Frequency-domain analysis of discrete wavelet transform coefficients and their adaptive shrinkage for anti-aliasing

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We present an antialiasing method using combined wavelet-Fourier transform and spatially adaptive shrinkage of the transform coefficients. Traditional antialiasing methods employ a simple low-pass filter onto the entire image, so the resulting image loses not only aliasing artifacts but also high-frequency components such as edges and ridges. The proposed algorithm analyzes the property of the LL subband of the discrete wavelet transform (DWT), and reduces aliasing artifacts using patch-adaptive shrinkage of the DWT coefficients. More specifically, an antialiased LL subband is obtained using adaptive patch-based aliasing reduction. To detect an aliased region, we subtract the discrete Fourier transform (DFT) coefficients of the LL subband from the DFT coefficients of antialiased LL subband. The detected aliasing artifacts in the LH, HL, and HH subbands are reduced by patch-wise adaptive shrinkage of the transform coefficients. The resulting antialiased image is obtained using the inverse DWT. The aliasing artifacts can be efficiently reduced by adaptively shrinking wavelet transform coefficients for preserving high-frequency image details. The proposed antialiasing algorithm is suitable for removing aliasing artifacts which frequently occur in imaging sensors with limited resolution.