수축 필드(이미지 복원)

수축 필드는 낮은 계산 오버헤드를 사용하여 고품질의 이미지 복원(디노이즈 및 디블러링)을 수행하는 것을 목표로 하는 랜덤 필드 기반 기계 학습 기술입니다.

방법

샘플 $이미지$ 세트 S $(\displaystyle$ S $S$ 에 대한 교육 후 손상된 $y$ 에서 복원된 $이미지$ x(\ $displaystyle$ x $)$ 가 $x$ $y$ 예측됩니다 $.$

수축 함수 f ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ ( v ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ ) ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ j ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ M ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ i , ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ exp ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ ( - ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ 2 ( ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ - ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ j ) ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ ) ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ { $displaystyle {f$ } _ { \ $pi } _$ { $i$ } \ left $( v$ \ $right$ ) = } _ { $jsum } _$ { $j$ } { { \ pi $}$ { \ pi } { \ pi } \ $right$ } \ exp } \ $exp$ } \ exp $left,$ $}^{2$ }\right $)$ 는 ${f}_{{\pi }_{i}}\left(v\right)={\sum }_{j=1}^{M}{\pi }_{i,j}\exp \left(-{\frac {\gamma }{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)$ 방사형 기저 함수 커널의 선형 조합으로 직접 모델링되며, 여기서 $δ {\displaystyle$ \gamma $}$ 는 $\gamma$ 공유 정밀도 $,$ μ ${\displaystyle$ \mu $}$ 는 (등가) 커널의 위치, M은 가우스 커널의 수이다.

수축함수를 직접 모델링하기 때문에 최적화 절차는 ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ - ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ [ ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ( ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ K ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ y + ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ i ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ F ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ( F ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ x ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ ) ] ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ K ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ 의 예측으로 나타나는 반복당 단일 2차 최소화로 감소한다. ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ $Theta }\leftmathcal {x}\right)=lbrack {F}{-1}\left(\frac {\mathcal {F}}\left(\lambda {K}^{T}y+{\sum}$ $T}$ { $f} _$ { \ $pi } _$ { $i$ } $_$ { $i$ } $x$ \ right $} }$ } { \ $lambda$ { \ $check$ { K } } { \ $text$ { * } } \ $circ$ { \ $check$ { $K$ } + { \ $sum$ } ${g}_{\mathrm {\Theta } }\left({\text{x}}\right)={\mathcal {F}}^{-1}\left\lbrack {\frac {{\mathcal {F}}\left(\lambda {K}^{T}y+{\sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{\pi }_{i}}\left({F}_{i}x\right)\right)}{\lambda {\check {K}}^{\text{*}}\circ {\check {K}}+{\sum }_{i=1}^{N}{\check {F}}_{i}^{\text{*}}\circ {\check {F}}_{i}}}\right\rbrack ={\mathrm {\Omega } }^{-1}\eta$ _ { n $= 1$ } { \ check { $F }$ { { { { \ $circ$ } { { \ $circ$ } { { \ cirlam } { \ cirlam } } { i } } { i } { } { } {2D 컨볼루션 ${\text{f}}\otimes {\text{x}}$ x { display $style$ \ $text$ { $f }$ ${\breve {F}}$ 、 F ${\$ ${\text{f}}\otimes {\text{x}}$ \ $display$ style \ $text$ { $f$ } ${\text{f}}$ 、 F ${\breve {F}}^{\text{*}}$ \ $display$ style $\$ $breve$ ${\breve {F}}$ { $F }$ f f ${\text{f}}$ f f f ${\breve {F}}^{\text{*}}$ f f ${\breve {F}}^{\text{*}}$ the the the the the the the the the the the the the the the the the the the the the the the the the the the the the the the the filter filter filter filter filter filter filter filter filter filter filter the the filter filter filter filter filter filter filter filter filterF ${\$ { $display$ { $F$ } ${\breve {F}}$ f $ate$ 。

${\hat {x}}_{t}$ ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ ${\hat {x}}_{t}$ ^ ${\hat {x}}_{t}$ { $displaystyle$ { $x } _$ { $t$ } } $=$ ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ t ( ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ ^ ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ - ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ ) ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ { $displaystyle$ { $x } _$ { $g$ } $_$ { \ $mathrm {$ \ } $Theta }_{t}\lefthat {x}_{t-1}\right}$ 은(는) 각 $반복$ t {\ $displaystyle$ t $}$ 에 ${\hat {x}}_{t}={g}_{{\mathrm {\Theta } }_{t}}\left({\hat {x}}_{t-1}\right)$ $t$ 대해 첫 번째 ${\hat {x}}_{0}=y$ $=$ { $displaystyle {hat {x}_{0$ }= $y$ 가우스 조건부 랜덤 필드(또는 수축 필드(CSF)의 캐스케이드)를 형성합니다. ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ 최소화는 모델 매개 변수 ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ { ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ t ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ , ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ t ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ , ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ ${\mathrm {\Theta } }_{t}={\left\lbrace {\lambda }_{t},{\pi }_{\mathit {ti}},{f}_{\mathit {ti}}\right\rbrace }_{i=1}^{N}$ N \ $display$ style \ $mathrm \$ $Theta }_{t}$ = $왼쪽\lbrace{t$ }, ${\pi}_{\mathit {ti},$ { $f}_{\mathit$ {ti $}}, 오른쪽\rbrace}_{i=1}^{N$

