Part2: Numerical problemsApproximation s.t. |Pα-yl≤s2minαllaGreedymethodsRelaxationmethodsBuild the solution onenonSmooth theLoand usezero element at a timecontinuous optimizationtechniques
Part2: Numerical problems Approximation 2 2 2 0 0 min s.t. y D Greedy methods Build the solution one non- zero element at a time Relaxation methods Smooth the L0 and use continuous optimization techniques
Part2:Numerical problemsGreedy methodsMatching Pursuit The MP is one of the greedy algorithms that finds one atom at atime[Mallat&Zhang(93)]. Step 1:find the oneatomthat bestmatchesthe signal.Next steps:given the previouslyfoundatoms,findthenextone tobest fitthe residual.The algorithm stopswhen the error Da-yl,is belowthedestinationthreshold
Part2: Numerical problems Greedy methods q The MP is one of the greedy algorithms that finds one atom at a time [Mallat & Zhang (’93)]. q Step 1: find the one atom that best matches the signal. qNext steps: given the previously found atoms, find the next one to best fit the residual. q The algorithm stops when the error is below the destination threshold. 2 D y Matching Pursuit