# Publications

### 1964

- B. R. Frieden, “Polynomial expansion in classical aberrations and spatial frequency for the wave-aberrated optical transfer function of an axially asymmetric lens system,” Optica Acta 11, 33-41 (1964).
- B. R. Frieden, “Microscopic observation of film cross sections having steep contours,” Appl. Opt. 3, 395-398 (1964).

### 1965

- B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4, 1400-1403 (1965).
- B. R. Frieden, “Use of a scanning slit in determination of radial irradiance distribution” (letter), J. Opt. Soc. Am. 55, 1696-1697 (1965).

### 1966

- B. R. Frieden, “Image evaluation by use of the sampling theorem,” J. Opt. Soc. Am. 56, 1355-1362 (1966).
- B. R. Frieden, “Optical transfer of the three dimensional object” (abstr.), J. Opt. Soc. Am. 56, 1420-1421 (1966); Optical Sciences Center Tech. Rept. 13, 35 pp., Jan. 1967; (paper) J. Opt. Soc. Am. 56, 56-66 (1967).
- B. R. Frieden, “Longitudinal image formation,” J. Opt. Soc. Am. 56, 1495-1501 (1966).

### 1967

- B. R. Frieden, “Band-unlimited reconstruction of optical objects and spectral sources,” Optical Sciences Center Tech. Rept. 18, 25 pp., June 16, 1967; J. Opt. Soc. Am. 57, 1013-1019 (1967).

### 1968

- B. R. Frieden, “Optimum, non-linear processing of noisy images,” Optical Sciences Center Tech. Rept. 23, 40 pp., Mar. 6, 1968; J. Opt. Soc. Am. 58, 1272-1275 (1968).
- B. R. Frieden, “How well can a lens system transmit information?” Optical Sciences Center Tech. Rept. 24, 38 pp., Mar. 29, 1968; “How well can a lens transmit entropy?” J. Opt. Soc. Am. 58, 1105-1112 (1968).

### 1969

- B. R. Frieden, “Maximum attainable MTF for rotationally symmetric lens systems,” Optical Sciences Center Tech. Rept. 29, 15 pp., Sept. 10, 1968; J. Opt. Soc. Am. 59, 402-406 (1969).
- B. R. Frieden, “On arbitrarily perfect imagery with a finite aperture,” Optical Sciences Center Tech. Rept. 34, 34 pp., Jan. 1969; Optica Acta 16, 795-807 (1969).

### 1970

- B. R. Frieden, “Information and the restorability of images” (letter), J. Opt. Soc. Am. 60, 575-576 (1970).
- B. R. Frieden, “The extrapolating pupil, image synthesis, and some thought applications,” Appl. Oct. 11, 2489-2496 (1970).

### 1972

- B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc. Am. 62, 511-518 (1972).
- B. R. Frieden and J. J. Burke, “Restoring with maximum entropy. II. Superresolution of photographs of diffraction-blurred impulses,” J. Opt. Soc. Am. 62, 1202-1211 (1972).

### 1973

- B. R. Frieden, “Statistical estimates of bounded optical scenes by the method of ‘prior probabilities’” (correspondence), IEEE Trans. Information Theory IT-19, 118-119 (1973).
- B. R. Frieden, “Statistical estimates of bounded optical scenes by the method of ‘prior probabilities’” (correspondence), IEEE Trans. Information Theory IT-19, 118-119 (1973).

### 1974

- B. R. Frieden, “Image restoration by discrete convolution of minimal length,” J. Opt. Soc. Am. 64, 682-686 (1974).
- M. Bendinelli, A. Constortini, L. Ronchi, and B. R. Frieden, “Degrees of freedom, and eigenfunctions, for the noisy image,” J. Opt. Soc. Am. 64, 1498-1502 (1974).
- B. R. Frieden, “Image restoration by discrete convolution of minimal length,” J. Opt. Soc. Am. 64, 682-686 (1974).
- M. Bendinelli, A. Consortini, L. Ronchi, and B. R. Frieden, “Degrees of freedom, and eigenfunctions, for the noisy image,” J. Opt. Soc. Am. 64, 1498-1502 (1974).

