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This paper introduces a novel method for reconstructing optical tomography images using pre-computed transforms. Our approach is to pre-compute and store the inverse matrix required for MAP reconstruction using lossy source coding techniques. We show how lossy source coding techniques can be used to store the large and non-sparse matrix by applying a wavelet transform in the image space and appropriate orthonormal transforms in the sensor space. Lossy coding dramatically reduces the number of non-zero coefficients, thereby proportionately reducing both the required storage and computation time. However, if the number of sensor measurements is large, the storage and computation of the orthonormal transforms can become prohibitive. For this purpose, we introduce a general method for approximating any orthonormal transform by a series of sparse binary transforms. This sparse matrix transform technique is then used together with lossy coding to result in a fast reconstruction algorithm for optical tomography. Simulations indicate that the technique can dramatically reduce the storage and computation requirements in reconstruction by exploiting redundancy in the transformed matrices.