Joint compression and de-speckling of SAR images by thresholding and encoding the rational Laplacian pyramid

We propose an original approach to near-lossless compression, based on quantizing and encoding the Rational Laplacian Pyramid (RLP) of a SAR image. The RLP features the desirable property that the noise on its layers, except for the base-band, is practically independent of the signal. The RLP has mean roughly equal to one and variance proportional to that of the speckle, sigma(u)**2, on homogeneous areas, and larger elsewhere. The base-band icon is encoded, and the bottom layer of the RLP, diminished by its expected value, is uniformly quantized with a step size Delta = sigma(u). The steps on the other layers are arbitrary because of the quantization noise feedback loop at the encoder. Whenever larger compression ratios are desired, instead of increasing the Delta, a dead-zone can be introduced in the quantizer: pyramid coefficients lying below the threshold (half of the dead-zone) are set at zero; those above are quantized and encoded. The procedure is equivalent to a hard thresholding, a widely used technique for image de-noising in the wavelet domain. Experimental results show that extremely high-quality images are obtained at reasonable rates; as the compression is increased, images are progressively de-noised to be accommodated in the available rate.