### 1976

- B. R. Frieden, “A new restoring algorithm for the preferential enhancement of edge gradients” (letter), J. Opt. Soc. Am. 66, 280-283 (1976).
- W. Swindell and B. R. Frieden, “Restored pictures of Ganymede,” Science 191, 1237-1241 (1976).
- B. R. Frieden, “Estimation – a new role for maximum entropy,” invited paper SPSE International Conference on Image Analysis and Evaluation, Toronto, Canada, July 19-23, 1976.
- A. Consortini and B. R. Frieden, “Quantum-mechanical solution for the simple harmonic oscillator in a box,” Il Nuovo Cimento 35B, 153-164 (1976).
- B. R. Frieden, “Problems associated with the maximum entropy image restoration technique,” invited paper, Symposium on Current Mathematical Problems in Image Science, Naval Postgraduate School, Monterey, California, Nov. 1976.
- B. R. Frieden, “Image analysis and evaluation,” SPSE International Conference, Toronto, Canada, July 19-23, 1976 (meeting report); Appl. Opt. 15, 2599-2601 (1976).
- B. R. Frieden, “Uncertainty product for a subensemble of particles,” Int. J. Theoret. Physics 15, 389-391 (1976).

### 1978

- B. R. Frieden and D. C. Wells, “Restoring with maximum entropy, III: Poisson sources and backgrounds,” J. Opt. Soc. Am. 68, 93-103, Jan. 1978.

### 1980

- B. R. Frieden, “Statistical models for the image restoration problem,” Computer Graphics and Image Processing 12, 40-59 (1980).
- B. R. Frieden, “Image restoration using a norm of maximum information,” Opt. Eng. 19, 290-296 (1980).

### 1981

- B. R. Frieden, “Maximum-information data processing: application to optical signals,” J. Opt. Soc. Am. 71, 294-303 (1981).

### 1983

- B. R. Frieden, “Unified theory for estimating frequency-of-occurrence laws and optical objects,” J. Opt. Soc. Am. 73, 927-938 (1983).

### 1984

- W. T. Cathey, B. R. Frieden, W. T. Rhodes, and C. K. Rushforth, “Image gathering and processing for enhanced resolution,” J. Opt. Soc. Am. A 1, 241-250 (1984).
- B. R. Frieden and C. K. Zoltani, “Maximum bounded entropy: a new method of tomographic reconstruction,” Topical meeting on Industrial Applications of Computed Tomography and NMR Imaging, Technical Digest, TuA41-TuA44 (1984).

### 1985

- B. R. Frieden and C. K. Zoltani, “Maximum bounded entropy: application to tomographic reconstruction,” Appl. Opt. 24, 201-207 (1985).
- B. R. Frieden and C. K. Zoltani, “Monte Carlo restoration of binary objects,” Acta Polytechnica Scandinavica, Appl. Physics Series 149, Proceedings of Image Science 85, Volume I, A. T. Friberg and Pirkko Oittinen, eds., Helsinki U. of Technology, Helsinki, 1985, pp. 115-118.
- B. R. Frieden, “Statistical techniques in image science,” in Addendum to preceding, pp. 19-30.
- B. R. Frieden, “Dice, entropy, and likelihood,” Proc. IEEE 73, 1764-1770 (1985).

### 1986

- B. R. Frieden and C. K. Zoltani, “Monte Carlo restoration of binary objects,” J. Opt. Soc. Am. A 3, 731-734 (1986).
- B. R. Frieden, “A probability law for the fundamental constants,” Found. Phys. 16, 883-906 (1986).
- B. R. Frieden, “Accurate determination of length in a routinely obtained picture,” Opt. Acta 33, 1453-1461 (1986).
- B. R. Frieden and Daniel T. Gillespie, “Another proof of the random variable transformation theorem,” Am. J. Phys. 54, 1149-1150 (1986).

