Greedy Signal Space Recovery Algorithm with Overcomplete Dictionaries in Compressive Sensing

TL;DR

This paper introduces a greedy signal space recovery algorithm called SSSP for signals sparse in overcomplete dictionaries, providing theoretical guarantees and demonstrating superior performance over existing methods.

Contribution

It develops a generalized iterative recovery algorithm for overcomplete dictionaries using D-RIP, with proven convergence and improved accuracy in noisy and noise-free settings.

Findings

Algorithm outperforms existing recovery methods

Provides theoretical bounds on measurement requirements

Demonstrates high accuracy and low complexity

Abstract

Compressive Sensing (CS) is a new paradigm for the efficient acquisition of signals that have sparse representation in a certain domain. Traditionally, CS has provided numerous methods for signal recovery over an orthonormal basis. However, modern applications have sparked the emergence of related methods for signals not sparse in an orthonormal basis but in some arbitrary, perhaps highly overcomplete, dictionary, particularly due to their potential to generate different kinds of sparse representation of signals. To this end, we apply a signal space greedy method, which relies on the ability to optimally project a signal onto a small number of dictionary atoms, to address signal recovery in this setting. We describe a generalized variant of the iterative recovery algorithm called Signal space Subspace Pursuit (SSSP) for this more challenging setting. Here, using the Dictionary-Restricted Isometry Property (D-RIP) rather than classical RIP, we derive a low bound on the number of measurements required and then provide the proof of convergence for the algorithm. The algorithm in noisy and noise-free measurements has low computational complexity and provides high recovery accuracy. Simulation results show that the algorithm outperforms best compared with the existing recovery algorithms.

Tables

Table 1. TABLE I: Units for Magnetic Properties

Symbol	Quantity	Conversion from Gaussian and CGS EMU to SI a
$\Phi$	magnetic flux	1 Mx $\to {10}^{-8}$ Wb $={10}^{-8}$ V$\cdot$s
$B$	magnetic flux density, magnetic induction	1 G $\to {10}^{-4}$ T $={10}^{-4}$ Wb/m2
$H$	magnetic field strength	1 Oe $\to {10}^3/\left(4\pi \right)$ A/m
$m$	magnetic moment	1 erg/G $=$ 1 emu $\to {10}^{-3}$ A$\cdot$m${}_{}{}^2={10}^{-3}$ J/T
$M$	magnetization	1 erg/(G$\cdot$cm${}_{}{}^3)=$ 1 emu/cm3 $\to {10}^3$ A/m
4$\pi M$	magnetization	1 G $\to {10}^3/\left(4\pi \right)$ A/m
$\sigma$	specific magnetization	1 erg/(G$\cdot$g) $=$ 1 emu/g $\to$ 1 A$\cdot$m2/kg
$j$	magnetic dipole moment	1 erg/G $=$ 1 emu $\to 4\pi \times {10}^{-10}$ Wb$\cdot$m
$J$	magnetic polarization	1 erg/(G$\cdot$cm${}_{}{}^3)=$ 1 emu/cm3 $\to 4\pi \times {10}^{-4}$ T
$\chi ,\kappa$	susceptibility	1 $\to 4\pi$
${\chi }_{\rho }$	mass susceptibility	1 cm3/g $\to 4\pi \times {10}^{-3}$ m3/kg
$\mu$	permeability	1 $\to 4\pi \times {10}^{-7}$ H/m $=4\pi \times {10}^{-7}$ Wb/(A$\cdot$m)
${\mu }_r$	relative permeability	$\mu \to {\mu }_r$
$w,W$	energy density	1 erg/cm${}_{}{}^3\to {10}^{-1}$ J/m3
$N,D$	demagnetizing factor	1 $\to 1/\left(4\pi \right)$
Vertical lines are optional in tables. Statements that serve as captions for the entire table do not need footnote letters.
aGaussian units are the same as cg emu for magnetostatics; Mx $=$ maxwell, G $=$ gauss, Oe $=$ oersted; Wb $=$ weber, V $=$ volt, s $=$ second, T $=$ tesla, m $=$ meter, A $=$ ampere, J $=$ joule, kg $=$ kilogram, H $=$ henry.

