The helical coordinate |

**Jon Claerbout**

For many years, it has been true that
our most powerful signal-analysis techniques
are in *one*-dimensional space,
while our most important applications are in *multi*dimensional space.
The helical coordinate system makes a giant step
toward overcoming this difficulty.

Many geophysical map estimation applications appear to be multidimensional, but in reality they are one-dimensional. To see the tip of the iceberg, consider this example: On a 2-dimensional Cartesian mesh, the function

has the autocorrelation .

Likewise, on a 1-dimensional cartesian mesh,

the function

has the autocorrelation .

Observe the numbers in the 1-dimensional world are identical with the numbers in the 2-dimensional world. This correspondence is no accident.

- FILTERING ON A HELIX
- Review of 1-D recursive filters
- Multidimensional deconvolution breakthrough
- Examples of simple 2-D recursive filters
- Coding multidimensional convolution and deconvolution

- KOLMOGOROFF SPECTRAL FACTORIZATION
- Constant Q medium
- Causality in two dimensions
- Causality in three dimensions
- Blind deconvolution and the solar cube

- FACTORED LAPLACIAN == HELIX DERIVATIVE
- HELIX LOW-CUT FILTER

- SUBSCRIPTING A MULTIDIMENSIONAL HELIX
- INVERSE FILTERS AND OTHER FACTORIZATIONS

- About this document ...

2015-03-25