### 1987

- B. R. Frieden, “Maximum-probable restoration of photon-limited images,” Appl. Opt. 26, 1755-1764 (1987).
- M. Hayworth, B. R. Frieden, and H. Roehrig, “Iterative MW enhancement of cardiac angiograms,” Proc. SPIE, Medical Imaging, R. Schneider and S. Dwyer, eds. 767, 471-478 (1987).
- B. R. Frieden, “Possibility image transform and logical convolution,” J. Opt. Soc. Am. A 4, 232-235 (1987).
- B. R. Frieden, “On the 3Ms of image enhancement, MAP, ME, and MW,” in Interferometric Imaging in Astronomy (First Joint ESO-NOAO Workshop, Oracle, Arizona, 1987), pp. 191-196.
- B. R. Frieden, “Speculations on unknown images, spectral sources, and physical constants,” Opt. News 13, 23-30 (1987).
- B. R. Frieden, H. G. Aumann, “Image reconstruction from multiple 1-D scans using filtered localized projection,” Appl. Opt. 26, 3615-3621 (1987).
- B. R. Frieden, “Maximum Cramer-Rao bound. Applications to: prior probabilities estimation, image restoration, and the generation of quantum mechanics,” Proc. SPIE, Applications of Digital Image Processing X, A. Tescher, ed., 829, 2-14 (1987).

### 1988

- Y. Hu and B. R. Frieden, “Restoration of longitudinal images,” Appl. Opt. 27, 414-418 (1988).
- B. R. Frieden, “Applications to optics and wave mechanics of the criterion of maximum Cramer-Rao bound,” J. Mod. Opt. 35, 1297-1316 (1988).
- B. R. Frieden, “A comparison of the maximum entropy (ME), maximum a posteriori (MAP), and median window (MW) restoring algorithms,” Proc. Of the 6th Pfefferkorn Conference at Niagara Falls, Canada, 1987 (publ. 1988).

### 1989

- B. R. Frieden, “Fisher information as the basis for diffraction optics,” Opt. Lett. 14, 199-201 (1989).
- B. R. Frieden and C. K. Zoltani, “Fast tracking algorithm for multi-frame particle-image velocimetry data,” Appl. Opt. 28, 652-655 (1989).
- B. R. Frieden, “Image recovery by minimum discrimination from a template,” Appl. Opt. 28, 1235-1243 (1989).
- B. R. Frieden, “Stochastic approaches to inversion problems in optics,” J. Appl. Stat. 16, 243-266 (1989).
- B. R. Frieden, “Fisher information as the basis for the Schrödinger wave equation,” Am. J. Physics 57, 1004-1008 (1989).
- B. R. Frieden, “Pseudolinear phase retrieval,” Opt. Commun. 73, 342-346 (1989).

### 1990

- B. R. Frieden, “Fisher information, disorder, and the equilibrium distributions of physics,” Phys. Rev. A 41, 4265-4276 (1990).
- S. Wang and B. R. Frieden, “Effects of third-order spherical aberration on the 3-D incoherent optical transfer function,” Appl. Opt. 29, 2424-2432 (1990).
- H. A. Ferwerda and B. R. Frieden, “Quantitative phase retrieval in the phase-contrast microscope,” Proc. SPIE Digital Image Synthesis and Inverse Optics, A. Gmitro, ed. 1351 (1990).

### 1991

- B. R. Frieden, “Fisher information and the complex nature of the Schrödinger wave equation,” Found. Physics 21, 757-771 (1991).
- B. R. Frieden, “Some analytical and statistical properties of Fisher information,” Proc. SPIE, Stochastic and Neural Methods in Signal Processing, S. Chen, ed., 1569, 311-316 (1991).

