A Study in Total Variation Denoising and its Validity in a Recently Proposed Denoising Algorithm

driver.py

The driver script for the algorithm. Outputs graphs and percent successfully denoised for learned model on train and test sets.

createStep.py

1. createSteps- Creates step (i.e. piece-wise constant) signals, where each function has a number of jumps equal to a multiple of the original signal’s length. Gaussian noise is then added to each signal.
2. speedCreateSteps - Creates step function (without noise) for each sample

sgd.py

1. multiSGDthres - Runs the stochastic gradient descent to minimize the the kernel (W) and/or the radial basis function parameter (alpha).
2. SGDSample - Updates alpha and W values after computing gradient per sample.

batchSGD.py

1. batchSGD - runs the mini-batch stochastic gradient descent algorithm to minimize the the kernel (W) and/or the radial basis function parameter (alpha).
2. batchSGDsample - Updates alpha and W values after computing gradient per batch.

rbf.py

1. rbfF - Calculates the Gaussian Radial Basis Functions (before being multiplied by the minimized parameter, alpha).

rbfCenters.py

1. GRBFCenters- Calculates the equally spaced centers of the Gaussian RBF’s, given the ranges of the noisy signals under the linear transform W.

estimateSignal.py

Computes the model’s predicted signal.

gradients.py

1. dFdGamma - calculates gradient of objective function w.r.t. variables inside the norm.
2. alphaGradient - calculates gradient of objective function w.r.t. alpha.
3. WGradient - calculates gradient of objective function w.r.t. the kernel (W).

dGammadW.py

1. dGammadW - Returns derivative of gamma (see gradients appendix in writeup) w.r.t the kernel (W).
2. dGammadWEntry - returns an entry of the above, dGammadW.

Armijo.py

1. armijoAlpha - Estimates the optimal step size for the alpha gradient using the Armijo Rule.
2. armijoW - Estimates the optimal step size for the W gradient using the Armijo Rule.

gradientCheck.py

1. alphaGradCheck - Checks if the gradient wrt alpha is correct.
2. speedAlphaGradCheck - Applies the limit derivative definition for each entry in alpha.
3. WGradCheck - Checks if the gradient wrt W is correct.
4. speedWGradCheck - Applies the limit derivative definition for each entry in the kernel, W.

exponentGradCheck.py

1. exponentGradCheck - Checks the dGamma/dW derivative referred to in the latex (involved in computing the W gradient)
2. speedExponentGradCheck - Applies the limit derivative definition to each entry of this derivative.