<FONT face=Verdana>The translation invariant analytic contourlet transform with low redundancy is proposed. In this transform

the circular symmetric filter banks decomposes image into multi-resolution detail subbands and one low-frequency subband

then the detail subbands are processed by Hilbert transform to generate two dimensional analytic signals. At last

the analytic signals are decomposed by directional filter bank to implement analytic contourlet transform with multi-scale

multi-direction

and translation invariant property. The real part and imaginary part of the analytic contourlet basis functions resemble Gabor wavelet

and conform well to the human visual system. The experiments show that the analytic contourlet transform can achieve higher performance in image denoising and compressed sensing.