1. | CH 1: The introduction of this course | The schedule for this semester. Reference book, requirments and evaluation method | ||
3. | CH 2: L0, L1, L2 Minimization as Regularization | 1. Underdetermined linear system; 2. The temptation of convexity; 3. Closer look at L1 minimization | ||
4. | CH 2: L0, L1, L2 Minimization as Regularization | 1. Closer look at L1 minimization; 2. Conversion of (P1) to linear programming; 3.Promoting sparse solution | ||
CH 2: L0, L1, L2 Minimization as Regularization | 1. Promoting sparse solution; 2. The L1-norm and implications; 3. The (P0) problem-sparsity optimization | |||
5. | CH 3: Uniqueness and Uncertainty | 1. Two orthogonal case; 2.. An uncertainty principle; 3. Heisenberg uncertainty | ||
6. | CH 3: Uniqueness and Uncertainty | 1. Uncertainty of redundant solutions; 2. From uncertainty to uniqueness; 3. | ||
CH 3: Uniqueness and Uncertainty | 1. Uniqueness via spark; 2. Uniqueness via the mutual-coherence | |||
7. | CH 4:Pursuit Algorithms- Practice (1) | 1. The core idea; 2. The orthogonal matching pursuit | ||
8. | CH 4:Pursuit Algorithms- Practice (2) | 1. Other greedy method; 2. Convex relaxation techniques | ||
10. | CH 5: Pursuit Algorithms--Guarantees | 1. OMP Performance Guarantee; 2. BP performance guarantee; 3. Performance of pursuit algorithms; 4. Tropps Exact recovery condition |
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11. | CH6: From Exact to Approximate Solutions (1) | 1. General motivation; 2. Stability of the sparsest solution; 3. Theoretical study of the stability of (P_0^e) |
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CH6: From Exact to Approximate Solutions (2) | 1. Theoretical study of the stability of (P_0^e); | |||
12. | CH6: From Exact to Approximate Solutions (3) | 1. Restricted isometry property; 2. Stability analysis; 3. Pursuit algorithms; 4. OMP and BP extension |
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13. | CH6: From Exact to Approximate Solutions (4) | 1. Basic pursuit denoising; 2. IRLS ; 3. Subgradients |
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CH6: From Exact to Approximate Solutions (5) | 1. LARS; 2. Unitary case; 3. BPDN stability guarantee |
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14. | CH6: From Exact to Approximate Solutions; Ch7: Compressed sensing/Compressive sampling | 1. stability of BPDN; 2. Overview; 3. Fourier analysis; |
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15. | Ch7: Compressed sensing/Compressive sampling (1) | 1. wavelets; 2. compressed sensing understanding |
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Ch7: Compressed sensing/Compressive sampling (2) | 1. sparsity and compression; | |||
16. | Ch7: Compressed sensing/Compressive sampling (3) | 1. compressed sensing understanding; 2. Sensing matrix |
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Ch7: Compressed sensing/Compressive sampling (4) | 1. Null space conditions; | |||
17. | Ch7: Compressed sensing/Compressive sampling (5) | 1. The restricted isometry property | ||
18. | Ch7: Compressed sensing/Compressive sampling (6) | 1. The restricted isometry property; 2. The relationship between RIP and NSP; 3. Coherence; |
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Ch7: Compressed sensing/Compressive sampling (7) | 1. The restricted isometry property; 2. Sensing matrix constructions; 3. Signal recovery via l1 minimization; 4. Noise free signal recovery |
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19. | Ch7: Compressed sensing/Compressive sampling (8) | 1. Noise free signal recovery; | ||
20. | Ch7: Compressed sensing/Compressive sampling (9) | 1. signal recovery in noise: bounded noise | ||
Ch7: Compressed sensing/Compressive sampling (10) | 1. signal recovery in noise: Gaussian noise; 2. Coherence guarantees |
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21. | The Johnson—Lindenstrauss lemma (1) | 1. Lemma explaination; 2. Main idea |
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The Johnson—Lindenstrauss lemma (2) | 1. Proof | |||
The Johnson—Lindenstrauss lemma (3) | 1.proof | |||
22. | Principle component analysis (1) | 1. Overview; 2. Motivation: A toy example; 3. Frame work |
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Principle component analysis (2) | 1. Covariance analysis; 2. Covariance matrix; |
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Principle component analysis (3) | 1. Covariance and correlation; 2. PCA using SVD |