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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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