A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all pos...

In this report, we present a number-theory-based approach for discrete tomography (DT),which is based on parallel projections of rational slopes. Using a well-controlled geometry of X-ray beams, we obtain a system of linear equations with integer coefficients. Assuming that the range of pixel values is a(i, j) = 0, 1, . . . , M − 1, with M being a prime number, we reduce the equations modulo M ...

Recent developments both in measurement echniques and reconstruction algorithms have shown the possibility of quasi-real time microwave tomography. These technical developments always require more sophisticated experimental arrangements in order to reduce the microwave circuits complexity, decrease the measurement time, and improve the resolution. This paper deals with the use of crossed linear...

The reconstruction of an unknown function $f$ from its line sums is the aim discrete tomography. However, two main aspects prevent being easy task. In general, many solutions are allowed due to presence switching functions. Even when uniqueness conditions available, results about NP-hardness algorithms make their implementation inefficient values in certain sets. We show that this not case take...