학습 목표 함수는 J $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ t $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ ) $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ s $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ l ( x $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ ^ $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ ( $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ ) ; $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ t ( $J\left({\mathrm {\Theta } }_{t}\right)={\sum }_{s=1}^{S}l\left({\hat {x}}_{t}^{\left(s\right)};{x}_{gt}^{\left(s\right)}\right)$ $)\$ J $\left({\mathrm$ {\m $})$ 로 정의됩니다. $Theta }_{t}_{t}\right)=sum$ } $_{s=1}^{S}l\$ left $({\hat {x}^{\left(s\$ right $)},$ {x $_{gt}^{\left(s\right)},$ $l$ 서 l ${displaystyle$ l $}$ 은 $l$ ${\left\lbrace {x}_{gt}^{\left(s\right)},{y}^{\left(s\right)},{k}^{\left(s\right)}\right\rbrace }_{s=1}^{S}$ { ${\left\lbrace {x}_{gt}^{\left(s\right)},{y}^{\left(s\right)},{k}^{\left(s\right)}\right\rbrace }_{s=1}^{S}$ 을 사용하여 최소화된 미분 가능한 손실 함수입니다. $_{gt}^{\left(s\right),$ { $y}^{\left(s\$ right $),$ { $k}^{\left(s\right)}\rbrace}$ ${\hat {x}}_{t}^{\left(s\right)}$ ${$ s $=$ 1}^{S} ${\hat {x}}_{t}^{\left(s\right)}$ x $}{$ right)}}^{\left(s\right ${\hat {x}}_{t}^{\left(s\right)}$ s\ $right$ )}}}}}}}}.

성능

저자에 의한 예비 테스트에서는 RTF가₅^[1] ${\text{CSF}}_{7\times 7}^{\left\lbrace \mathrm {3,4,5} \right\rbrace }$ × ${\text{CSF}}_{7\times 7}^{\left\lbrace \mathrm {3,4,5} \right\rbrace }$ { ${\text{CSF}}_{7\times 7}^{\left\lbrace \mathrm {3,4,5} \right\rbrace }$ , ${\text{CSF}}_{7\times 7}^{\left\lbrace \mathrm {3,4,5} \right\rbrace }$ , 5 ${\text{CSF}}_{7\times 7}^{\left\lbrace \mathrm {3,4,5} \right\rbrace }$ 보다 약간 뛰어난 노이즈 제거 성능을 얻을 수 있음을 알 수 있습니다.\ displaystyle \ $text$ { $C$ $SF}_{7\times$ 7 $}^{\left\lbrace\mathrm {3,4,5}\right\rbrace$ 뒤에 ${\text{CSF}}_{5\times 5}^{5}$ × $(\$ 가 표시됩니다. $SF}_{5\times$ 5 $}^{5$ ${\text{CSF}}_{7\times 7}^{2}$ × ${\text{CSF}}_{7\times 7}^{2}$ $(\$ $SF}_{7\times$ 7 $}^{2$ ${\text{CSF}}_{5\times 5}^{\left\lbrace \mathrm {3,4} \right\rbrace }$ × ${\text{CSF}}_{5\times 5}^{\left\lbrace \mathrm {3,4} \right\rbrace }$ { ${\text{CSF}}_{5\times 5}^{\left\lbrace \mathrm {3,4} \right\rbrace }$ , $}(\$ style ${\text{C$ } $표시$ ) $SF}_{5\times$ 5 $}^{\left\lbrace\mathrm {3,4}\right\rbrace$ 및 BM3D.

BM3D 노이즈 제거 속도는 ${\text{CSF}}_{5\times 5}^{4}$ 5 ${\text{CSF}}_{5\times 5}^{4}$ × ${\text{CSF}}_{5\times 5}^{4}$ 4 (\ $displaystyle\text{C$ })의 속도 사이에 있습니다. $SF}_{5\times$ 5 $}^{4}$ 및 ${\text{CSF}}_{5\times 5}^{4}$ ${\text{CSF}}_{7\times 7}^{4}$ × ${\text{CSF}}_{7\times 7}^{4}$ $(\$ $SF}_{7\times$ 7 $}^{4$ RTF는 몇 배 느립니다.

이점

결과는 BM3D에 의해 얻어진 결과와 유사하다(2007년 시작 이후 최신 노이즈 제거 참조).
다른 고성능 방법에 비해 최소한의 실행 시간(임베디드 디바이스 내에서 적용 가능)
병렬화 가능 (예: GPU 구현 가능)
예측 가능성: $O(D\log D)$ ( $O(D\log D)$ log $O(D\log D)$ D $O(D\log D)$ ) { $displaystyle$ $O(D\log D)$ O ( $D$ \ $log$ D )runtime $O(D\log D)$ ( $D$ 는 픽셀 $D$ 수 $)$
CPU 사용 시에도 신속한 트레이닝

실장

레퍼런스 실장은 MATLAB에 기술되어 BSD 2-Clause 라이센스: 수축 필드로 릴리즈되었습니다.

「」를 참조해 주세요.

레퍼런스

^ Jancsary, Jeremy; Nowozin, Sebastian; Sharp, Toby; Rother, Carsten (10 April 2012). Regression Tree Fields – An Efficient, Non-parametric Approach to Image Labeling Problems. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Providence, RI, USA: IEEE Computer Society. doi:10.1109/CVPR.2012.6247950.

Schmidt, Uwe; Roth, Stefan (2014). Shrinkage Fields for Effective Image Restoration (PDF). Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on. Columbus, OH, USA: IEEE. doi:10.1109/CVPR.2014.349. ISBN 978-1-4799-5118-5.

[1] Jancsary, Jeremy; Nowozin, Sebastian; Sharp, Toby; Rother, Carsten (10 April 2012). Regression Tree Fields – An Efficient, Non-parametric Approach to Image Labeling Problems. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Providence, RI, USA: IEEE Computer Society. doi:10.1109/CVPR.2012.6247950.

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