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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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    En lugar de tiradas gratis, los casinos pueden optar por dar creditos gratis a los jugadores que tienen bonos sin deposito. Estos creditos pueden ser utilizados dentro de un periodo de tiempo enumerado para apostar en juegos en los casinos y ganar dinero real. Los bonos sin deposito y los creditos gratuitos se ofrecen tanto en las tragaperras gratuitas como en otros juegos de los casinos.


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    En la mayoria de los casos, puede hacer uso de los bonos sin deposito al crear una cuenta en cualquier sitio de juego en linea que ofrezca este tipo de oferta. En la version online del casino, la bonificacion puede aparecer en la pagina de promociones del casino o en una ventana emergente. Algunos casinos requieren que introduzca un codigo promocional para acceder al bono.

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    Los bonos sobre los depositos son accesibles para todos, sin embargo, cobrar los bonos es un asunto un poco mas controlado. La mayoria de los casinos en linea le permitiran retirar sus ganancias despues de haber podido apostar una cantidad especifica.

    Los requisitos de apuesta se muestran como multiplicadores. Representan la cantidad de veces que tienes que apostar en un bono para poder retirar el dinero. Por lo general, puede jugar a una serie de juegos seleccionados por el operador del casino. Una vez que haya alcanzado el requisito de apuesta, podra dar el siguiente paso para cobrar su bono.


    PLAZO

    Segun el casino online, el bono para juegos de tragaperras de deposito puede caducar en cuestion de dias o durar hasta 30 dias. Para asegurarte de que cumples los requisitos de apuestas, es posible que tengas que planificar tu rutina de juego a lo largo del bono.


    TAMANOS DE APUESTA

    Un metodo para lograr su objetivo de apostar mas rapido es realizar la mayor cantidad de apuestas posible en cada juego. Es un metodo sensato, a menos que el operador del casino decida controlar la cantidad de la apuesta y limitar la cantidad de apuestas en la respectiva tragamonedas con bono sin deposito.


    SE REQUIERE UN DEPOSITO

    Aunque suene contradictorio, algunos casinos online pueden incluso exigir a los jugadores que depositen dinero antes de poder retirar su bono. Suelen anadir este requisito adicional por razones de seguridad.


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    A veces, se le puede negar el acceso a un bono con oferta de deposito gratuito. Esto solo ocurre en muy raras circunstancias, ya sea por el hecho de haber intentado dos bonos a la vez o por tener una direccion IP compartida con un jugador que tambien reclamo el mismo bono, o por residir en una zona restringida.
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