tv_denoise

Builtin index · Noise

result = tv_denoise(y, [lambda=1.0])

Input: y, lambda · Output: result

What it is

Total-variation denoising: y is a length-N number vector; lambda is an optional positional number, the smoothing penalty, default 1.0 — larger values remove more variation. Assumes few CHANGES rather than few non-zeros, so a step survives where an l1 method would flatten it. Condat's direct algorithm, one pass.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = tv_denoise(y, [lambda=1.0])`	`y` number or vectorTotal-variation denoising: `y` is a length-N number vector. `lambda` number, optional (default `1.0`)`lambda` is an optional positional number, the smoothing penalty, default `1.0` — larger values remove more variation.	`result` vector	Returns a length-N vector.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

clean = zeros(200)
for i in 60 to 129
    clean[i] = 1.0
end for
noisy = clean + 0.15 * randn(200, seed = 3)

tv = tv_denoise(noisy, 0.3)
print("total variation {sum(abs(diff(noisy))):.1f} -> {sum(abs(diff(tv))):.1f}")

output

total variation 36.5 -> 2.5

from compressed-sensing

How it works

tv_denoise(y, lambda) — total variation. A different sparsity assumption: few CHANGES rather than few non-zeros, so a step survives where an l1 method would flatten it.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.