Fast and Efficient Stored Matrix Techniques for Optical Tomography

A barrier to the use of optical tomography in practical applications is the high computational cost of iterative image reconstruction. This paper introduces a novel method for direct reconstruction of the image from a pre-computed and stored inverse matrix. Since the inverse matrix for optical tomography is generally quite large and not sparse, it is necessary to store the inverse matrix using lossy source coding techniques. A key innovation is the method used for matrix representation and the technique used for computing the required matrix-vector product. This representation is based on transforms of the image and sensor spaces which are designed to minimize reconstructed image distortion. Simulations indicate that the technique can dramatically reduce the storage and computation requirements by exploiting redundancy in the transformed matrix.