Sparse and Redundant Representations and Their Applications in

Slides:

Advertisements

Similar presentations

MMSE Estimation for Sparse Representation Modeling

Advertisements

Joint work with Irad Yavneh

Introduction to Markov Random Fields and Graph Cuts Simon Prince

* * Joint work with Michal Aharon Freddy Bruckstein Michael Elad

More MR Fingerprinting

Dictionary-Learning for the Analysis Sparse Model Michael Elad The Computer Science Department The Technion – Israel Institute of technology Haifa 32000,

Image Super-Resolution Using Sparse Representation By: Michael Elad Single Image Super-Resolution Using Sparse Representation Michael Elad The Computer.

Image Denoising via Learned Dictionaries and Sparse Representations

New Results in Image Processing based on Sparse and Redundant Representations Michael Elad The Computer Science Department The Technion – Israel Institute.

II–2 DC Circuits I Theory & Examples.

Part III: Inference Topic 6 Sampling and Sampling Distributions

SOS Boosting of Image Denoising Algorithms

A Weighted Average of Sparse Several Representations is Better than the Sparsest One Alone Michael Elad The Computer Science Department The Technion –

A Sparse Solution of is Necessarily Unique !! Alfred M. Bruckstein, Michael Elad & Michael Zibulevsky The Computer Science Department The Technion – Israel.

Topics in MMSE Estimation for Sparse Approximation Michael Elad The Computer Science Department The Technion – Israel Institute of technology Haifa 32000,

Strategy BSNS7340 Studio 9 semester two >>FACULTY OF CREATIVE INDUSTRIES AND BUSINESS Industry Based Learning – attend the pre course session to.

ECE 8443 – Pattern Recognition ECE 8423 – Adaptive Signal Processing Objectives: Deterministic vs. Random Maximum A Posteriori Maximum Likelihood Minimum.

Web Image Retrieval Re-Ranking with Relevance Model Wei-Hao Lin, Rong Jin, Alexander Hauptmann Language Technologies Institute School of Computer Science.

Sparse & Redundant Representation Modeling of Images Problem Solving Session 1: Greedy Pursuit Algorithms By: Matan Protter Sparse & Redundant Representation.

Image Decomposition, Inpainting, and Impulse Noise Removal by Sparse & Redundant Representations Michael Elad The Computer Science Department The Technion.

A Weighted Average of Sparse Representations is Better than the Sparsest One Alone Michael Elad and Irad Yavneh SIAM Conference on Imaging Science ’08.

Markov Random Fields in Vision

From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images Alfred M. Bruckstein (Technion), David L. Donoho (Stanford), Michael.

Your teacher has announced that the class will be taking a field trip

Are 4(5x + 2) and 4(5x) +4(2) equivalent expressions?

Problems With Assistance Module 2 – Problem 1

Chapter 9 Includes Crash Course Videos part 1 and 2

Problems With Assistance Module 2 – Problem 5

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

For example, how can you use exponents to write

7 x 2 5 LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try.

2 3 = …. LearnZillion Notes:

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Sparse and Redundant Representations and Their Applications in

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do.

How do you determine an author’s purpose? LearnZillion Notes:

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Find the first six multiples of 4.

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Problems With Assistance Module 2 – Problem 6

Sparse and Redundant Representations and Their Applications in

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Sparse and Redundant Representations and Their Applications in

Sparse and Redundant Representations and Their Applications in

Sparse and Redundant Representations and Their Applications in

Sparse and Redundant Representations and Their Applications in

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

1 2 ÷ 4 LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?”

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Intelligent Systems (AI-2) Computer Science cpsc422, Lecture 7

LearnZillion Notes: --This is your hook. Start with a question to draw the student in. We want that student saying, “huh, how do you do X?” Try to be specific.

Presentation transcript:

Sparse and Redundant Representations and Their Applications in Signal and Image Processing (236862) Section 4: MAP vs. MMSE Estimation 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 – MMSE Estimation via the Stochastic Resonance Concept – Given by Dror Simon Administrative issues

Overview of the Material Sparseland: An Estimation Point of View A Strange Experiment A Crash-Course on Estimation Theory Sparseland: Approximate Estimation MMSE: Back to Reality

Your Questions and Feedback Answer: MAP Estimation and the Relation to OMP: In the slides we derive the MAP estimation and get a strange looking expression, and yet we claim that OMP approximates it. We did see that for |s|=1 the two align, but is there a clearer view of the connection between the estimation approach and the OMP or the pursuit we saw so many times in this course? Answer: Let’s Try … Here is an attempt to clarify this connection. It will be obtained by deriving the MAP little bit differently, and by relying on different assumptions

Your Questions and Feedback Lets define our estimation goal: In this step we add the support as an unknown, so that we search for the most probable representation and its support TOGETHER Using Bayes rule we obtain:

Your Questions and Feedback Returning to our MAP goal:

Your Questions and Feedback So, this is what we just got: Suppose that this is our probability Elastic Net This leads to: which is the P0 we kept advocating, with a twist

Your Questions and Feedback

New Material? MMSE Estimation: Another Point of View We are hooked to the idea that noise is … noise, i.e. an annoying disturbance to be avoided For example, consider the previous chapter about denoising … Could noise be helpful in engineering processes? Are you aware of cases in which noise (or randomness) is beneficial? Observe that the RandOMP described in this chapter used randomness to achieve its MMSE estimation How could we offer a parallel to the RandOMP that is BP-based? This brings us to Dror Simon’s presentation on Stochastic Resonance

Administrative Issues Lets talk about the following: Your feedback is very much needed in the Technion’s course 236862 (MISHAAL HAMARTZE) & (+ free text comments) Are there questions about the final project?