Accelerated Monotonic Algorithms for Transmission Tomography

We present a framework for designing fast and monotonic algorithms for transmission tomography penalized likelihood image reconstruction. The new algorithms are based on paraboloidal surrogate functions for the log-likelihood. Due to the form of the log-likelihood function, it is possible to find low curvature surrogate functions that guarantee monotonicity. Unlike previous methods, the proposed surrogate functions lead to monotonic algorithms even for the nonconvex log-likelihood that arises due to background events such as scatter and random coincidences. The gradient and the curvature of the likelihood terms are evaluated only once per iteration. Since the problem is simplified, the CPU time per iteration is less than that of current algorithms which directly minimize the objective, yet the convergence rate is comparable. The simplicity, monotonicity and speed of the new algorithms are quite attractive. The convergence rates of the algorithms are demonstrated using real PET transmission scans.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85953/1/Fessler149.pd

Antenna Array Pattern Synthesis via Coordinate Descent Method

This paper presents an array pattern synthesis algorithm for arbitrary arrays based on coordinate descent method (CDM). With this algorithm, the complex element weights are found to minimize a weighted L2 norm of the difference between desired and achieved pattern. Compared with traditional optimization techniques, CDM is easy to implement and efficient to reach the optimum solutions. Main advantage is the flexibility. CDM is suitable for linear and planar array with arbitrary array elements on arbitrary positions. With this method, we can configure arbitrary beam pattern, which gives it the ability to solve variety of beam forming problem, e.g. focused beam, shaped beam, nulls at arbitrary direction and with arbitrary beam width. CDM is applicable for phase-only and amplitude-only arrays as well, and furthermore, it is a suitable method to treat the problem of array with element failures