This paper proposes a statistically matched wavelet based textured image coding scheme for efficient representation of texture data in a compressive sensing (CS) frame work. Statistically matched wavelet based data representation causes most of the captured energy to be concentrated in the approximation subspace, while very little information remains in the detail subspace. We encode not the full-resolution statistically matched wavelet subband coefficients but only the approximation subband coefficients (LL) using standard image compression scheme like JPEG2000. The detail subband coefficients, that is, HL, LH, and HH, are jointly encoded in a compressive sensing framework. Compressive sensing technique has proved that it is possible to achieve a sampling rate lower than the Nyquist rate with acceptable reconstruction quality. The experimental results demonstrate that the proposed scheme can provide better PSNR and MOS with a similar compression ratio than the conventional DWT-based image compression schemes in a CS framework and other wavelet based texture synthesis schemes like HMT-3S. 1. Introduction Texture data contain spatial, temporal, statistical, and perceptual redundancies. Representing texture data using standard compression schemes like MPEG-2 [1] and H.264 [2] is not efficient, as they are based on Shannon-Nyquist sampling [3] and do not account for perceptual redundancies. They are often resource consuming (as they acquire too many samples) due to its fine details in textured image and high frequency content. Variety of applications in computer vision, graphics, and image processing (such as robotics, defence, medicine, and geosciences) demands better compression with good perceptual reconstruction quality, instead of bit accurate (high PSNR) reconstruction. This is because the human brain is able to decipher important variations in data at scales smaller than those of the viewed objects. Ndjiki-Nya et al. [4–8], Bosch et al. [9, 10], Byrne et al. [11, 12], and Zhang et al. [13, 14] have proposed techniques to reconstruct visually similar texture from sample data. Statistically matched wavelet [15] is aimed at designing a filter bank that matches a given pattern in the image and can better represent the corresponding image as compared to other wavelet families. Compressive sensing (CS) technique [16] has proved that it is possible to achieve a sampling rate lower than the Nyquist rate [3] with acceptable reconstruction quality. Leveraging the concept of transform coding, compressive sensing enables a potentially large reduction in
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