INSA 5e année - génie mathématique
Compressive Sensing 2022-2023
Compressive Sensing 2022-2023
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Compressive Sensing 2022-2023 |
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Educational material
NEWS : les notes de lecture sont à jour.
NEWS : ne pas hésiter à me contacter si vous avez des questions.
NEWS : quiz 2 : la correction est en ligne.
Slides de Cédric Herzet sur la NSP.
NEWS : format de l'oral: 15' de préparation (sans document), 15' de présentation / questions.
(Small) Class diary
- Introducing the four lectures.
- Definition of the compressive sensing : sample and compress at the same time.
- Example of a film and a digital camera : sampling, quantify and compress.
- Two fundamental questions about sampling and compressing.
- Answer to the first question: the Nyquist-Fourier sampling Theorem; undersampling and aliasing.
- Answer to the second question: DCT, one method of compression. Sparsity of the DCT.
- Difference between classical digital signal processing and compressive sensing.
- Mathematical tools: norms, support, definition of sparsity, structure of sparse subsets.
- Approximate sparsity: compressible signal, best s-term approximation.
- The sensing process model: just an undetermined linear system to solve.
- The minimum l-0 norm solution and three philosopphy for solving it.
- The difference between a sparse vector and a vector sparse in an unknown basis.
- The difference between Sparse Approximation and Compressive Sensing.
- What is a good sensing matrix ?
- The RIP property (introduction).
- Quiz 1.
- Computer lab part 1.
An introduction to Compressive Sensing, Candés and Wakin article :
- Properties of the RIP.
- Exercice: convergence of IHT algorithm under RIP hypothesis.
- Concentration inequalities.
- The Johnson-Lindenstrauss Lemma.
- Computer Lab with Python: end of part 1.
FLAC audio compression documentation :
A review of lossless audio compression standards and algorithms :
- Computer Lab with Python, part 2.
- Proof of the RIP as an exercice: end.
- Guarantees of recovery: course.
- And to motivate oneself: the (very small) Chrismas tea party !
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