<title>Multiscale method for tomographic reconstruction</title>

Abstract

We use a natural pixel type representation of an object to construct almost orthogonal basis functions. The coefficients of expansion of an object into these basis functions can be computed from the projection (i.e. the strip integral) data by using the Wavelet Transform. This enables us to formulate a multiscale tomographic reconstruction technique wherein the object is reconstructed at multiple scales or resolutions. A complete reconstruction can be obtained by combining these. The almost orthonormal behavior of the basis functions results in a system matrix, relating the input (the object coefficients) and the output (the projection data), which is extremely sparse. The system matrix, in addition to being sparse, has a symmetric block-Toeplitz structure for which fast inversion algorithms exist. The multiscale reconstruction technique can find applications in object feature recognition directly from projection data, tackling ill-posed imaging problems where the projection data are incomplete and/or noisy, and construction of multiscale stochastic models for which fast estimation algorithms exist.