Recent advancements in transformer architectures have significantly enhanced image-denoising algorithms, surpassing the limitations of traditional convolutional neural networks by more effectively modeling global interactions through advanced attention mechanisms. In the domain of single-image denoising, noise manifests across various scales. This is especially evident in intricate scenarios, necessitating the comprehensive capture of multi-scale information inherent in the image. To solve transformer's lack of multi-scale image analysis capability, a discrete wavelet and transformer based network (DTSIDNet) is proposed. The network adeptly resolves the inherent limitations of the transformer architecture by integrating the discrete wavelet transform. DTSIDNet independently manages image data at various scales, which greatly improves both adaptability and efficiency in environments with complex noise. The network's self-attention mechanism dynamically shifts focus among different scales, efficiently capturing an extensive array of image features, thereby significantly enhancing the denoising outcome. This approach not only boosts the precision of denoising but also enhances the utilization of computational resources, striking an optimal balance between efficiency and high performance. Experiments on real-world and synthetic noise scenarios show that DTSIDNet delivers high image quality with low computational demands, indicating its superior performance in denoising tasks with efficient resource use.