수치시뮬레이션기반공학특강1

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페이스북 트위터 카카오톡 네이버밴드 링크복사

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공학 >컴퓨터ㆍ통신 >정보통신공학
강의학기

2012년 1학기

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7,030
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5/5.0 (1)

For graduate student in science and engineering. The purpose of this course is twofold; sparse and redundant representation in signal and image processing and compressed sensing or compressive sampling in imaging.

수강안내 및 수강신청
※ 수강확인증 발급을 위해서는 수강신청이 필요합니다

CH 1: The introduction of this course

차시별 강의

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
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)
	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
13.	CH6: From Exact to Approximate Solutions (4)	1. Basic pursuit denoising; 2. IRLS ; 3. Subgradients
	CH6: From Exact to Approximate Solutions (5)	1. LARS; 2. Unitary case; 3. BPDN stability guarantee
14.	CH6: From Exact to Approximate Solutions； Ch7: Compressed sensing/Compressive sampling	1. stability of BPDN; 2. Overview; 3. Fourier analysis;
15.	Ch7: Compressed sensing/Compressive sampling (1)	1. wavelets; 2. compressed sensing understanding
	Ch7: Compressed sensing/Compressive sampling (2)	1. sparsity and compression;
16.	Ch7: Compressed sensing/Compressive sampling (3)	1. compressed sensing understanding; 2. Sensing matrix
	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;
	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
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
21.	The Johnson—Lindenstrauss lemma (1)	1. Lemma explaination; 2. Main idea
	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
	Principle component analysis (2)	1. Covariance analysis; 2. Covariance matrix;
	Principle component analysis (3)	1. Covariance and correlation; 2. PCA using SVD