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Occam's razor in massive data acquisition: a statistical physics approach
Published on Oct 16, 20124290 Views
Acquiring a large amount of information in short time is crucial for many tasks in control. Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse s
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Occam’s razor in massive data acquisition: a statistical physics approach00:00
General perspective00:37
Sparse signals - 102:26
Sparse signals - 202:59
Compressed sensing03:34
An example: tomography of binary mixtures - 105:03
An example: tomography of binary mixtures - 205:33
An example: tomography of binary mixtures - 306:27
An example: tomography of binary mixtures - 407:48
An example: tomography of binary mixtures - 508:27
An example: tomography of binary mixtures - 608:29
Second example: group testing - 110:00
Second example: group testing - 212:41
Third example from magnetic resonance imaging13:18
The simplest problem: getting a signal from some measurement = linear transforms14:05
The problem - 115:48
The problem - 216:54
The problem - 316:55
The problem - 418:40
(N/R) possible guesses18:44
Compressed sensing as an optimization problem: the L 1 norm approach - 119:55
Compressed sensing as an optimization problem: the L 1 norm approach - 222:16
Phase diagram of the L 1 norm approach23:06
Phase diagram - 124:07
Phase diagram - 225:19
Alternative approach, able to reach the optimal rate α = ρ - 128:21
Step 1: Probabilistic approach to compressed sensing - 131:24
Step 1: Probabilistic approach to compressed sensing - 233:31
Hint of why the theorem is correct34:57
Step 2: Sampling from the constrained measure - 135:10
Step 2: Sampling from the constrained measure - 237:17
Belief propagation = mean field (TAP) equations - 137:33
Belief propagation = mean field (TAP) equations - 238:00
Belief propagation = mean field (TAP) equations - 338:47
Belief propagation = mean field (TAP) equations - 439:10
BP equations - 145:44
BP equations - 246:24
NB: Validity of mean field BP equations?47:20
Parameter learning48:37
Performance of the probabilistic approach + message passing + parameter learning49:26
Analytic study: cavity equations, density evolution, replicas, state evolution - 149:47
Analytic study: cavity equations, density evolution, replicas, state evolution - 250:27
When α is too small, BP is trapped in a glass phase51:15
Performance of BP with parameter learning: phase diagram53:51
Step 3: design the measurement matrix in order to get around the glass transition - 155:59
Nucleation and seeding56:37
Step 3: design the measurement matrix in order to get around the glass transition - 257:51
Structured measurement matrix - 157:54
Structured measurement matrix - 258:41
Structured measurement matrix - 359:41
Structured measurement matrix - 459:42
Structured measurement matrix - 559:43
Numerical study - 159:44
Numerical study - 201:00:24
Numerical study - 301:00:51
Performance of the probabilistic approach + message passing + parameter learning + seeding matrix01:01:16
Numerical study - 401:01:47
Analytic study: cavity equations, density evolution, replicas01:02:08
Theory: seeded-BP threshold at α = ρ when L → ∞01:02:09
Shepp-Logan phantom, in the Haar-wavelet representation - 101:03:09
Shepp-Logan phantom, in the Haar-wavelet representation - 201:04:01
Summary01:04:06