Application Areas

Use Different Wavelet Thresholding Methods 

In[1]:=

X data = Table[ 10 Cos[x^2] + RandomReal[NormalDistribution[]], {x, 0, 5, 0.001}];

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X dwd = StationaryWaveletTransform[data, SymletWavelet[6], 10];

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X wthresh[th_] := InverseWaveletTransform[WaveletThreshold[dwd, th]]

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X ShowThresholdPlot[name_, info_] := Framed[Column[{Style[name, 13, Bold, Opacity[0.9], FontFamily -> "Helvetica"], info}, Alignment -> Center], RoundingRadius -> 50, FrameStyle -> None, Background -> Lighter[Orange, 0.85]]

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X thPlots = Table[ListLinePlot[wthresh[m], PlotStyle -> Darker@Orange, Axes -> None, ImageSize -> 270, AspectRatio -> 0.3], {m, {"Universal", "VisuShrink", "SURE", "SUREShrink", "GCV", "FDR", "SUREHybrid", "SURELevel", {"SmoothGarrote", "SURE", 2}, {"LargestCoefficients", 15}}}];

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X methods = {"Hard \[CirclePlus] Universal Threshold", "Soft \[CirclePlus] Universal Threshold", "Hard \[CirclePlus] SURE Threshold", "Soft \[CirclePlus] SURE Threshold", "Soft \[CirclePlus] GCV Threshold", "Soft \[CirclePlus] FDR Threshold", "Hard \[CirclePlus] Universal \[LightBulb] SURE Threshold", "Hard \[CirclePlus] Adaptive SURE Threshold", "SmoothGarrote \[CirclePlus] SURE", "LargestCoefficients \[DoubleRightArrow] 15"};

In[7]:=

X Grid[Join[{{ShowThresholdPlot["Noisy Data", ListLinePlot[{data}, Axes -> False, PlotStyle -> {Orange, Red}, ImageSize -> 250, AspectRatio -> 0.3]], SpanFromLeft}}, Partition[MapThread[ShowThresholdPlot, {methods, thPlots}], 2]], Spacings -> {0.5, 0.5}]

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