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Many popular image compression schemes are based on block-transform coding, a technique where images are broken into small blocks of pixels prior to transformation and compression. Block-transform coding often introduces blocking artifacts which are particularly prevalent at low bit-rates due to quantization errors. A novel algorithm for deblocking block-transform compressed images is proposed in this paper. This algorithm is based on a phase-adaptive, shifted thresholding technique that estimates the original uncompressed image as the weighted sum of shifted versions of the decompressed image subjected to a threshold. An efficient integer transform is used to construct the shifted versions of the decompressed image. The aggregation weights are obtained adaptively using the local phase moment characteristics of the underlying image content. The proposed algorithm utilizes important human perceptual characteristics to provide effective image deblocking while preserving image detail. Experimental results show that the proposed algorithm is more efficient than comparable methods and yields both subjective results and peak signal-to-noise ratio (PSNR) results comparable to existing methods.