Equations

$$E=m{c}^2.$$

Full text

I Introduction

This document is a template for LaTeX. If you are reading a brief or PDF version of this document, please download the electronic file, trans_jour.tex, from the IEEE Web site at http://www.ieee.org/authortools/trans_jour.tex so you can use it to prepare your manuscript. If you would prefer to use LaTeX, download IEEE’s LaTeX style and sample files from the same Web page. You can also explore using the Overleaf editor at https://www.overleaf.com/blog/278-how-to-use-overleaf-with-ieee-collabratec-your-quick-guide-to-getting-started#.xsVp6tpPkrKM9

If your brief is intended for a conference, please contact your conference editor concerning acceptable word processor formats for your particular conference.

IEEE will do the final formatting of your brief. If your brief is intended for a conference, please observe the conference page limits.

I-A Abbreviations and Acronyms

Define abbreviations and acronyms the first time they are used in the text, even after they have already been defined in the abstract. Abbreviations such as IEEE, SI, ac, and dc do not have to be defined. Abbreviations that incorporate periods should not have spaces: write “C.N.R.S.,” not “C. N. R. S.” Do not use abbreviations in the title unless they are unavoidable (for example, “IEEE” in the title of this article).

I-B Other Recommendations

Use one space after periods and colons. Hyphenate complex modifiers: “zero-field-cooled magnetization.” Avoid dangling participles, such as, “Using (1), the potential was calculated.” [It is not clear who or what used (1).] Write instead, “The potential was calculated by using (1),” or “Using (1), we calculated the potential.”

Use a zero before decimal points: “0.25,” not “.25.” Use “cm3,” not “cc.” Indicate sample dimensions as “0.1 cm $\times$ 0.2 cm,” not “0.1 $\times$ 0.2 cm2.” The abbreviation for “seconds” is “s,” not “sec.” Use “Wb/m2” or “webers per square meter,” not “webers/m2.” When expressing a range of values, write “7 to 9” or “7–9,” not “7$\sim$9.”

A parenthetical statement at the end of a sentence is punctuated outside of the closing parenthesis (like this). (A parenthetical sentence is punctuated within the parentheses.) In American English, periods and commas are within quotation marks, like “this period.” Other punctuation is “outside”! Avoid contractions; for example, write “do not” instead of “don’t.” The serial comma is preferred: “A, B, and C” instead of “A, B and C.”

If you wish, you may write in the first person singular or plural and use the active voice (“I observed that $\ldots$” or “We observed that $\ldots$” instead of “It was observed that $\ldots$”). Remember to check spelling. If your native language is not English, please get a native English-speaking colleague to carefully proofread your brief.

Try not to use too many typefaces in the same article. You’re writing scholarly papers, not ransom notes. Also please remember that MathJax can’t handle really weird typefaces.

I-C Equations

Number equations consecutively with equation numbers in parentheses flush with the right margin, as in (1). To make your equations more compact, you may use the solidus ( / ), the exp function, or appropriate exponents. Use parentheses to avoid ambiguities in denominators. Punctuate equations when they are part of a sentence, as in

[TABLE]

Be sure that the symbols in your equation have been defined before the equation appears or immediately following. Italicize symbols ($T$ might refer to temperature, but T is the unit tesla). Refer to “(1),” not “Eq. (1)” or “equation (1),” except at the beginning of a sentence: “Equation (1) is $\ldots$ .”

I-D LaTeX*-Specific Advice*

Please use “soft” (e.g., \eqref{Eq}) cross references instead of “hard” references (e.g., (1)). That will make it possible to combine sections, add equations, or change the order of figures or citations without having to go through the file line by line.

Please don’t use the {eqnarray} equation environment. Use {align} or {IEEEeqnarray} instead. The {eqnarray} environment leaves unsightly spaces around relation symbols.

Please note that the {subequations} environment in LaTeX will increment the main equation counter even when there are no equation numbers displayed. If you forget that, you might write an article in which the equation numbers skip from (17) to (20), causing the copy editors to wonder if you’ve discovered a new method of counting.

BibTEX does not work by magic. It doesn’t get the bibliographic data from thin air but from .bib files. If you use BibTEX to produce a bibliography you must send the .bib files.

LaTeX can’t read your mind. If you assign the same label to a subsubsection and a table, you might find that Table I has been cross referenced as Table IV-B3.

LaTeX does not have precognitive abilities. If you put a \label command before the command that updates the counter it’s supposed to be using, the label will pick up the last counter to be cross referenced instead. In particular, a \label command should not go before the caption of a figure or a table.

