The Theory of Compressive Sensing Matching Pursuit Considering Time-domain Noise with Application to Speech Enhancement
Bibliographic record
Abstract
Compressive sampling matching pursuit (CoSaMP) is an efficient compressive sensing algorithm holding rigorous estimation error bounds and low computational complexity, when it deals with an additive noise signal model in the observation domain. However, in some applications, e.g., speech enhancement (SE), noise is added to a signal in the time domain, where the conventional CoSaMP cannot be directly applied. In this paper, we establish the theory of CoSaMP to address the time-domain noise, referred to as Tdn-CoSaMP, which extends the canonical theory of CoSaMP. In particular, we prove the existence of a new upper bound of Tdn-CoSaMP, which is found to be larger than that of the conventional CoSaMP by appending two additional terms: a multiplier$1+\sqrt{{N\over s}}$, where$N$is the dimension of the signal, and an${\ell_1}$norm of the noise${1\over\sqrt{s}}\Vert {\mbi{e}}\Vert_1$scaled by the sparse level$s$of the signal. We also apply Tdn-CoSaMP to the SE task based on the sequential denoising of overlapped frames in the discrete cosine transform (DCT) domain. The proposed system, CoSaMP-based speech enhancement (CoSaMPSE), has been evaluated in terms of both objective and subjective criteria on various types of noise. Positive results have been achieved for denoising stationary and nonstationary white Gaussian noise (WGN) and are comparable to other SE methods. Moreover, due to its low computational complexity, CoSaMPSE is possible to be combined with optimally modified log-spectrum amplitude estimation (OMLSA) and able to achieve complementary denoising effects in various noisy conditions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".