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The representation of an image with several multiscale singular points has been the main concern in image processing. Based on the dual-tree complex wavelet transform (DT-CWT), a new image reconstruction (IR) algorithm from multiscale singular points is proposed. First, the image was transformed by DT-CWT, which provided multiresolution wavelet analysis. Then, accurate multiscale singular points for IR were detected in the DT-CWT domain due to the shift invariance and directional selectivity properties of DT-CWT. Finally, the images were reconstructed from the phases and magnitudes of the multiscale singular points by alternating orthogonal projections between the CT-DWT space and its affine space. Theoretical analysis and experimental results show that the proposed IR algorithm is feasible, efficient, and offers a certain degree of denoising. Furthermore, the proposed IR algorithm outperforms other classical IR algorithms in terms of performance metrics such as peak signal-to-noise ratio, mean squared error, and structural similarity.

Image Reconstruction from Multiscale Singular Points Based on the Dual-Tree Complex Wavelet Transform