### 1992

- B. R. Frieden, “Fisher information as the basis for Maxwell’s equations,” Physica A 180, 359-385 (1992).
- B. R. Frieden and C. Oh, “Multiple-filter approach to phase retrieval from modulus data,” Appl. Opt. 31, 1103-1108 (1992).
- B. R. Frieden and C. Oh, “Integral logarithmic transform: theory and applications,” Appl. Opt. 31, 1138-1145 (1992).
- B. R. Frieden, “Fisher information and uncertainty complementarity,” Phys. Lett. A 169, 123-130 (1992).

### 1993

- B. R. Frieden and C. Oh, “Turbulent image reconstruction from a superposition model,” Opt. Comm. 98, 241-244 (1993).
- B. R. Frieden, “Estimation of distribution laws, and physical laws, by a principle of extremized physical information,” Physica A 198, 262-338 (1993).
- B. R. Frieden and A. T. Bajkova, “Entropic reconstruction of complex images,” Opt. Comm. 102, 515-522 (1993).
- R. P. Bocker and B. R. Frieden, “Solution of the Maxwell field equations in vacuum for arbitrary charge and current distributions using the methods of matrix algebra,” IEEE Trans. Educ. 36, 350-356 (1993).

### 1994

- B. R. Frieden and A. T. Bajkova, “Bayesian cross-entropy reconstruction of complex images,” Appl. Opt. 33, 219-226 (1994).
- B. R. Frieden and R. J. Hughes, “Spectral 1/f noise derived from extremized physical information,” Phys. Rev. E 49, 2644-2649 (1994).
- B. Nikolov and B. R. Frieden, “Limitation on entropy increase imposed by Fisher information,” Phys. Rev. E 49, 4815-4820 (1994).
- B. R. Frieden, “Turbulent image reconstruction using object power spectrum information,” Opt. Comm. 109, 227-230 (1994).

### 1995

- B. R. Frieden and A. T. Bajkova, “Reconstruction of complex signals using minimum Renyi information,” Appl. Opt. 34, 4086-4093 (1995).
- B. R. Frieden, Proc. SPIE, Optical and Photonic Applications of Electroactive and Conducting Polymers, S. Yang, ed., 2528 (1995).
- B. R. Frieden and B. H. Soffer, “Lagrangians of physics and the game of Fisher-information transfer,” Phys. Rev. E 52, 2274-2286 (1995).
- Y. Wang and B. R. Frieden, “Minimum entropy-neural network approach to turbulent-image reconstruction,” Appl. Opt. 34, 5938-5944 (1995).

### 1996

- B. R. Frieden and W. J. Cocke, “Foundation for Fisher information-based derivations of physical laws,” Phys. Rev. E 54, 257-260 (1996).

### 1997

- B. R. Frieden, “Fisher information as a measure of time,” Astrophysics and Space Science 244, 387-391 (1996); reprinted in Modern Mathematical Models of Time and their Applications to Physics and Astronomy (Kluwer, Dordrecht, 1997) 387-391.
- W. J. Cocke and B. R. Frieden, “Information and gravitation,” Founds. Phys. 243, 1397-1412 (1997).
- B. R. Frieden and David J. Graser, “Closed-form maximum entropy image restoration,” Opt. Comm. 146, 79-84 (1998); also in Proc. SPIE 3164, Applications of Digital Image Processing XX, A. Tescher, ed., 140-148 (1997).

### 1998

- B. R. Frieden and H. C. Rosu, “Fisher’s arrow of time in quantum cosmology,” Mod. Phys. Lett. A 13, 39 (1998).
- B. R. Frieden, “An exact, linear solution to the problem of imaging through turbulence,” Opt. Comm. 150, 15-21 (1998).

### 1999

- S. Barraza and B. R. Frieden, “Regularization of the image division approach to blind deconvolution”, Appl. Opt. 38, 2232-2239 (1999).
- B. R. Frieden, A. Plastino, A.R. Plastino and B.H. Soffer, “Fisher-based thermodynamics: Its Legendre transform and concavity properties”, Phys. Rev. E 60, 48-53 (1999).
- B. R. Frieden, “F-Information, a unitless variant of Fisher Information”, Founds Phys. 29, 1521-1541 (1999).

