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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Eine andere Möglichkeit ist, dass es Unregelmäßigkeiten bei den Ein- oder Auszahlungen gab. Hier kann das Casino die Zahlungen zur Überprüfung blockieren, um sicherzustellen, dass alles korrekt abläuft.
Es ist wichtig, nicht in Panik zu geraten, wenn das Geld geblockt wird. In den meisten Fällen handelt es sich um eine routinemäßige Prüfung, die das Casino durchführt, um die Sicherheit der Spieler zu gewährleisten.
Um eine schnelle Klärung des Problems zu erreichen, sollte der Spieler den Kundenservice kontaktieren und alle erforderlichen Informationen bereitstellen. Oftmals lässt sich das Problem schnell und unkompliziert lösen.
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Hello, cryptonauts!
Today, I want to share an insider perspective with you. We have all journeyed through the worlds of Bitcoin, Ethereum, cute dogs and frogs pictures, trading, AMM, NFTs… But it’s been a while since we encountered new acronyms that will “definitely conquer the world”.
Let me show you a fresh topic - the tokenization of real-world assets (RWA), in other words the conversion of real-world assets into crypto. For instance, think about tokenizing gold, precious metals, and real-estate assets. You might ask, what are the benefits? Tokenization gives opportunities to buy and transfer real world assets, as well as trade them on the crypto exchanges which we all are so used to. And then casually send those tokens through regular MetaMask.
I have taken a look at what people are searching for on Google regarding this topic. Yes, the number of queries is currently low, but that only signals the beginning of this trend… which means, it’s time to catch the wave.
Aut.finance
Currently there are approximately 80 platforms in the world that are experimenting in the field of RWA tokenization. Mostly, these are not yet crypto technologies but rather pilot projects aimed at understanding the legal aspects of RWA tokenization. Nevertheless, there are quite promising projects with highly experienced teams showing track records of their development which certainly looks trustworthy. I’ve explored the Autentic.Capital project, looked through their social media, and prepared a brief insider info for you.
They are conducting a token sale of their AUT token, which offers many perks such as voting rights, discounts for launching/purchasing RWA projects.
They have launched the testnet of the platform, and judging by the internal details, their plans are highly ambitious.
They’ve initiated a referral program with USDT payouts of up to 20%!
The AUT token is a utility token. They have issued 150 million tokens, and the second presale round is currently ongoing with a price of just 8 cents. The first listing is scheduled for May on p2b2b. You see what needs to be done, right?
Aut.finance
How to earn?
Referral program: Currently single-tier, but rumors suggest they will soon release a two-tier system.
Staking: They promise to unlock staking by the end of the month.
Bug hunting program: They recently distributed $12,000 to bug hunters and are preparing a second program. I even reached out to the winners, and they confirmed that the rewards were indeed transferred.
Aut.finance
Listing: Scheduled on May
Airdrops: They haven’t done any yet, which implies there will be for sure some in the future.
Community: they are giving some bonuses and benefits regularly (for example, recently they had Zealy campaign, looks like it was a test and they were preparing for something bigger).
In a nutshell, I believe that tokenization of real assets is the next trend after Bitcoin. Liquidity, globality, transparency and security indicate the high potential of this area. Investing in a new promising AUT utility token today is an opportunity to get big profits in the future.
Follow the link, sign up and start earning money with Autentic.
Aut.finance
Great weekend to everyone!