Double-polarization interferometry (DPI) is an emerging technique for the quantitative study of molecular interactions, offering benefits such as high sensitivity, label-free operation, and the ability to acquire real-time data on molecular recognition dynamics and structures. However, during the acquisition of interferometric images, various interferences, such as speckle noise, may occur. DPI relies on phase shifts in interference fringes to calculate key parameters, including intermolecular forces. Therefore, it is essential to denoise the acquired complex interferometric images to minimize noise interference during phase shift extraction. The interferometric images obtained through DPI typically feature pronounced bright and dark fringes, along with clear boundary information. However, traditional denoising methods often result in excessive filtering, leading to blurred boundaries and loss of critical information. Thus, the development of a denoising algorithm tailored for complex interference fringes is crucial for improving the quality of subsequent analyses in DPI and its practical applications.

We propose a denoising algorithm that combines sine-cosine decomposition with the discrete cosine transform (DCT) for processing complex DPI interference fringe images. The algorithm first decomposes the interference image into sine and cosine components, generating the corresponding sine and cosine maps. By exploiting the energy concentration properties of DCT in the frequency domain, noise components in the maps are effectively removed. The denoised image is then restored through an arctangent operation. Comparative experiments are conducted on both simulated and real interference fringe datasets. Various denoising techniques are evaluated, including mean filtering, median filtering, wavelet-based frequency domain denoising, isotropic and anisotropic methods, the fast nonlocal means (FNLM) and weighted nuclear norm minimization (WNNM) algorithms, and N2N training strategies. These methods are compared with the proposed algorithm to assess the performance of each and to validate the effectiveness of the proposed approach. Additionally, phase shift curves are extracted and compared before and after denoising to further demonstrate the reliability of the proposed algorithm.

We use MATLAB software to generate simulated interferogram images, and the simulation results (Fig. 9) demonstrate the superior performance of the proposed algorithm. After processing, the images exhibit higher contrast and finer textures, with edge details fully preserved. Both the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) metrics (Table 1) consistently outperform those of other algorithms. In contrast, traditional filtering methods lack sufficient denoising capability, resulting in blurred edge textures. The results from wavelet, isotropic, and anisotropic algorithms are less satisfactory, as some noise remains in the images. Although the FNLM and WNNM algorithms display some competitiveness, their denoising effects and edge clarity still fall short of those of the proposed algorithm. Furthermore, although the N2N algorithm outperforms the proposed algorithm in terms of PSNR, its SSIM value is lower, and its denoising effect is not significantly better. In experiments with real interferogram images (Fig. 10), the proposed algorithm continues to perform the best, with previously blurred areas becoming clearer and providing more reliable data for subsequent analysis and processing. In contrast, traditional filtering methods perform poorly, leaving significant noise in the images. The results of wavelet, isotropic, and anisotropic filtering are suboptimal, producing blurred edge textures. While FNLM and WNNM algorithms demonstrate relatively good denoising effects, with WNNM slightly outperforming the proposed algorithm in SSIM, its PSNR value is 0.9533 dB lower (Table 2), and both algorithms are inferior to the proposed method in preserving edge details. In real image denoising experiments, the performance of the N2N training strategy does not match that of the simulation experiments. Although its denoising level surpasses other comparison algorithms and preserves edge textures well, some noise remains. Finally, by applying the proposed algorithm to denoise a set of interferogram images, we compare the phase shift curves before and after denoising (Fig. 11). The results confirm that the proposed algorithm effectively eliminates abnormal jumps in the phase shift curve, further validating its reliability.

In DPI, interferometric images often contain complex structures and substantial noise, making denoising a critical step in accurately extracting phase shifts. This paper presents a novel algorithm that combines sine-cosine decomposition with the discrete cosine transform to achieve high-precision denoising of interferogram images. Comparative experiments demonstrate that the proposed algorithm significantly reduces noise levels while preserving edge and texture details to the greatest extent possible, effectively avoiding edge blurring due to over-filtering. The evaluation of different denoising methods indicates that the proposed algorithm achieves higher PSNR and SSIM values, signifying effective noise reduction with minimal loss of information. The processed interferometric image set successfully eliminates abnormal jumps in the phase shift curve, enhancing the accuracy and reliability of phase shift extraction. This contributes to improving the quality of analyses and applications in DPI.