Do not use \nonumber inside the {array} environment. It will not stop equation numbers inside {array} (there won’t be any anyway) and it might stop a wanted equation number in the surrounding equation.

II Units

Use either SI (MKS) or CGS as primary units. (SI units are strongly encouraged.) English units may be used as secondary units (in parentheses). This applies to briefs in data storage. For example, write “15 Gb/cm2 (100 Gb/in${}^{2})$.” An exception is when English units are used as identifiers in trade, such as “3½-in disk drive.” Avoid combining SI and CGS units, such as current in amperes and magnetic field in oersteds. This often leads to confusion because equations do not balance dimensionally. If you must use mixed units, clearly state the units for each quantity in an equation.

The SI unit for magnetic field strength $H$ is A/m. However, if you wish to use units of T, either refer to magnetic flux density $B$ or magnetic field strength symbolized as $\mu_{0}H$. Use the center dot to separate compound units, e.g., “A$\cdot$m2.”

III Some Common Mistakes

The word “data” is plural, not singular. The subscript for the permeability of vacuum $\mu_{0}$ is zero, not a lowercase letter “o.” The term for residual magnetization is “remanence”; the adjective is “remanent”; do not write “remnance” or “remnant.” Use the word “micrometer” instead of “micron.” A graph within a graph is an “inset,” not an “insert.” The word “alternatively” is preferred to the word “alternately” (unless you really mean something that alternates). Use the word “whereas” instead of “while” (unless you are referring to simultaneous events). Do not use the word “essentially” to mean “approximately” or “effectively.” Do not use the word “issue” as a euphemism for “problem.” When compositions are not specified, separate chemical symbols by en-dashes; for example, “NiMn” indicates the intermetallic compound Ni0.5Mn0.5 whereas “Ni–Mn” indicates an alloy of some composition NixMn1-x.

Be aware of the different meanings of the homophones “affect” (usually a verb) and “effect” (usually a noun), “complement” and “compliment,” “discreet” and “discrete,” “principal” (e.g., “principal investigator”) and “principle” (e.g., “principle of measurement”). Do not confuse “imply” and “infer.”

Prefixes such as “non,” “sub,” “micro,” “multi,” and “ultra” are not independent words; they should be joined to the words they modify, usually without a hyphen. There is no period after the “et” in the Latin abbreviation “et al.” (it is also italicized). The abbreviation “i.e.,” means “that is,” and the abbreviation “e.g.,” means “for example” (these abbreviations are not italicized).

A general IEEE styleguide is available at http://www.ieee.org/authortools.

IV Guidelines for Graphics Preparation and Submission

IV-A Types of Graphics

The following list outlines the different types of graphics published in IEEE journals. They are categorized based on their construction, and use of color/shades of gray:

IV-A1 Color/Grayscale figures

Figures that are meant to appear in color, or shades of black/gray. Such figures may include photographs, illustrations, multicolor graphs, and flowcharts.

IV-A2 Line Art figures

Figures that are composed of only black lines and shapes. These figures should have no shades or half-tones of gray, only black and white.

IV-A3 Author photos

Head and shoulders shots of authors that appear at the end of our briefs.

IV-A4 Tables

Data charts which are typically black and white, but sometimes include color.

IV-B Multipart figures

Figures compiled of more than one sub-figure presented side-by-side, or stacked. If a multipart figure is made up of multiple figure types (one part is lineart, and another is grayscale or color) the figure should meet the stricter guidelines.

IV-C File Formats For Graphics

Format and save your graphics using a suitable graphics processing program that will allow you to create the images as PostScript (PS), Encapsulated PostScript (.EPS), Tagged Image File Format (.TIFF), Portable Document Format (.PDF), Portable Network Graphics (.PNG), or Metapost (.MPS), sizes them, and adjusts the resolution settings. When submitting your final brief, your graphics should all be submitted individually in one of these formats along with the manuscript.

IV-D Sizing of Graphics

Most charts, graphs, and tables are one column wide (3.5 inches/88 millimeters/21 picas) or page wide (7.16 inches/181 millimeters/43 picas). The maximum depth a graphic can be is 8.5 inches (216 millimeters/54 picas). When choosing the depth of a graphic, please allow space for a caption. Figures can be sized between column and page widths if the author chooses, however it is recommended that figures are not sized less than column width unless when necessary.

