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A Bayesian Nonparametric Approach to Image Super-resolution

2012-12-28 (fri)|カテゴリー:

arxivからの論文

http://arxiv.org/pdf/1209.5019.pdf

A Bayesian Nonparametric Approach to Image
Super-resolution

Gungor Polatkan, Mingyuan Zhou, Lawrence Carin, David Blei, and Ingrid
Daubechies

 

ノンパラメトリックベイズでは有名な Bleiのグループとの共同研究といった感じでしょうか?

超解像技術(super-resolution)は低解像度画像から高解像度画像を作る技術.

全画素の組み合わせに対して,実際に観測される組み合わせは非常にスパースであることから,

パッチを組み合わせることで,高解像度画像を低解像度画像から復元することができます.

そのためには,辞書(Dictionary)を持つ必要があるのですが,

それをどのように作るかが問題となります.

 

筆者らは過去に

NIPSで

Non-Parametric Bayesian Dictionary Learning for
Sparse Image Representations

http://books.nips.cc/papers/files/nips22/NIPS2009_0190.pdf

を発表しており,ノンパラメトリックベイズを用いて,Dictionary Learning にノンパラメトリックベイズを

応用するということをやっています.

 

それをsuper resolutionに応用するというのが主な筋立てです.

 

基本的にスパースな表現を得る場合には,L1ノルムを用いて刈り込む事が多くて,

超解像でもこれがよく用いられます.

Image Super-Resolution via Sparse Representation
Jianchao Yang et al.

などが良くリファレンスされるらしいです.

 

これに対して,ノンパラメトリックベイズ業界(?)ではスパースな表現にする,

つまり用いない次元を作るような場合には,ベータ・ベルヌーイ分布を導入し,スイッチを作るのが定石です.

 

例えば,

Sharing Features among Dynamical Systems
with Beta Processes

Emily B. Fox et al.

http://videolectures.net/nips09_fox_sfa/

では,HDP-HMM の各隠れ状態に対してストリーム毎にベータ・ベルヌーイのスイッチを設けて,使わない隠れ状態をオフにします.

ちなみに, @k_ishiguro  さんの,

Subset Infinite Relational Models
Katsuhiko Ishiguro et al.

でも,ベータ・ベルヌーイのスイッチをつくって,汎用的な出力分布を用いる(IRMの外に吐き出してしまう)か,

通常のIRMの側に入れるかをえらぶようにしていたりします.

 

というわけで,

「L1刈り込みの代わりを,ノンパラベイズでやるなら,やっぱベータ・ベルヌーイっしょ!」

という,結構ストレートフォワードな適用があるわけです.

 

image

グラフィカルモデルはこんな感じ.

l と h はlow resolution と high resolutionを表している.

xl と xh が観測.

Di と Dh が辞書.

で si が係数なんですが,

zi がいわゆるベータ・ベルヌーイのスイッチで,0,1 をとる.

これによって,使う基底,使わない基底が,0,1でオン・オフされることで,

スパース表現を得るわけである.

なんとも,ストレートフォワードな論理である.

 

ちなみに,これだけでは綺麗にならないみたいで,最後に平滑化処理っぽいことをやる.

image

 

実験の結果は

image

こんなかんじなのだが,正直,よくわからない・・・.

 

どうも既存手法に勝てているか微妙なのだが,

なるほどな,とおもったのは, Fig.8 で

image

こんな図がある.

これは,辞書の要素数(もとの次元数)を大きくしていった際,BPの場合は打ち切り最大数を大きくしていった時にどうなるか

を示しているのだと思うが,

その時に,ScSR(L1ノルムでのスパースコーディング)はピークを持ってしまう.

これに対しノンパラメトリックベイズのアプローチでは,十分な 要素数があれば,良い値を推定できるので,その良さが維持される.

 

これは,BPのアプローチがもともと無限の状態数を前提として組まれているのに対して,

L1の正則化項は 無次元量でもなく,要素数に影響を受けてしまうからだろう.

 

なるほどねー.

とは思うが,計算量とか考えても,実用的にはL1で行ったほうが,楽で実用的なのかなぁ,と思った次第でございます.

 

本内容は,

Xian-Hua Han (韓 先花) Ph.D にご紹介いただいて (Thank you very much

http://www.iipl.is.ritsumei.ac.jp/XHHan/index.html

それを,僕が勝手に理解したものを書いたものであり,

この記事の内容に誤りがあった場合は,僕を責めてくださいませ.

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    Astronomers discovered the black hole while combing through observations taken by European Space Agency’s Gaia space telescope for an upcoming data release to the scientific community. The researchers weren’t expecting to find anything, but a peculiar motion — caused by Gaia BH3’s gravitational influence on a nearby companion — caught their eye.

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    The wobbling movement of an old giant star in the Aquila constellation revealed that it was in an orbital dance with a dormant black hole, and it’s the third such dormant black hole spotted by Gaia.

    The researchers used the European Southern Observatory’s Very Large Telescope in Chile’s Atacama Desert and other ground-based observatories to confirm the mass of Gaia BH3, and their study has also offered new clues to how such huge black holes came to be. The findings appeared Tuesday in the journal Astronomy & Astrophysics.

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