rLifting: high-performance wavelet lifting for R

rLifting is a high-performance R package for wavelet-based signal denoising. It implements the Lifting Scheme (Sweldens, 1996) with a zero-allocation C++ core via Rcpp, supporting both offline (batch) and causal (real-time) processing modes through a unified API.

Why rLifting?

Most wavelet packages in R are designed for offline use: they require the entire signal before processing. To perform causal filtering (where the output at time t depends only on data up to t), the user must write a sliding-window loop that re-computes the transform at every point — an O(N·W) operation.

rLifting solves this with a specialized ring-buffer architecture that provides efficient O(T) processing for the complete signal (where T is the number of observations), while maintaining full compatibility with standard offline denoising.

Key features

• Offline and causal denoising in a single package — same wavelet scheme, same API, different processing guarantees.
• Zero-allocation C++ engine via Rcpp. All transforms, thresholding, and reconstruction run at native speed.
• Ring-buffer stream processor (new_wavelet_stream) for real-time applications: fixed memory, high-speed updates, microsecond latency.
• No look-ahead bias. Causal mode guarantees zero data leakage from future to past (verified via counterfactual leakage tests against wavethresh).
• Adaptive thresholding based on Liu et al. (2014): recursive MAD-based noise estimation with three shrinkage methods (hard, soft, semisoft).
• Six built-in wavelets: Haar, DB2, CDF 5/3, CDF 9/7 (JPEG 2000), DD4, and Lazy. Plus a simple API for custom wavelets via lift_step() + custom_wavelet().
• Diagnostic suite (diagnose_wavelet): automatic verification of perfect reconstruction, vanishing moments, orthogonality, compact support, and shift sensitivity.

Performance

Benchmarks against wavethresh, adlift, and nlt on a Doppler signal (N = 1024, Haar, 50 simulations):

Metric	rLifting	wavethresh	adlift	nlt
Median time (ms)	< 1	< 1	~600	~900
MSE	0.009	0.025	0.009	0.009

rLifting matches the reconstruction accuracy of the adaptive lifting packages (adlift, nlt) while running orders of magnitude faster. wavethresh is fast but uses a fixed global threshold, resulting in higher MSE.

For causal processing, rLifting's ring-buffer architecture is ~700× faster than a naive sliding-window loop built on wavethresh.

Installation

# install.packages("remotes")
remotes::install_github("mkyou/rLifting")

Quick start

Offline denoising

Process an entire signal at once using global statistics.

library(rLifting)

# Generate a noisy Doppler signal
x <- rLifting:::.generate_signal("doppler", n = 1024)
x_noisy <- x + rnorm(1024, sd = 0.2)

scheme <- lifting_scheme("cdf97")

x_clean <- denoise_signal_offline(
  x_noisy, scheme,
  levels = floor(log2(length(x_noisy))),
  method = "semisoft"
)

plot(x_noisy, col = "grey", type = "l", main = "Offline denoising")
lines(x_clean, col = "blue", lwd = 2)
lines(x, col = "black", lty = 2)

Causal denoising

Process a signal without using future data. Useful for financial backtesting, real-time control, and streaming applications.

x_causal <- denoise_signal_causal(
  x_noisy, scheme,
  window_size = 256,
  levels = floor(log2(256)),
  method = "semisoft"
)

Real-time stream processing

Feed one sample at a time and get a denoised estimate immediately.

processor <- new_wavelet_stream(
  scheme, window_size = 256,
  levels = floor(log2(256))
)

stream_output <- numeric(length(x_noisy))
for (i in seq_along(x_noisy)) {
  stream_output[i] <- processor(x_noisy[i])
}

Custom wavelets

Define wavelets by specifying predict and update steps:

p <- lift_step("predict", coeffs = c(0.5, 0.5), start_idx = 0)
u <- lift_step("update", coeffs = c(0.25, 0.25), start_idx = -1)
my_wavelet <- custom_wavelet("MyCDF53", list(p, u), c(sqrt(2), 1/sqrt(2)))

# Works in any function
result <- denoise_signal_offline(x_noisy, my_wavelet, levels = 5)

Documentation

Detailed vignettes are available after installation:

Vignette	Topic
introduction	Package overview, basic usage
benchmark_offline	Speed and MSE comparison with wavethresh, adlift, nlt
benchmark_causal	Causal speed benchmark + counterfactual leakage test
realtime	Real-time stream processing with latency analysis
extensions	Custom wavelets, diagnostics, thresholding, low-level API

vignette("introduction", package = "rLifting")

Roadmap

Based on the current development of the FATE estimator research, the following features are planned:

• Irregular grids: native handling of non-equispaced data (Second Generation Wavelets) without interpolation.
• Multivariate denoising: joint denoising of correlated signals to incorporate covariance structure.
• Boundary refinements: implement local linear predictors for edge handling to improve reconstruction at signal boundaries (crucial for real-time causal estimation).

License

MIT License.