### 2000

- R. Frieden and B. H. Soffer, “A critical comparison of three information-based approaches to physics”, Found. Phys. Lett. 13, 89-96 (2000).
- R. Frieden and A. Plastino, “Composite fermion particles and Fisher Information”, Phys. Lett. A 272, 326-332 (2000).

### 2001

- B. R. Frieden and A. Plastino, “Higgs mass generation from the standpoint of information”, Phys. Lett. A. 278, 299-306 (2001).
- B. R. Frieden, A. Plastino and B. H. Soffer, “Population genetics from an information perspective”, J. Theor. Biol. 208, 49-64 (2001).
- B. R. Frieden, “Physics from Fisher Information”, Mathematics Today 37, 115-119 (2001)
- B. R. Frieden and A. Plastino, “Alternative classical trajectories compatible with quantum mechanics”, Phys. Lett. A 287, 325-330 (2001).

### 2002

- R.A. Gatenby and B.R. Frieden, “Application of information theory and extreme physical information to carcinogenesis,” Cancer Research 62, 3675-3684 (2002).
- B.R. Frieden, “Relations between parameters of a decoherent system and Fisher information”, Phys. Rev. A 66, 022107-1 – 022107-6 (2002).
- B.R. Frieden, A. Plastino, A.R.Plastino and B.H. Soffer, “A Schroedinger link between non-equilibrium thermodynamics and Fisher information,” Phys. Rev. E 66, 046128-1 – 046128-8 (2002).
- B.R. Frieden, A. Plastino, A.R. Plastino and B.H. Soffer, “Non-equilibrium thermodynamics and Fisher information: an illustrative example,” Phys. Lett. A 304, 73-78 (2002).
- B.R. Frieden and B.H. Soffer, “Black holes and optimum coding,” Phys. Lett. A 304, 4 Nov., 1-7 (2002).

### 2003

- S.P. Flego, B.R. Frieden et al., “Nonequilibrium thermodynamics and Fisher information: sound wave propagation in a dilute gas,” Phys. Rev. E 68, 016105 (2003).

### 2004

- R.J. Hawkins and B.R. Frieden, “Fisher information and equilibrium distributions in econophysics,” Phys. Lett. A 322, 126 (2004)
- B.R. Frieden, “Aberration reduction by multiple relays of an incoherent image”, J. Opt. Soc. Amer. A 21, 1834-1840 (2004)

### 2005

- R.A. Gatenby and B.R. Frieden, “The role of non-genomic information in maintaining thermodynamic stability in living systems”, Math. Biosciences and Eng. 2, 43 51 (2005)
- M. Yolles and B.R. Frieden, “A Metahistorical information theory of social change: the theory,” J. Organizational Transf. & Social Change 2, 29-62; “an application,” 63-77 (2005).
- R.J. Hawkins, B.R. Frieden and J.L. D’Anna, “Ab initio yield curve dynamics,” Phys.Lett A 344, 317-323 (2005).
- B.R. Frieden and R.A. Gatenby, “Power laws of complex systems from extreme physical information,” Phys. Rev. E 72, 036101, 1-10 (2005).

### 2006

- B.R. Frieden and B.H. Soffer, “Information-theoretic significance of the Wigner Distribution,” Phys. Rev. A 74, 052108, 1-8 (2006).

### 2007

- B.R. Frieden, “Information-based uncertainty for a photon,” Opt. Comm. 271, 71-72 (2007).

