A Bayesian Nonparametric Approach to Image Super-resolution
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.
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.
実験の結果は
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
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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