Image denoising based on iterative generalized cross-validation and fast translation invariant

•The IWT, which keeps the coefficients as integers, makes the join operation possible.•Join operation uses statistical data instead of each coefficient to compute the value of GCV.•An iterative GCV is proposed to reduce complexity of acquiring the GCV threshold.•Fast translation invariant is applied to reduce ringing effect of singularities.

Wavelet shrinkage is a promising method in image denoising, the key factor of which lies in the threshold selection. A fast and effective wavelet denoising method, called Iterative Generalized Cross-Validation and Fast Translation Invariant (IGCV–FTI) is proposed, which reduces the computation cost of the standard Generalized Cross-Validation (GCV) method and efficiently suppresses the Pseudo-Gibbs phenomena with an extra gain of 1–1.87 dB in PSNR compared with GCV. In the proposed approach, we establish a novel functional relation between the GCV results of two neighboring thresholds based on integer wavelet transform, and combine it with threshold-search interval optimization. As a result, the proposed IGCV reduces the time complexity of original GCV algorithm by two orders of magnitude. In addition, a recursion strategy is applied to expedite the translation invariant. The high efficiency and proficient capacity to remove noise make IGCV–FTI a good choice for image denoising.