### 2008

- R.A. Gatenby and B.R. Frieden, “Inducing catastrophe in malignant growth,” J. Math. Med. Biol. 25, 267-283 (2008)
- B.R. Frieden and R.A. Gatenby, “Conditions for correspondence between Hartree scattering and biological growth,” Phys. Rev. E 78, 041902 (2008)

### 2009

- B.R. Frieden and B.H. Soffer, “De Broglie’s wave hypothesis from Fisher information,” Physica A 388, 1315-1330 (2009)

### 2010

- R.J. Hawkins, M. Aoki and B.R. Frieden, “Asymmetric information and macroeconomic dynamics,” Physica A 389, 3565-3571 (2010)
- B.R. Frieden and B.H. Soffer, “Weighted Fisher informations, their derivation and use,” Physics Letts. A 374, 3895-3898 (2010)
- R.A. Gatenby and B.R. Frieden, “Coulomb Interactions between Cytoplasmic Electric Fields and Phosphorylated Messenger Proteins Optimize Information Flow in Cells,” PLoS ONE 5(8): e12084. doi:10.1371/journal.pone (2010)
- B.R. Frieden and R.J. Hawkins, “Quantifying system order for full and partial coarse graining,” Phys. Rev. E 82, 066117, 1-8 (2010)

### 2011

- B.R. Frieden and R.A. Gatenby, “Order in a Multiply-Dimensioned System,” Phys. Rev. E 84, 011128, 1-9 (2011)
- B.R. Frieden and R.A. Gatenby, “Information Dynamics in Living Systems: Prokaryotes, Eukaryotes, and Cancer,” PLoS ONE 6(7): e22085. doi:10.1371/journal.pone.0022085 (2011)
- R.A. Gatenby and B.R. Frieden, “Cell Development Pathways Follow from a Principle of Extreme Fisher Information,” J. Physic Chem Biophysic 2011, 1:1 http://dx.doi.org/10.4172/2161-0398.1000102

### 2012

- B.R. Frieden, A. Plastino and A.R. Plastino, “Effect upon universal order of Hubble expansion,” Physica A doi: 10.1016/j.physa.2011.08.005 (2011); Physica A 391 410-413 (2012)
- B.R. Frieden, A. Plastino and A.R. Plastino, “Fisher order measure and Petri’s Universe model,” Physica A 391 2300-2305 (2012)
- B.R. Frieden and M. Petri, “Motion-dependent levels of order in a relativistic universe” (PDF), Phys. Rev E 86, 032102, 1-5 (2012)

### 2013

- B.R. Frieden and R.A. Gatenby (invited paper), “Cell development obeys maximum Fisher information,” Frontiers in Bioscience E5, 1017-1032 (2013)
- B.R. Frieden and R.A. Gatenby, “Principle of maximum Fisher information from Hardy’s axioms applied to statistical systems,” Phys. Rev. E 88, 042144 (2013) [6 pages]

### 2014

- B.R. Frieden and R.A. Gatenby, “Derivation of Principle of Extreme Physical Information,” arXiv:1406.3615 [physics.data-an] 2014 [13 pages]
- B.R. Frieden and R.A. Gatenby, “Cancer Suppression by Compression,” Bulletin of Mathematical Biology 10.1007/s11538-014-0051-7 (2014)

### 2015

- B.R. Frieden, “Estimating a repeatable statistical law by requiring its stability during observation,” Entropy 17, 7453-7467 (2015);doi:10.3390/e17117453 (2015)

### 2016

- R.A. Gatenby and B.R. Frieden “Investigating Information Dynamics in Living Systems through the Structure and Function of Enzymes,” PLoS ONE 11(5): e0154867. doi:10.1371/ journal. pone.0154867 (2016)
- P. Zegers, B.R. Frieden, C. Alarcon, A. Fuentes, “Information theoretical measures for achieving robust learning machines,” Entropy 18, 295-314 (2016); doi:10.3390/e18080295 (2016)

### 2017

- R.A. Gatenby and B.R. Frieden,
*Nature*, “Cellular Information Dynamics through Transmembrane Flow of Ions,” Scientific Reports 7, 15075 (2017); doi:10.1038/s41598-017-15182-2

### 2019

- B.R. Frieden and R.A. Gatenby,
*Nature*, “Signal transmission through elements of the cytoskeleton form an optimized information network in eukaryotic cells,” Scientific Reports 9, 6110 (2019), doi:10:1038/s41598-019-42343-2