Image Enhancement Through Two-Dimensional Wavelet Decomposition

When an image undergoes two-dimensional wavelet decomposition, its structural contours are captured in the low-frequency components, while fine details are represented in the high-frequency components. Consequently, image enhancement can be achieved by applying amplification algorithms to low-frequency decomposition coefficients and implementing attenuation techniques to high-frequency coefficients. This enhancement methodology significantly improves image quality by sharpening contours and accentuating detailed features. From an implementation perspective, this process typically involves: 1. Performing 2D wavelet decomposition using functions like wavedec2() in MATLAB or pywt.wavedec2() in Python's PyWavelets library 2. Applying gain factors to low-frequency approximation coefficients (e.g., LL subband) 3. Implementing threshold-based attenuation to high-frequency detail coefficients (LH, HL, HH subbands) 4. Reconstructing the enhanced image through inverse wavelet transform Furthermore, different enhancement algorithms - such as histogram equalization for low-frequency components or adaptive thresholding for high-frequency components - can be selected based on specific requirements to achieve precise and customized enhancement effects. Through two-dimensional wavelet decomposition coupled with strategic coefficient processing, we can effectively enhance visual quality to meet diverse application demands in fields like medical imaging and remote sensing.