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It is proposed that an efficient and fast image compression scheme based on all level curvelet coefficients with SPIHT (Set Partitioning in Hierarchical Trees). For images with textures, the high frequency wavelet coefficients are likely to become significant after several code passes of SPIHT, which degrades the coding performance. The basic flaw that wavelet transform exhibits, is its inability to represent edge discontinuities along curves. Less number of coefficients is required in compression process but several wavelet coefficients are used to reconstruct edges properly along the curves. This is due to the reason that in a map of large wavelet coefficients, edges repeat at scale after scale. There was a need of a transform that handles two dimensional singularities along the curves sparsely. This led to the birth of new multi-resolution curvelet transform. Curvelet basis elements possess wavelet basis function qualities but these also oriented at a variety of directions and so represent edge discontinuities and other singularities well than wavelet transform. In the proposed method, a curvelet transform of an image is taken and selected all level curvelet coefficients information. Then, it has been applied with SPIHT encoding. The SPIHT encoded output is stored as a bit stream. Run Length Encoding has been applied to the bit stream. It produces further compressed bit stream. Then run length decoding and SPIHT decoding have been applied and inverse curvelet transform has been taken to reconstruct the image. Images of different sizes have been tested in the experiment and the results are listed in the tables.