Cost function abstract type.

See also: LSDBCost, JBBCost, BBCost

LSDBCost <: CostFunction

Cost function abstract type specifically for LSDB.

See also: CostFunction, JBBCost, BBCost

JBBCost <: CostFunction

Cost function abstract type specifically for JBB.

See also: CostFunction, LSDBCost, BBCost

BBCost <: CostFunction

Cost function abstract type specifically for BB.

See also: CostFunction, LSDBCost, JBBCost

LoglpCost <: JBBCost

$\log \ell^p$ information cost used for JBB. Typically, we set p=2 as in Wickerhauser's original algorithm.

See also: CostFunction, JBBCost, NormCost

NormCost <: JBBCost

$p$-norm information cost used for JBB.

See also: CostFunction, JBBCost, LoglpCost

DifferentialEntropyCost <: LSDBCost

Differential entropy cost used for LSDB.

See also: CostFunction, LSDBCost

ShannonEntropyCost <: LSDBCost

Shannon entropy cost used for BB.

See also: CostFunction, BBCost, LogEnergyEntropyCost

LogEnergyEntropyCost <: LSDBCost

Log energy entropy cost used for BB.

See also: CostFunction, BBCost, ShannonEntropyCost

tree_costs(X, method)

Returns the cost of each node in a binary tree in order to find the best basis.

Arguments

• X::AbstractArray{T} where T<:AbstractFloat: A set of decomposed signals, of sizes (n,L,k) for 1D signals or (n,m,L,k) for 2D signals, where:
  • n: Length of signal (1D) or vertical length of signal (2D).
  • m: Horizontal length of signal (2D).
  • L: Number of decomposition levels plus 1 (for standard wavelet decomposition) or number of nodes in the tree (for redundant transforms such as ACWT and SWT).
  • k: Number of signals.
• method::BestBasisType: Type of best basis, ie. BB(), JBB() or LSDB().

Returns

• Vector{T}: A vector containing the costs at each node.

Examples

using Wavelets, WaveletsExt

X = generatesignals(:heavisine, 6) |> x -> duplicatesignals(x, 5, 2, true)
wt = wavelet(WT.db4)
Xw = wpdall(X, wt)

tree_costs(Xw, JBB())
tree_costs(Xw, LSDB())

See also: bestbasistree, bestbasis_treeselection

coefcost(x, et[, nrm])

Arguments

• x::AbstractArray{T} where T<:AbstractFloat: An array of values to compute the cost.
• et::CostFunction: Type of cost function.
• nrm::T where T<:AbstractFloat: The norm of the x. Only applicable when et is a BBCost.

Returns

• ::T: Cost of x.

See also: bestbasistree

bestbasis_treeselection(costs, n[, type])
bestbasis_treeselection(costs, n, m[, type])

Computes the best basis tree based on the given cost vector.

Arguments

• costs::AbstractVector{T}: Vector containing costs for each node.
• n::Integer: Length of signals (for 1D cases) or vertical length of signals (for 2D cases).
• m::Integer: Horizontal length of signals (for 2D cases).
• type::Symbol: (Default: :min) Criterion used to select the best tree. Supported types are :min and :max. Eg. Setting type = :min results in a basis tree with the lowest cost to be selected.

Returns

• ::BitVector: Best basis tree selected based on cost.

See also: bestbasistree, tree_costs

delete_subtree!(bt, i, tree_type)

Deletes a subtree of the entire tree due to children's inferior costs.

Arguments

• bt::BitVector: Tree.
• i::Integer: Root of the subtree to be deleted.
• tree_type::Symbol: Type of tree (:binary or :quad).

Returns

bt::BitVector: Tree with deleted subtree.

See also: bestbasistree, bestbasis_treeselection

BestBasisType

Abstract type for best basis. Current available types are:

• LSDB
• JBB
• BB

LSDB([; cost, redundant])

Least Statistically Dependent Basis (LSDB).

Keyword Arguments

• cost::LSDBCost: (Default: DifferentialEntropyCost()) Cost function for LSDB.
• redundant::Bool: (Default: false) Whether the performed wavelet transform is redundant. Set redundant=true when running LSDB with redundant wavelet transforms such as SWT or ACWT.

See also: BestBasisType, JBB, BB

JBB([; cost, redundant])

Joint Best Basis (JBB).

Keyword Arguments

• cost::JBBCost: (Default: LoglpCost(2)) Cost function for JBB.
• redundant::Bool: (Default: false) Whether the performed wavelet transform is redundant. Set redundant=true when running LSDB with redundant wavelet transforms such as SWT or ACWT.

See also: BestBasisType, LSDB, BB

BB([; cost, redundant])

Standard Best Basis (BB).

Keyword Arguments

• cost::BBCost: (Default: ShannonEntropyCost()) Cost function for BB.
• redundant::Bool: (Default: false) Whether the performed wavelet transform is redundant. Set redundant=true when running LSDB with redundant wavelet transforms such as SWT or ACWT.

See also: BestBasisType, LSDB, JBB

bestbasistree(X[, method])

Extension to the best basis tree function from Wavelets.jl. Given a set of decomposed signals, returns different types of best basis trees based on the methods specified. Available methods are the joint best basis (JBB), least statistically dependent basis (LSDB), and individual regular best basis (BB).

Arguments

• X::AbstractArray{T} where T<:AbstractFloat: A set of decomposed signals, of sizes (n,L,k) for 1D signals or (n,m,L,k) for 2D signals, where:
  • n: Length of signal (1D) or vertical length of signal (2D).
  • m: Horizontal length of signal (2D).
  • L: Number of decomposition levels plus 1 (for standard wavelet decomposition) or number of nodes in the tree (for redundant transforms such as ACWT and SWT).
  • k: Number of signals.
• method::BestBasisType: Type of best basis, ie. BB(), JBB() or LSDB().

Returns

• ::BitVector: Best basis tree.

Examples

using Wavelets, WaveletsExt

X = generatesignals(:heavisine, 6) |> x -> duplicatesignals(x, 5, 2, true)
wt = wavelet(WT.db4)
Xw = wpdall(X, wt)

bestbasistree(Xw, JBB())
bestbasistree(Xw, LSDB())

See also: getbasiscoef, getbasiscoefall, tree_costs, delete_subtree!

bestbasistreeall(X, method)

Compute the standard best basis tree of a set of signals.

Arguments

• X::AbstractArray{T} where T<:AbstractFloat: A set of decomposed signals, of sizes (n,L,k) for 1D signals or (n,m,L,k) for 2D signals, where:
  • n: Length of signal (1D) or vertical length of signal (2D).
  • m: Horizontal length of signal (2D).
  • L: Number of decomposition levels plus 1 (for standard wavelet decomposition) or number of nodes in the tree (for redundant transforms such as ACWT and SWT).
  • k: Number of signals.
• method::BB: Standard best basis method, eg. BB().

Returns

• ::BitMatrix: (nₜ,k) matrix where each column corresponds to a tree.

Examples

using Wavelets, WaveletsExt

X = generatesignals(:heavisine, 6) |> x -> duplicatesignals(x, 5, 2, true)
wt = wavelet(WT.db4)

Xw = wpdall(X, wt)
bestbasistreeall(Xw, BB())

Xw = swpdall(X, wt)
bestbasistree(Xw, BB(redundant=true))

See also: bestbasistree