Acceleration of iterative image restoration algorithms

Abstract

A new technique for the acceleration of iterative image restoration algorithms is proposed. The method is based on the principles of vector extrapolation and does not require the minimization of a cost function. The algorithm is derived and its performance illustrated with Richardson-Lucy (R-L) and maximum entropy (ME) deconvolution algorithms and the Gerchberg-Saxton magnitude and phase retrieval algorithms. Considerable reduction in restoration times is achieved with little image distortion or computational overhead per iteration. The speedup achieved is shown to increase with the number of iterations performed and is easily adapted to suit different algorithms. An example R-L restoration achieves an average speedup of 40 times after 250 iterations and an ME method 20 times after only 50 iterations. An expression for estimating the acceleration factor is derived and confirmed experimentally. Comparisons with other acceleration techniques in the literature reveal significant improvements in speed and stability.

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

“…Both deconvolutions are performed in Matlab using the LucyRichardson method [78]. For the measurements in Figure 13, the power gain of the measurement chain was increased by 5 dB relative to the bounds quoted in Appendix D 2.…”

Dependent component analysis for blind restoration of images degraded by turbulent atmosphere

“…Other BSS approaches that can deal with statistically dependent sources include: independent subspace analysis (ISA) [24][25], nonnegative matrix and tensor factorization (NMF/NTF) [27][28][29][30], and the blind Richardson-Lucy (BRL) algorithm [33][34][35][36], which are used for comparison purpose in this paper. They are briefly described as follows.…”

“…It has been later formulated in [35] for blind deconvolution, and then modified by an iterative restoration algorithm in [36]. To briefly introduce BRL algorithm we need to write a single frame image g n , n {1,…,N}, in the lexicographical notation: …”

Optimal stopping condition for iterative image deconvolution by new orthogonality criterion

“…In the experiments an iterative, non-blind deconvolution algorithm, the RichardsonLucy (RL) method was used: [2,3].…”

“…), and this is why the problem is ill-posed. As stated in [3,4] this problem affects the quality of the solution of the iterative algorithms highly.…”