1. The signal | 2. Offline denoising — regular grid | Residual diagnostics | 3. Irregular grid — handling sensor dropouts | rLifting irregular-grid denoising | Baseline: interpolate then denoise | Comparison | 4. Streaming mode — sample-by-sample monitoring | 5. Summary | Further reading

1. The three modes at a glance | 2. Setup | 3. Choosing a wavelet | 4. Offline denoising | 5. Causal denoising | 6. Stream processing | 7. Irregular grids | 8. Comparing the three modes | Where to go next | References

1. Why parameter choice matters | 2. The MAD noise estimate | 3. Universal vs SURE | 4. The α/β recursion | 5. tune_alpha_beta() walkthrough | 6. Shrinkage choice (hard, soft, semisoft, SCAD) | 7. Decision guide | 7.1 Recommendations grounded in the regular-grid benchmark | 7.2 Recommendations from the wavelet-denoising literature | 7.3 Scope: irregular-grid companion | References

1. Why causal mode exists | 2. The cost of causality | 3. Choosing window_size | 4. Choosing update_freq | 5. Per-sample latency | 6. Causal-specific wavelet recommendations | 7. Leakage check by construction | 8. Decision guide | 8.1 When the benchmark gives a direct answer | 8.2 Recommendations from the wavelet-denoising literature | References

1. Why boundary handling matters | 2. The five modes — semantics | 3. The ll_k parameter for local_linear | 4. Empirical impact in offline mode | 5. Empirical impact in causal and stream mode | 5.1 With haar (the causal-mode default) | 5.2 With longer filters (CDF 5/3 and beyond) | 6. one_sided constraints | 7. Decision guide | 7.1 Bench-grounded recommendations | 7.2 Heuristics from the literature | References

1. What makes a grid irregular | 2. Mechanism — Lagrange in the predict step | 3. Wavelet eligibility | 4. The API in each mode | 5. Two robust defaults | 6. Why these choices | Offline: cdf53 + local_linear + SURE + SCAD | Causal / stream: haar + zero + tuned universal + SCAD | 7. How close to optimal these defaults are | 8. Does position-aware processing actually help? | 9. When to deviate from the robust default | 9.1 Pitfalls | 10. Worked example — Doppler on a log-normal grid | 11. Where to look next | References

1. Built-in wavelet families | 2. Defining custom wavelets | Example: recreating CDF 5/3 manually | Using the custom wavelet | 3. Diagnosing a wavelet | 4. Low-level transform pipeline | 5. Boundary extension modes | local_linear: k-point extrapolation | one_sided: filter renormalisation | Causal stream: symmetric vs one_sided | 6. Irregular grids and custom wavelets | Irregular grid: cumulative spacing with high variance | Smooth underlying signal | Denoise using the custom wavelet on the irregular grid | Summary | References

1. Methodology and scope | 1.1 Which package appears where, and why | 1.2 What is not measured | 2. Regular grid — MSE | Best achievable configuration | Out-of-the-box configuration | Tuning cost | 3. Regular grid — speed | 4. rLifting modes — regular grid | rLifting ranking per mode | 5. Irregular grid — MSE | Tuning cost on irregular grids | 6. Irregular grid — speed | 7. rLifting modes — irregular grid | 8. The speed–quality picture | 9. Honest limitations | 10. Decision guide | 11. Where to look next | References