@@ -52,7 +52,7 @@ Since measure spaces are in particular vector spaces, given a family of weights
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ω<sub >i</sub > >0, and a family of curves γ<sub >i</sub >, we can now consider μ,
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a weighted sum of these transported Dirac deltas
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<p align =" center " >
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- <img src =" https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_5.gif " width =" 140 " >
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+ <img src =" https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_5.gif " width =" 800 " >
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</p >
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which is also a dynamic Radon measure.
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@@ -63,7 +63,9 @@ considered dynamic Radon measures are simply Radon measures. We therefore
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consider at each of these time samples t<sub >i</sub >, a forward operator
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mapping from the space of Radon measures, into some data space H<sub >i</sub >
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- ![ eq_6] ( https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_6.gif )
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+ <p align =" center " >
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+ <img src =" https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_6.gif " width =" 300 " >
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+ </p >
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Where at each time sample t<sub >i</sub >, the respective data spaces
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H<sub >i</sub > are allowed to be different. Theoretically, these data spaces
@@ -75,13 +77,17 @@ f<sub>1</sub> ∈ H<sub>1</sub>, ... f<sub>T</sub> ∈ H<sub>T</sub>, and given
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any dynamical Radon measure ν, the data discrepancy term of our minimization
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problem is
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- ![ eq_7] ( https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_7.gif )
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+ <p align =" center " >
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+ <img src =" https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_7.gif " width =" 400 " >
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+ </p >
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And putting together the data discrepancy term with the proposed
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energy J<sub >α, β</sub > to minimize, we build up the target
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functional that is minimized by our algorithm.
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- ![ main_equation] ( https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_1.gif )
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+ <p align =" center " >
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+ <img src =" https://github.com/panchoop/DGCG_algorithm/blob/assets/tex/eq_1.gif " width =" 500 " >
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+ </p >
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The energy J<sub >α, β</sub > will promote sparse solutions μ, and the proposed
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algorithm will return one such measure.
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