API Reference

dst(x; dims=1)

Compute the Type-I Discrete Sine Transform (DST) of x along dims.

Arguments

• x: an AbstractArray (vector or matrix).
• dims: dimension to transform (default 1).

Returns

• transformed array of the same shape as x.

Example

y = dst([1.0,2.0,3.0])

dst!(x; dims=1)

In-place DST that overwrites x with its transform when possible. Falls back to a safe out-of-place compute and copy if the in-place routine is not available on the current platform.

plan_dst(x; dims=1, flags=FFTW.MEASURE)

Create an FFTW r2r plan for the DST (RODFT00) on x. The returned plan can be executed with plan * x.

idst(y; dims=1)

Inverse Type-I Discrete Sine Transform (IDST) of y along dims.

Arguments

• y: an AbstractArray of DST coefficients.
• dims: dimension to transform (default 1).

Returns

• reconstructed array in the original domain.

plan_idst(y; dims=1, flags=FFTW.MEASURE)

Create an FFTW r2r plan suitable for the IDST (uses the DST plan internally).

idst!(y; dims=1)

In-place inverse DST: overwrite y with the reconstructed data when possible. Falls back to computing out-of-place and copying the result. Uses an FFTW r2r plan for the in-place computation when available. The result is scaled by 1/(N+1) to account for the normalization of the DST. Note that the input y should contain the DST coefficients, and after this function, it will contain the reconstructed data in the original domain.

llst2d(data)

Compute the 2D LLST (localized lattice-sine transform) decomposition of data.

Returns a level-list representation suitable for further processing.

llst2d!(data)

In-place variant of llst2d that writes the decomposition back into data when possible.

illst2d(data)

Inverse 2D LLST: reconstruct the data from a level-list decomposition.

illst2d!(data)

In-place inverse LLST that attempts to reconstruct into data without allocation.

illst(coef, ll)

Reconstruct an image from LLST coefficients coef using level-list ll. This is a thin wrapper around llst(..., inverse=true).

llst2(data, ll; inverse=false)

Perform the LLST block-based transform using level-list ll on data.

• data: input 2D array.
• ll: level-list describing the quadtree partition.
• inverse: when true performs the inverse transform.

Returns the transformed array.

llst2!(data, ll; inverse=false)

In-place variant of llst2 that overwrites data with the transformed result. Uses broadcasting assignment as a safe fallback.

llstapprox2(data, levlist, krange; bdrykeep=false)

Evaluate LLST approximation quality for data using levlist over a range of retained coefficient counts krange. Returns PSNR values for each k.

phlct_backward(input, N)

Reconstruct an image from block-based PHLCT DCT coefficients.

Arguments

• input: m×n array of DCT coefficients (block-based, m and n multiples of N).
• N: block size (integer).

Returns

• reconstructed m×n image (real array).

phlct_backward!(input, N)

In-place variant: overwrite input with the reconstructed image. Computes phlct_backward and assigns the result into input.

phlct_forward(input, N)

Compute block-based PHLCT forward transform (returns DCT coefficients).

Arguments

• input: m×n image array (m and n must be multiples of N).
• N: block size.

Returns

• m×n array of DCT coefficients for the PHLCT representation.

phlct_forward!(input, N)

In-place variant: overwrite input with its PHLCT coefficients.

phlct_restore(in, qt)

Restore truncated DCT coefficients in using PHLCT and quantization table qt.

Returns the restored coefficient matrix.

phlct2d(F, N)

Compute the 2D PHLCT coefficients for block-DCT coefficient matrix F.

• F: m×n block-based DCT coefficient matrix (m,n multiples of N).
• N: block size.

Returns the PHLCT coefficients V = F - U.

qtllst2dl1(signal, lmax)

Find a quadtree level-list up to depth lmax that minimizes a DST-based cost.

Returns (liste, cost) where liste encodes the partition and cost is the objective value.

solvelaplace(image)

Solve the Laplace (Poisson) equation on the interior of image using DST/IDST.

Arguments

• image: m×n array with boundary values; the routine solves for the interior (returns array sized m×n with boundary preserved).

Returns

• array with the computed solution where interior values have been solved and boundaries are unchanged.