In fiber Bragg grating (FBG) sensing demodulation systems, high-precision peak detection is a core requirement for demodulation algorithms. However, practical spectral signals are often susceptible to environmental noise interference, which leads to significant degradation in the accuracy of traditional demodulation methods. This study proposes a self-adaptive K-SVD (SAK-SVD) denoising algorithm based on adaptive window parameter optimization, establishing a closed-loop iterative feedback mechanism through dual iterations between dictionary learning and parameter adjustment. This approach achieves a synergistic enhancement of noise suppression and signal fidelity. First, a dictionary learning framework based on K-SVD is constructed for initial denoising, and the peak feature region is extracted by differentiating the denoised signals. By constructing statistics on the number of sign changes, an adaptive adjustment model for the window size is established. This model dynamically tunes the window parameters in dictionary learning for iterative denoising, establishing a closed-loop architecture that integrates denoising evaluation with parameter optimization. The performance of SAK-SVD is evaluated through three experimental scenarios, demonstrating that SAK-SVD overcomes the rigid parameter limitations of traditional K-SVD in FBG spectral processing, enhances denoising performance, and thereby improves wavelength demodulation accuracy. For denoising undistorted waveforms, the optimal mean absolute error (MAE) decreases to 0.300 pm, representing a 25% reduction compared to the next-best method. For distorted waveforms, the optimal MAE drops to 3.9 pm, achieving a 63.38% reduction compared to the next-best method. This study provides both theoretical and technical support for high-precision fiber-optic sensing under complex working conditions. Crucially, the SAK-SVD framework establishes a universal, adaptive denoising paradigm for fiber Bragg grating (FBG) sensing. This paradigm has direct applicability to Raman spectroscopy, industrial ultrasound-based non-destructive testing, and biomedical signal enhancement (e.g., ECG artefact removal), thereby advancing high-precision measurement capabilities across photonics and engineering domains.