On the Optimal Stacking of Information-plus-Noise Matrices - Archive ouverte HAL Access content directly
Journal Articles IEEE Transactions on Signal Processing Year : 2011

## On the Optimal Stacking of Information-plus-Noise Matrices

Ryan Oyvind
• Function : Author

#### Abstract

Observations of the form D + X, where D is a matrix representing information, and X is a random matrix representing noise, can be grouped into a compund observation matrix, on the same information + noise form. There are many ways the observations can be stacked into such a matrix, for instance vertically, horizontally, or quadratically. An unbiased estimator for the spectrum of D can be formulated for each stacking scenario in the case of Gaussian noise. We compare these spectrum estimators for the different stacking scenarios, and show that all kinds of stacking actually decrease the variance of the corresponding spectrum estimators when compared to just taking an average of the observations, and find which stacking is optimal in this sense. When the number of observations grow, however, it is shown that the difference between the estimators is marginal. with only the cases of vertical and horizontal stackings having a higher variance asymptotically.

### Dates and versions

hal-00648043 , version 1 (05-12-2011)

### Identifiers

• HAL Id : hal-00648043 , version 1
• DOI :

### Cite

Ryan Oyvind. On the Optimal Stacking of Information-plus-Noise Matrices. IEEE Transactions on Signal Processing, 2011, 59 (2), pp.506-514. ⟨10.1109/TSP.2010.2091276⟩. ⟨hal-00648043⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

51 View
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8327620029449463, "perplexity": 1960.041562819041}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949644.27/warc/CC-MAIN-20230331144941-20230331174941-00304.warc.gz"}