There is currently one publication with column measurements that do not coincide with those listed above. Proceedings of the IEEE has a column measurement of 3.25 inches (82.5 millimeters/19.5 picas).

The final printed size of author photographs is exactly 1 inch wide by 1.25 inches tall (25.4 millimeters$\,\times\,$31.75 millimeters/6 picas$\,\times\,$7.5 picas). Author photos printed in editorials measure 1.59 inches wide by 2 inches tall (40 millimeters$\,\times\,$50 millimeters/9.5 picas$\,\times\,$12 picas).

IV-E *Resolution *

The proper resolution of your figures will depend on the type of figure it is as defined in the “Types of Figures” section. Author photographs, color, and grayscale figures should be at least 300dpi. Line art, including tables should be a minimum of 600dpi.

IV-F Vector Art

In order to preserve the figures’ integrity across multiple computer platforms, we accept files in the following formats: .EPS/.PDF/.PS. All fonts must be embedded or text converted to outlines in order to achieve the best-quality results.

IV-G Color Space

The term color space refers to the entire sum of colors that can be represented within the said medium. For our purposes, the three main color spaces are Grayscale, RGB (red/green/blue) and CMYK (cyan/magenta/yellow/black). RGB is generally used with on-screen graphics, whereas CMYK is used for printing purposes.

All color figures should be generated in RGB or CMYK color space. Grayscale images should be submitted in Grayscale color space. Line art may be provided in grayscale OR bitmap colorspace. Note that “bitmap colorspace” and “bitmap file format” are not the same thing. When bitmap color space is selected, .TIF/.TIFF/.PNG are the recommended file formats.

IV-H Accepted Fonts Within Figures

When preparing your graphics IEEE suggests that you use of one of the following Open Type fonts: Times New Roman, Helvetica, Arial, Cambria, and Symbol. If you are supplying EPS, PS, or PDF files all fonts must be embedded. Some fonts may only be native to your operating system; without the fonts embedded, parts of the graphic may be distorted or missing.

A safe option when finalizing your figures is to strip out the fonts before you save the files, creating “outline” type. This converts fonts to artwork what will appear uniformly on any screen.

IV-I Using Labels Within Figures

IV-I1 Figure Axis labels

Figure axis labels are often a source of confusion. Use words rather than symbols. As an example, write the quantity “Magnetization,” or “Magnetization M,” not just “M.” Put units in parentheses. Do not label axes only with units. As in Fig. 1, for example, write “Magnetization (A/m)” or “Magnetization (A$\cdot$m*-1*),” not just “A/m.” Do not label axes with a ratio of quantities and units. For example, write “Temperature (K),” not “Temperature/K.”

Multipliers can be especially confusing. Write “Magnetization (kA/m)” or “Magnetization (103 A/m).” Do not write “Magnetization (A/m)$\,\times\,$1000” because the reader would not know whether the top axis label in Fig. 1 meant 16000 A/m or 0.016 A/m. Figure labels should be legible, approximately 8 to 10 point type.

IV-I2 Subfigure Labels in Multipart Figures and Tables

Multipart figures should be combined and labeled before final submission. Labels should appear centered below each subfigure in 8 point Times New Roman font in the format of (a) (b) (c).

IV-J File Naming

Figures (line artwork or photographs) should be named starting with the first 5 letters of the author’s last name. The next characters in the filename should be the number that represents the sequential location of this image in your article. For example, in author “Anderson’s” brief, the first three figures would be named ander1.tif, ander2.tif, and ander3.ps.

Tables should contain only the body of the table (not the caption) and should be named similarly to figures, except that ‘.t’ is inserted in-between the author’s name and the table number. For example, author Anderson’s first three tables would be named ander.t1.tif, ander.t2.ps, ander.t3.eps.

Author photographs should be named using the first five characters of the pictured author’s last name. For example, four author photographs for a brief may be named: oppen.ps, moshc.tif, chen.eps, and duran.pdf.

If two authors or more have the same last name, their first initial(s) can be substituted for the fifth, fourth, third$\ldots$ letters of their surname until the degree where there is differentiation. For example, two authors Michael and Monica Oppenheimer’s photos would be named oppmi.tif, and oppmo.eps.

IV-K Referencing a Figure or Table Within Your Brief

When referencing your figures and tables within your brief, use the abbreviation “Fig.” even at the beginning of a sentence. Do not abbreviate “Table.” Tables should be numbered with Roman Numerals.

