Name

pw_extract - Approximate the background noise or envelope function by polynomials, and use constrained simplex method (in L1 sense) to extract image formation parameters (the coefficients of the polynomials) from 1D rotationally averaged power spectrum in logrithm scale. By adjusting the rank of polynomials, one can flexibly fit the background noise, and envelope function (non-Gaussian type).

Usage

• res = pw_extract(1dpw2, n1,iswi, Pixel_size)

Input

1dpw2

1D rotationally averaged power spectrum of particles or noise

n1

n1=n+1, n is the rank of polynomial, which is used to approximate baseline noise, or envelope function.

iswi

an integer number, which can control the fitting objects - either envelope function or background noise.

Pixel_size

Pixel size of the input image. Given it, one can output frequencies with unit of 1/`Å`.

Output

res

contains extracted background noise, or envelope function, frequencies, and associated fitting parameters.

Options

Description

• 1. The pw_extract c++ code calls the following functions to perform the parameters fitting:
  1. call_cl1, b. lsfit. c. CL1. These called functions are converted from Fortran 77 by f2c program. CL1 is the core code to perform constrained simplex optimization.
• 2. iswi is the control switch to perform either background or envelope fitting.

Method

• Simplex method

Reference

.1. Barrodale and F.D.K. Roberts L1 solution to linear equations subject to linear equality and inequality constraints ACM TOMS 6 (1980), 231-235.

.2. Z. Huang, P. R. Baldwin, S.Mullapudi, and P .A. Penczek, Automated determination of parameters describing power spectra of micrograph images in electron microscopy. J. Struct. Biol. 144 (2003), pp. 79–94.

Author / Maintainer

Zhong Huang

Keywords

category 1

UTILITIES

category 2

ADAPTIVE

Files

utilities.py

See also

• get_params_cl1

Maturity

stable

works for most people, has been tested; test cases/examples available.

Bugs

None. It is perfect.