0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
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1 | Category | Topics | Sparsity | Type of | Information | Type of | Min number | Conventional | Applications |
domain | sparsity | domain | sampling in | of required | reconstruction | ||||
info. domain | samples | methods | |||||||
2 | Sampling | Uniform | Frequency | Lowpass | Time/space | Uniform | 2×BW−1 | Lowpass | A/D |
sampling | filtering/ | ||||||||
Interpolation | |||||||||
3 | Nonuniform | Frequency | Lowpass | Time/space | Missing samp- | 2×BW−1 | Iterative metho- | Seismic/ | |
sampling | -les/jitter/per- | (in some cases | -ds/filter banks/ | MRI/CT/ | |||||
-iodic/random | even BW) | spline interp. | FM/ PPM | ||||||
4 | Sampling of | Frequency | Union of | Time/pace | Uniform/jit- |
| Iterative metho- | Data | |
multiband | disjoint | -ter/periodic/ | -ds/filter banks/ | compression/ | |||||
signals | intervals | random | interpolation | radar | |||||
5 | Random | Frequency | Random | Time/space | Random/ |
| Iterative methods: | Missing samp. | |
sampling | uniform | coeff. | adapt. thresh. | recovery/ | |||||
RDE/ELP | data comp. | ||||||||
6 | Compressed | An arbitrary | Random | Random | Random |
| Basis pursuit/ | Data | |
sensing | orthonormal | mapping of | mixtures | matching | compression | ||||
transform | time/space | of samples | pursuit | ||||||
7 | Finite | Time and | Random | Filtered | Uniform | # Coeff. + 1 + | Annihilating | ECG/ | |
rate of | polynomial | time | 2·(# discont. | filter | OCT/ | ||||
innovation | coeff. | domain | epochs) | (ELP) | UWB | ||||
8 | Channel | Galois | Time | Random | Syndrome | Uniform | 2×# errors | Berlekamp | Digital |
coding | field | or | -Massey/Viterbi/ | communic- | |||||
codes | random | belief prop. | -tion | ||||||
9 | Real | Time | Random | Transform | Uniform | 2×# impulsive | Adaptive | Fault | |
field | domain | or | noise | thresholding | tolerant | ||||
codes | random | RDE/ELP | system | ||||||
10 | Spectral | Spectral | Frequency | Random | Time/ | Uniform | 2×# tones | MUSIC/ | Military/ |
estimation | estimation | autocor- | −1 | pisarenko/ | radars | ||||
-relation | prony/MDL | ||||||||
11 | Array | MSL/ | Space | Random | Space/ | Uniform | 2× | MDL+ | Radars/ |
processing | DOA | autocor- | # sources | MUSIC/ | sonar/ | ||||
estimation | -relation | ESPRIT | ultrasound | ||||||
12 | Sparse arr- | Space | Random/ | Space | Peaks of | 2×# desired | Optimiz- | Radars/sonar/ | |
-ay beam- | missing | sidelobes/ | array | -ation: LP/ | ultrasound/ | ||||
-forming | elements | [non]uniform | elements | SA/GA | MSL | ||||
13 | Sensor | Space | Random | Space | Uniform | 2× BW | Similar | Seismic/ | |
networks | of random | to row 5 | meteorology/ | ||||||
field | environmental | ||||||||
14 | SCA | BSS | Active | Random | Time | Uniform | 2×# active | ℓ l /ℓ2/ | Biomedical |
source/time | sources | SL0 | |||||||
15 | SDR | Dictionary | Uniform/ | Linear mix- | Random | 2× # sparse | ℓ l /ℓ2/ | Data compression | |
random | -ture of time | words | SL0 | ||||||
samples | |||||||||
16 | Channel | Multipath | Time | Random | Frequency | Uniform/ | 2×# Spa- | ℓ l / | Channel equaliz- |
estimation | channels | or time | nonuniform | -rse channel | MIMAT | -ation/OFDM | |||
components |