CalculateSampling(in)

Calculate the sampling operator of an n-dimension input. The output has the same size as the input.

ConjugateGradients(d,operators,parameters;<keyword arguments>)

Conjugate Gradients following Algorithm 2 from Scales, 1987. The user provides an array of linear operators. Verify that linear operator(s) pass the dot product. See also: DotTest

Arguments

• Niter=10 : Number of iterations
• mu=0
• tol=1.0e-15

DotTest(m_rand,d_rand,operators,parameters)

Dot product test for a vector of linear operators See also: ConjugateGradients

FISTA(x0,y,Hop,PARAM,mu,Nit)

FISTA: Solves the l2-l1 problem via Fast Iterative Shrinkage-Thresholdng Algorithm Given a linear operator H and it's adjoint H', the algorithm minimizes J = ||H x - y||2^2 + mu ||x||1, where H is the linear operator encapsulated in Hop

Arguments

• y:data
• Hop:linear operator
• PARAM:parameters to run Hop and it's adjoint
• mu:trade-off parameter
• x0:initial sol just to get size of x

Reference: Beck and Teboulle, 2009, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems∗ SIAM J. Imaging Science, Vol 2 (1), 183-202

IRLS(d,operators,parameters;<keyword arguments>)

Non-quadratic regularization with Iteratively Reweighted Least Squares (IRLS).

Arguments

• Niter_external=3
• 'Niter_internal=10'
• mu=0

SeisPOCS(in;<keyword arguments>)

Projection Onto Convex Sets interpolation of seismic records.

Arguments

• in: input data that can have up to 5 dimensions. Time is in the first dimension.
• p=1. : exponent for thresholding (1 is equivalent to soft thres. high number is equivalent to hard thresholding)
• alpha=1 : add-back ratio for imputation step. Use 1 for noise free data, and < 1 for denoising of original traces.
• dt=0.001 : sampling rate along the time axis (in seconds)
• fmax=99999. : maximum temporal frequency to process.
• padt=2 : padding in the time axis, first dimension.
• padx=1 : padding in the spatial axes. (Dim 2 to 5).
• Niter=100 : number of iterations
• alpha=1

power_method(x0,Hop,PARAM)

POWER_METHOD: Power iteration method to computes max eigenvalue of H'H where H and H' are given by Hop. This function is needed to evaluate the step parameter of FISTA.

Arguments

• x0:initial seed with dimensions such that H'Hx0 does not abort
• Hop:liner operator that encapsulates H and H' such that Hop(x,PARAM, 1) = H x Hop(y,PARAM,-1) = H'y
• PARAM:parameters to run Hop and it's adjoint