IV-L Checking Your Figures: The IEEE Graphics Analyzer

The IEEE Graphics Analyzer enables authors to pre-screen their graphics for compliance with IEEE Transactions and Journals standards before submission. The online tool, located at http://graphicsqc.ieee.org/, allows authors to upload their graphics in order to check that each file is the correct file format, resolution, size and colorspace; that no fonts are missing or corrupt; that figures are not compiled in layers or have transparency, and that they are named according to the IEEE Transactions and Journals naming convention. At the end of this automated process, authors are provided with a detailed report on each graphic within the web applet, as well as by email.

For more information on using the Graphics Analyzer or any other graphics related topic, contact the IEEE Graphics Help Desk by e-mail at graphics@ieee.org.

IV-M Submitting Your Graphics

Because IEEE will do the final formatting of your brief, you do not need to position figures and tables at the top and bottom of each column. In fact, all figures, figure captions, and tables can be placed at the end of your brief. In addition to, or even in lieu of submitting figures within your final manuscript, figures should be submitted individually, separate from the manuscript in one of the file formats listed above in Section IV-C. Place figure captions below the figures; place table titles above the tables. Please do not include captions as part of the figures, or put them in “text boxes” linked to the figures. Also, do not place borders around the outside of your figures.

IV-N Color Processing/Printing in IEEE Journals

All IEEE Transactions, Journals, and Letters allow an author to publish color figures on IEEE Xplore® at no charge, and automatically convert them to grayscale for print versions. In most journals, figures and tables may alternatively be printed in color if an author chooses to do so. Please note that this service comes at an extra expense to the author. If you intend to have print color graphics, include a note with your final brief indicating which figures or tables you would like to be handled that way, and stating that you are willing to pay the additional fee.

V Conclusion

A conclusion section is not required. Although a conclusion may review the main points of the brief, do not replicate the abstract as the conclusion. A conclusion might elaborate on the importance of the work or suggest applications and extensions.

Appendixes, if needed, appear before the acknowledgment.

Acknowledgment

The preferred spelling of the word “acknowledgment” in American English is without an “e” after the “g.” Use the singular heading even if you have many acknowledgments. Avoid expressions such as “One of us (S.B.A.) would like to thank $\ldots$ .” Instead, write “F. A. Author thanks $\ldots$ .” In most cases, sponsor and financial support acknowledgments are placed in the unnumbered footnote on the first page, not here.

References and Footnotes

-A References

References need not be cited in text. When they are, they appear on the line, in square brackets, inside the punctuation. Multiple references are each numbered with separate brackets. When citing a section in a book, please give the relevant page numbers. In text, refer simply to the reference number. Do not use “Ref.” or “reference” except at the beginning of a sentence: “Reference [3] shows $\ldots$ .” Please do not use automatic endnotes in Word, rather, type the reference list at the end of the brief using the “References” style.

Reference numbers are set flush left and form a column of their own, hanging out beyond the body of the reference. The reference numbers are on the line, enclosed in square brackets. In all references, the given name of the author or editor is abbreviated to the initial only and precedes the last name. Use them all; use et al. only if names are not given. Use commas around Jr., Sr., and III in names. Abbreviate conference titles. When citing IEEE transactions, provide the issue number, page range, volume number, year, and/or month if available. When referencing a patent, provide the day and the month of issue, or application. References may not include all information; please obtain and include relevant information. Do not combine references. There must be only one reference with each number. If there is a URL included with the print reference, it can be included at the end of the reference.

Other than books, capitalize only the first word in a brief title, except for proper nouns and element symbols. For briefs published in translation journals, please give the English citation first, followed by the original foreign-language citation See the end of this document for formats and examples of common references. For a complete discussion of references and their formats, see the IEEE style manual at http://www.ieee.org/authortools.

-B Footnotes

Number footnotes separately in superscript numbers.111It is recommended that footnotes be avoided (except for the unnumbered footnote with the receipt date on the first page). Instead, try to integrate the footnote information into the text. Place the actual footnote at the bottom of the column in which it is cited; do not put footnotes in the reference list (endnotes). Use letters for table footnotes (see Table I).

Appendix A Submitting Your Brief for Review

A-A Final Stage

When you submit your final version (after your brief has been accepted), print it in two-column format, including figures and tables. You must also send your final manuscript on a disk, via e-mail, or through a Web manuscript submission system as directed by the society contact. You may use Zip for large files, or compress files using Compress, Pkzip, Stuffit, or Gzip.

