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Advancing Image Processing with Sparseland: A Model of Sparse Representations

Explore the Sparseland model by Michael Elad for image patches, utilizing redundant dictionaries to enhance denoising, compression, and more. Uncover challenges and successes in employing this emerging model for state-of-the-art results in various applications. Discover the potential and necessity of simple yet effective signal and image models for optimizing algorithms. Continuous research is crucial to expanding Sparseland's versatility across diverse domains.

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Advancing Image Processing with Sparseland: A Model of Sparse Representations

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  1. New Results in Image Processing based on Sparse and Redundant Representations Michael Elad The Computer Science Department The Technion – Israel Institute of technology Haifa 32000, Israel Medical Imaging Workshop RAMBAM Hospital 25.2.07

  2. Model? Effective removal of noise (and many other applications) relies on an proper modeling of the signal Michael Elad The Computer-Science Department The Technion

  3. Reliability Simplicity Which Model to Choose? • There are many different ways to model signals and images with varying degrees of success. • The following is a partial list of such models for images: • Good models should be simple while matching the signals: Principal-Component-Analysis Anisotropic diffusion Markov Random Field Wienner Filtering DCT and JPEG Wavelet & JPEG-2000 Piece-Wise-Smooth C2-smoothness Besov-Spaces Total-Variation Beltrami-Flow Michael Elad The Computer-Science Department The Technion

  4. Approximation Theory Wavelet Theory Signal Transforms Multi-Scale Analysis Linear Algebra Optimization Theory Inpainting Compression Blind Source Separation Super-Resolution Demosaicing Denoising Sparseland SparselandA new Model for Signals / Images Michael Elad The Computer-Science Department The Technion

  5. Σ α1 α4 α3 α2 The Sparseland Model for Images • Task: model image patches of size 10×10 pixels. • We assume that a dictionary of such image patches is given, containing 256 atom images. • The Model: every image patch can be described as a linear combination of few atoms. • This model describes every image patch as a sparse combination over a redundant dictionary. Michael Elad The Computer-Science Department The Technion

  6. Σ α1 α4 α3 α2 Difficulties With Sparseland • Problem 1: Given an image patch, how can we find its atom decomposition? • Problem 2: Given a family of signals, how do we find the dictionary to represent it well? • Problem 3: Is this model flexible enough to describe various sources? ALL ANSWERED POSITIVELY AND CONSTRUCTIVELY Michael Elad The Computer-Science Department The Technion

  7. Source Result 30.829dB Noisy image The obtained dictionary after 10 iterations Initial dictionary (overcomplete DCT) 64×256 Image Denoising (Gray) [Elad & Aharon (`06)] The results of this algorithm compete favorably with the state-of-the-art: E.g., • We get ~1dB better results compared to GSM+steerable wavelets [Portilla, Strela, Wainwright, & Simoncelli (‘03)]. • Competitive works are [Hel-Or & Shaked (`06)] and [Rusanovskyy, Dabov, & Egiazarian (’07)]. Both also lean on Sparseland. Michael Elad The Computer-Science Department The Technion

  8. Original Noisy (12.77dB) Result (29.87dB) Denoising (Color) [Mairal, Elad & Sapiro, (‘06)] Our experiments lead to state-of-the-art denoising results, giving ~1dB better results compared to [Mcauley et. al. (‘06)] which implements a learned MRF model (Field-of-Experts) Michael Elad The Computer-Science Department The Technion

  9. Inpainting [Mairal, Elad & Sapiro, (‘06)] Our experiments lead to state-of-the-art inpainting results. Original 80% missing Result Michael Elad The Computer-Science Department The Technion

  10. Video Denoising [Protter & Elad (‘06)] Our experiments lead to state-of-the-art video denoising results, giving ~0.5dB better results on average, compared to [Boades, Coll & Morel (‘05)] and [Rusanovskyy, Dabov, & Egiazarian (’06)] Original Noisy (σ=25) Denoised Original Noisy (σ=50) Denoised Michael Elad The Computer-Science Department The Technion

  11. 15.81 13.89 10.66 6.60 14.67 12.41 9.44 5.49 15.30 12.57 10.27 6.36 Facial Image Compression [Brytt and Elad (`07)] Results for 550 Bytes per each file Michael Elad The Computer-Science Department The Technion

  12. ? 18.62 12.30 7.61 ? 16.12 11.38 6.31 ? 16.81 12.54 7.20 Facial Image Compression [Brytt and Elad (`07)] Results for 400 Bytes per each file Michael Elad The Computer-Science Department The Technion

  13. Which model to choose? Is it working well? To Conclude Effective (yet simple) model for signals/images is key in getting better algorithms for various applications Sparseland is an emerging model with high potential. It is based on sparse and redundant representations of signals, and learned dictionaries It has been deployed to many applications, in all leading to state-of-the-art results. More work is required to extend its usability to other domains. Michael Elad The Computer-Science Department The Technion

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