Synthetic aperture radar (SAR) images map Earth’s surface at high resolution, regardless of the weather conditions or sunshine phenomena. Therefore, SAR images have applications in various fields. Speckle noise, which has the characteristic of multiplicative noise, degrades the image quality of SAR images, which causes information loss. This study proposes a speckle noise reduction algorithm while using the speckle reducing anisotropic diffusion (SRAD) filter, discrete wavelet transform (DWT), soft threshold, improved guided filter (IGF), and guided filter (GF), with the aim of removing speckle noise. First, the SRAD filter is applied to the SAR images, and a logarithmic transform is used to convert multiplicative noise in the resulting SRAD image into additive noise. A two-level DWT is used to divide the resulting SRAD image into one low-frequency and six high-frequency sub-band images. To remove the additive noise and preserve edge information, horizontal and vertical sub-band images employ the soft threshold; the diagonal sub-band images employ the IGF; while, the low- frequency sub-band image removes additive noise using the GF. The experiments used both standard and real SAR images. The experimental results reveal that the proposed method, in comparison to state-of-the art methods, obtains excellent speckle noise removal, while preserving the edges and maintaining low computational complexity.