estimate_sparsity.lastw

LastWave

setproc sparsity {{&book book} {&float tau}} {{"<book> <tau>" "Computes an upper estimate of the l^tau norm of a signal from its matching pursuit decomposition."}} {
    coeff2Sig=[new &signal]
    residuSig=[new &signal]
    sparsitySig=[new &signal]

    coeff2Sig   = book.wcoeff2
    residuSig   = book.resEnergy[1:@>]
    sparsitySig = prim(coeff2Sig^(tau/2))+(book.signalSize)^(1-tau/2)*residuSig^(tau/2) 

    set "xmin xmax" [stats minmax sparsitySig]
    set min [= [setsig y sparsitySig $xmin]^(1/$tau)]
#    disp  sparsitySig
    return $min
}

setproc optsparsity {{&book book} {&signal norm}} {{"<book> <signal>" "Puts in output signal the upper estimates of the l^tau norm of a signal from its matching pursuit decomposition."}} {
    set taumin 0.3
    set taumax 2
    N=book.signalSize

    s= Zero(20) norm
    for {set i 0} {$i<20} {incr i} {
       set tau [= $taumin+($i)*($taumax-$taumin)/19]
       setsig y norm $i [= [sparsity book $tau]/(sqrt(book.resEnergy[0]))]
    }
    setsig dx norm ($taumax-$taumin)/19
    setsig x0 norm $taumin
}