Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Signal Processing Course: Denoising
Search
Gabriel Peyré
January 01, 2012
Research
0
1.3k
Signal Processing Course: Denoising
Gabriel Peyré
January 01, 2012
Tweet
Share
More Decks by Gabriel Peyré
See All by Gabriel Peyré
Optimal and Diffusion Transports in Machine Learning
gpeyre
0
1.2k
The many faces of AI and the role of mathematics
gpeyre
1
1.7k
Transformers are Universal in Context Learners
gpeyre
0
720
Ground Metric Learning with applications in genomics
gpeyre
0
630
Generative AI - practice and theory
gpeyre
2
1k
10-ot-generic-bio.pdf
gpeyre
2
360
Conservation Laws for Gradient Flows
gpeyre
2
1.3k
The Mathematics of Neural Networks
gpeyre
4
5.1k
On the Training of Infinitely Deep and Wide ResNets
gpeyre
1
690
Other Decks in Research
See All in Research
Global Evidence Summit (GES) 参加報告
daimoriwaki
0
240
Zipf 白色化:タイプとトークンの区別がもたらす良質な埋め込み空間と損失関数
eumesy
PRO
8
1.3k
Weekly AI Agents News! 10月号 論文のアーカイブ
masatoto
1
510
文書画像のデータ化における VLM活用 / Use of VLM in document image data conversion
sansan_randd
2
520
セミコン地域における総合交通戦略
trafficbrain
0
120
書き手はどこを訪れたか? - 言語モデルで訪問行動を読み取る -
hiroki13
0
140
ダイナミックプライシング とその実例
skmr2348
3
600
Weekly AI Agents News! 1月号 アーカイブ
masatoto
1
170
ラムダ計算の拡張に基づく 音楽プログラミング言語mimium とそのVMの実装
tomoyanonymous
0
400
ソフトウェア研究における脅威モデリング
laysakura
0
1.6k
Tiaccoon: コンテナネットワークにおいて複数トランスポート方式で統一的なアクセス制御
hiroyaonoe
0
420
複数データセットを用いた動作認識
yuyay
0
110
Featured
See All Featured
10 Git Anti Patterns You Should be Aware of
lemiorhan
PRO
656
59k
RailsConf & Balkan Ruby 2019: The Past, Present, and Future of Rails at GitHub
eileencodes
133
33k
VelocityConf: Rendering Performance Case Studies
addyosmani
328
24k
Design and Strategy: How to Deal with People Who Don’t "Get" Design
morganepeng
129
19k
Done Done
chrislema
182
16k
Unsuck your backbone
ammeep
669
57k
Writing Fast Ruby
sferik
628
61k
BBQ
matthewcrist
87
9.5k
個人開発の失敗を避けるイケてる考え方 / tips for indie hackers
panda_program
100
18k
KATA
mclloyd
29
14k
Creating an realtime collaboration tool: Agile Flush - .NET Oxford
marcduiker
27
1.9k
GitHub's CSS Performance
jonrohan
1030
460k
Transcript
Linear and Non Linear Denoising Gabriel Peyré www.numerical-tours.com
Overview • Noise in Signals and Images • Linear Denoising
by Blurring • Non-linear Wavelet Denoising • Translation Invariant Thresholding • Other Diagonal Thresholders • Non-diagonal Block Thresholding • Data-dependent Noise
Noise in Images
Denoising Problem
Denoising Problem
Additive Noise Model
Noise Distributions −0.3 −0.2 −0.1 0 0.1 0.2 0.3 −0.3
−0.2 −0.1 0 0.1 0.2 0.3
Noise Distributions −0.3 −0.2 −0.1 0 0.1 0.2 0.3 −0.3
−0.2 −0.1 0 0.1 0.2 0.3
Noise Distributions −0.3 −0.2 −0.1 0 0.1 0.2 0.3 −0.3
−0.2 −0.1 0 0.1 0.2 0.3
Data-dependent Noise
Overview • Noise in Signals and Images • Linear Denoising
by Blurring • Non-linear Wavelet Denoising • Translation Invariant Thresholding • Other Diagonal Thresholders • Non-diagonal Block Thresholding • Data-dependent Noise
Linear Denoising Estimator
Fourier and Denoising
Optimal Filter Choice
Oracle Estimation of Optimal Filter
Overview • Noise in Signals and Images • Linear Denoising
by Blurring • Non-linear Wavelet Denoising • Translation Invariant Thresholding • Other Diagonal Thresholders • Non-diagonal Block Thresholding • Data-dependent Noise
Diagonal Thresholding
Wavelet Diagonal Hard Thresholding
Sparse Signal Estimation
Optimal Threshold Selection
W unit variance white noise. Non-linear Approximation and Estimation
Hard vs. Soft Thresholding
Hard vs. Soft Thresholding
Optimal Threshold
Overview • Noise in Signals and Images • Linear Denoising
by Blurring • Non-linear Wavelet Denoising • Translation Invariant Thresholding • Other Diagonal Thresholders • Non-diagonal Block Thresholding • Data-dependent Noise
Translation Invariant Denoising
Translation Invariant Wavelets
Translation Invariant Haar (1D)
Translation Invariant Transform (2D)
Translation Invariant Thresholding
Optimal Invariant Threshold
Overview • Noise in Signals and Images • Linear Denoising
by Blurring • Non-linear Wavelet Denoising • Translation Invariant Thresholding • Other Diagonal Thresholders • Non-diagonal Block Thresholding • Data-dependent Noise
Between Hard and Soft Thresholding
Stein Quadratic-Soft Thresholder
Overview • Noise in Signals and Images • Linear Denoising
by Blurring • Non-linear Wavelet Denoising • Translation Invariant Thresholding • Other Diagonal Thresholders • Non-diagonal Block Thresholding • Data-dependent Noise
Block Thresholding
Optimal Block Choice
Comparison
Overview • Noise in Signals and Images • Linear Denoising
by Blurring • Non-linear Wavelet Denoising • Translation Invariant Thresholding • Other Diagonal Thresholders • Non-diagonal Block Thresholding • Data-dependent Noise
Poisson Noise
Poisson Noise Variance Stabilization 1 2 3 4 5 6
7 8 9 10 0.75 0.8 0.85 0.9 0.95 1 1.05
Multiplicative Noise
Multiplicative Noise Stabilization 0 0.5 1 1.5 2 2.5 −1.5
−1 −0.5 0 0.5 1 1.5
Conclusion