Also, send a sheet of brief or PDF with complete contact information for all authors. Include full mailing addresses, telephone numbers, fax numbers, and e-mail addresses. This information will be used to send each author a complimentary copy of the journal in which the brief appears. In addition, designate one author as the “corresponding author.” This is the author to whom proofs of the brief will be sent. Proofs are sent to the corresponding author only.

A-B Review Stage Using ScholarOne® Manuscripts

Contributions to the Transactions, Journals, and Letters may be submitted electronically on IEEE’s on-line manuscript submission and peer-review system, ScholarOne® Manuscripts. You can get a listing of the publications that participate in ScholarOne at http://www.ieee.org/publications_standards/publications/authors/authors_submission.html. First check if you have an existing account. If there is none, please create a new account. After logging in, go to your Author Center and click “Submit First Draft of a New Manuscript.”

Along with other information, you will be asked to select the subject from a pull-down list. Depending on the journal, there are various steps to the submission process; you must complete all steps for a complete submission. At the end of each step you must click “Save and Continue”; just uploading the brief is not sufficient. After the last step, you should see a confirmation that the submission is complete. You should also receive an e-mail confirmation. For inquiries regarding the submission of your brief on ScholarOne Manuscripts, please contact oprs-support@ieee.org or call +1 732 465 5861.

ScholarOne Manuscripts will accept files for review in various formats. Please check the guidelines of the specific journal for which you plan to submit.

You will be asked to file an electronic copyright form immediately upon completing the submission process (authors are responsible for obtaining any security clearances). Failure to submit the electronic copyright could result in publishing delays later. You will also have the opportunity to designate your article as “open access” if you agree to pay the IEEE open access fee.

A-C Final Stage Using ScholarOne Manuscripts

Upon acceptance, you will receive an email with specific instructions regarding the submission of your final files. To avoid any delays in publication, please be sure to follow these instructions. Most journals require that final submissions be uploaded through ScholarOne Manuscripts, although some may still accept final submissions via email. Final submissions should include source files of your accepted manuscript, high quality graphic files, and a formatted pdf file. If you have any questions regarding the final submission process, please contact the administrative contact for the journal.

In addition to this, upload a file with complete contact information for all authors. Include full mailing addresses, telephone numbers, fax numbers, and e-mail addresses. Designate the author who submitted the manuscript on ScholarOne Manuscripts as the “corresponding author.” This is the only author to whom proofs of the brief will be sent.

A-D Copyright Form

Authors must submit an electronic IEEE Copyright Form (eCF) upon submitting their final manuscript files. You can access the eCF system through your manuscript submission system or through the Author Gateway. You are responsible for obtaining any necessary approvals and/or security clearances. For additional information on intellectual property rights, visit the IEEE Intellectual Property Rights department web page at http://www.ieee.org/publications_standards/publications/rights/index.html.

Appendix B IEEE Publishing Policy

The general IEEE policy requires that authors should only submit original work that has neither appeared elsewhere for publication, nor is under review for another refereed publication. The submitting author must disclose all prior publication(s) and current submissions when submitting a manuscript. Do not publish “preliminary” data or results. The submitting author is responsible for obtaining agreement of all coauthors and any consent required from employers or sponsors before submitting an article. The IEEE Transactions and Journals Department strongly discourages courtesy authorship; it is the obligation of the authors to cite only relevant prior work.

The IEEE Transactions and Journals Department does not publish conference records or proceedings, but can publish articles related to conferences that have undergone rigorous peer review. Minimally, two reviews are required for every article submitted for peer review.

Appendix C Publication Principles

The two types of contents of that are published are; 1) peer-reviewed and 2) archival. The Transactions and Journals Department publishes scholarly articles of archival value as well as tutorial expositions and critical reviews of classical subjects and topics of current interest.

Authors should consider the following points:

Technical briefs submitted for publication must advance the state of knowledge and must cite relevant prior work. 2. 2.

The length of a submitted brief should be commensurate with the importance, or appropriate to the complexity, of the work. For example, an obvious extension of previously published work might not be appropriate for publication or might be adequately treated in just a few pages. 3. 3.

Authors must convince both peer reviewers and the editors of the scientific and technical merit of a brief; the standards of proof are higher when extraordinary or unexpected results are reported. 4. 4.

