIGHTS RESERVED. % This is UNPUBLISHED PROPRIETARY SOURCE CODE of ————-; the % contents of this file may not be disclosed to third parties, copied or % duplicated in any form, in whole or in part, without the prior written % permission of ————–. PUT YOUR CODE HERE