Piecewise linear quadratic (plq), deconvolution (via LFT)
plqic = plq_deconv_lft(plqf, plqg)
matrix. A PLQ function.
matrix. A PLQ function.
matrix. The PLQ function that is the deconvolution of plqf and plqg.
Computes the deconvolution of two convex PLQ functions. The deconvolution is defined by the formula
Under certain conditions, deconvolution can be rewritten to use the Legendre-Fenchel conjugate (denoted *),
This deconvolution is also a PLQ function. This algorithm runs in O(n + m) time, where n and m are the size of f and g, respectively.
plqf = [-2.5,0,-1,-1.25; -2,1,4,5; 0,0,0,1; 0.5,1,0,1; %inf,0,1,0.75]; plqg = [%inf,1,2,1]; plqdc = plq_deconv_lft(plqf, plqg), plq_plotMultiple(-4, 3, plqf, plqg, plqdc); xtitle("PLQ Convex Deconvolution"); legend(["f", "g", "f dc g"]); | ![]() | ![]() |
Bryan Gardiner
, University of British Columbia, BC, Canada