Machine Learning for Signal
Processing
Sparse and Overcomplete
Representations
Bhiksha Raj
(slides from Sourish Chaudhuri)
Oct 14, 2014
1
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Sparse and Overcomplete Representations: Learning Dictionaries and Image Denoising, Essays (university) of Digital Image Processing
The concepts of sparse and overcomplete representations, focusing on learning dictionaries and image denoising. The basics of component-based representations, pursuit algorithms, and the importance of overcomplete representations. It also delves into the sparsity problem and methods for obtaining sparse solutions, such as matching pursuit and basis pursuit. The document concludes with a summary of the benefits of overcomplete representations.
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2018/2019
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Machine Learning for Signal
Processing
Sparse and Overcomplete Representations Bhiksha Raj (slides from Sourish Chaudhuri) Oct 14, 2014 1
Key Topics in this Lecture
- (^) Basics – Component-based representations
- (^) Overcomplete and Sparse Representations,
- (^) Dictionaries
- (^) Pursuit Algorithms
- (^) How to learn a dictionary
- (^) Why is an overcomplete representation powerful?
Representing Data Dictionary Atoms
Representing Data Dictionary Atoms Each atom is a basic unit that can be used to “compose” larger units.
Representing Data Atoms
Representing Data Atoms
Representing Data
Representing Data
- 6. - 0. - 12. - 4. - 9. - w Representing Data - w ………….
- w
- w Representing Data - w ………….
- w
- w - w - w
Overcomplete Representations
- (^) What is the dimensionality of the input image? (say 64x64 image)
- (^) What is the dimensionality of the dictionary? (each image = 64x64 pixels)
(^) N x 4096
Overcomplete Representations
- (^) What is the dimensionality of the input image? (say 64x64 image)
- (^) What is the dimensionality of the dictionary? (each image = 64x64 pixels)
N x 4096 VERY LARGE!!!
Overcomplete Representations
- (^) What is the dimensionality of the input image? (say 64x64 image)
- (^) What is the dimensionality of the dictionary? (each image = 64x64 pixels)
N x 4096 VERY LARGE!!!