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Sparse and Redundant Representations and Their Applications in Signal and Image Processing (236862) Section 3: Image Denoising Winter Semester, 2018/2019 Michael (Miki) Elad

Meeting Plan Quick review of the material covered Answering questions from the students and getting their feedback Discussing a new material – Facial Image Compression Administrative issues

Overview of the Material Image Denoising – The Sparseland Way The Denoising Problem and its Importance First Steps in Image Denoising Variations on the Global Thresholding Algorithm SURE for Parameter Tuning: The Theory SURE for Parameter Tuning: The Practice Patch-Based Denoising – Basics Patch-Based Denoising: Theoretical Foundations The K-SVD Image Denoising Algorithm Patch-Based Denoising – Other Methods Image Denoising - Summary

Your Questions and Feedback Question: L2 – Good or Bad? The message in this course about the suitability of the L2 seems to be confusing. When discussing Wiener filter, L2 was said to be a bad option, yet in defining pursuit algorithms we keep using L2. Now, when discussing denoising, we are aiming to get a minimal L2 error. So, what is the bottom line: L2 – bad or good? Answer: Sorry for the confusion – lets put some order to this picture. We use the L2 in three very different contexts, each with it’s own story: 𝐃α−y 2 2 Here the L2 represents the knowledge that the noise is white & Gaussian – this is well-justified L2 Here the L2 is used as a prior on the representation, causing a spread of the non-zeros everywhere - something that we know to be a VERY BAD choice α 2 2 𝐸 x −x 2 2 →min This is the Mean-Squared-Error between the recovered and the original image. While there are some attacks on this option, it is still important and popular &

Your Questions and Feedback

New Material? Face Image Compression Here is a chapter that we omitted from the MOOC after a debate, despite its importance and elegance: image compression using the Sparseland model Rather than discussing general purpose compression, we focus on a specific family of images – frontal faces This work is a brilliant MSc research by Ori Bryt

Administrative Issues Lets talk about: Please provide your feedback to the Technion’s course 236862 (MISHAAL HAMARTZE) & especially with free text comments Remember the deadline on the 6th for the course mid-project