Current self-supervised denoising methods for paired noisy images typically involve mapping one noisy image through the network to the other noisy image. However, after measuring the spectral bias of such methods using our proposed Image Pair Frequency-Band Similarity, it suffers from two practical limitations. Firstly, the high-frequency structural details in images are not preserved well enough. Secondly, during the process of fitting high frequencies, the network learns high-frequency noise from the mapped noisy images. To address these challenges, we introduce a Spectral Controlling network (SCNet) to optimize self-supervised denoising of paired noisy images. First, we propose a selection strategy to choose frequency band components for noisy images, to accelerate the convergence speed of training. Next, we present a parameter optimization method that restricts the learning ability of convolutional kernels to high-frequency noise using the Lipschitz constant, without changing the network structure. Finally, we introduce the Spectral Separation and low-rank Reconstruction module (SSR module), which separates noise and high-frequency details through frequency domain separation and low-rank space reconstruction, to retain the high-frequency structural details of images. Experiments performed on synthetic and real-world datasets verify the effectiveness of SCNet.