Because replication is required for scientific progress, briefs submitted for publication must provide sufficient information to allow readers to perform similar experiments or calculations and use the reported results. Although not everything need be disclosed, a brief must contain new, useable, and fully described information. For example, a specimen’s chemical composition need not be reported if the main purpose of a brief is to introduce a new measurement technique. Authors should expect to be challenged by reviewers if the results are not supported by adequate data and critical details. 5. 5.

Briefs that describe ongoing work or announce the latest technical achievement, which are suitable for presentation at a professional conference, may not be appropriate for publication.

Appendix D Reference Examples

• •

Basic format for books:

J. K. Author, “Title of chapter in the book,” in Title of His Published Book, xth ed. City of Publisher, (only U.S. State), Country: Abbrev. of Publisher, year, ch. $x$, sec. $x$, pp. xxx–xxx.

See [1, 2].

• •

Basic format for periodicals:

J. K. Author, “Name of brief,” Abbrev. Title of Periodical, vol. x, no. $x,$pp*. xxx–xxx, *Abbrev. Month, year, DOI. 10.1109.XXX.123456.

See [3]–[5].

• •

Basic format for reports:

J. K. Author, “Title of report,” Abbrev. Name of Co., City of Co., Abbrev. State, Country, Rep. xxx, year.

See [6, 7].

• •

Basic format for handbooks:

Name of Manual/Handbook, x ed., Abbrev. Name of Co., City of Co., Abbrev. State, Country, year, pp. xxx–xxx.

See [8, 9].

• •

Basic format for books (when available online):

J. K. Author, “Title of chapter in the book,” in Title of Published Book, $x$th ed. City of Publisher, State, Country: Abbrev. of Publisher, year, ch. $x$, sec. $x$, pp. xxx–xxx. [Online]. Available: http://www.web.com

See [10]–[13].

• •

Basic format for journals (when available online):

J. K. Author, “Name of brief,” Abbrev. Title of Periodical, vol. $x$, no. $x$, pp. xxx–xxx, Abbrev. Month, year. Accessed on: Month, Day, year, DOI: 10.1109.XXX.123456, [Online].

See [14]–[16].

• •

*Basic format for briefs presented at conferences (when available online): *

J.K. Author. (year, month). Title. presented at abbrev. conference title. [Type of Medium]. Available: site/path/file

See [17].

• •

Basic format for reports and handbooks (when available online):

J. K. Author. “Title of report,” Company. City, State, Country. Rep. no., (optional: vol./issue), Date. [Online] Available: site/path/file

See [18, 19].

• •

*Basic format for computer programs and electronic documents (when available online): *

Legislative body. Number of Congress, Session. (year, month day). Number of bill or resolution, Title. [Type of medium]. Available: site/path/file

**NOTE: ****ISO recommends that capitalization follow the accepted practice for the language or script in which the information is given.

**See [20].

• •

Basic format for patents (when available online):

Name of the invention, by inventor’s name. (year, month day). Patent Number [Type of medium]. Available: site/path/file

See [21].

• •

Basic format**for conference proceedings (published):

J. K. Author, “Title of brief,” in Abbreviated Name of Conf., City of Conf., Abbrev. State (if given), Country, year, pp. xxxxxx.

See [22].

• •

Example for briefs presented at conferences (unpublished):

See [23].

• •

Basic format for patents$:$

J. K. Author, “Title of patent,” U.S. Patent x xxx xxx, Abbrev. Month, day, year.

See [24].

• •

Basic format for theses (M.S.) and dissertations (Ph.D.):

J. K. Author, “Title of thesis,” M.S. thesis, Abbrev. Dept., Abbrev. Univ., City of Univ., Abbrev. State, year. 2. 2.

J. K. Author, “Title of dissertation,” Ph.D. dissertation, Abbrev. Dept., Abbrev. Univ., City of Univ., Abbrev. State, year.

See [25, 26].

• •

Basic format for the most common types of unpublished references:

J. K. Author, private communication, Abbrev. Month, year. 2. 2.

J. K. Author, “Title of brief,” unpublished. 3. 3.

J. K. Author, “Title of brief,” to be published.

See [27]–[29].

• •

Basic formats for standards:

Title of Standard, Standard number, date. 2. 2.

Title of Standard, Standard number, Corporate author, location, date.

See [30, 31].

• •

Article number in reference examples:

See [32, 33].

• •

Example when using et al.:

See [34].