Sampling Sparsity - Revision history

Dattorro: /* History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling */

Dattorro — Thu, 25 Nov 2010 03:35:03 GMT

History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling

←Older revision		Revision as of 03:35, 25 November 2010
Line 15:		Line 15:
	The breakthrough came when Thierry Blu made the connection		The breakthrough came when Thierry Blu made the connection
	to spectral estimation methods, and the annihilation filter, also known		to spectral estimation methods, and the annihilation filter, also known
-	in error control coding. This ~~lead~~ to a complete report in 2001 [2],	+	in error control coding. This led to a complete report in 2001 [2],
	published in part as conference papers in [3] [4],		published in part as conference papers in [3] [4],
	and to a patent application [5], all in 2001.		and to a patent application [5], all in 2001.

-	This all went into a journal paper [6] '''('''published in 2002, it received the IEEE Signal Processing Society 2006 Best Paper Award''')'''	+	This all went into a journal paper [6]
		+	'''('''published in 2002, it received the IEEE Signal Processing Society 2006 Best Paper Award''')'''
	which basically shows how to sample continuous-time parametric classes of		which basically shows how to sample continuous-time parametric classes of
	signals that are very far from being bandlimited, like sequences of Dirac pulses,		signals that are very far from being bandlimited, like sequences of Dirac pulses,

Dattorro: /* History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling */

Dattorro — Wed, 24 Nov 2010 04:46:56 GMT

History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling

←Older revision		Revision as of 04:46, 24 November 2010
Line 19:		Line 19:
	and to a patent application [5], all in 2001.		and to a patent application [5], all in 2001.

-	This all went into a journal paper [6] '''('''published in 2002, ~~and which got~~ the	+	This all went into a journal paper [6] '''('''published in 2002, it received the IEEE Signal Processing Society 2006 Best Paper Award''')'''
-	IEEE Signal Processing Society ~~best paper award in 2008~~''')''',	+
	which basically shows how to sample continuous-time parametric classes of		which basically shows how to sample continuous-time parametric classes of
	signals that are very far from being bandlimited, like sequences of Dirac pulses,		signals that are very far from being bandlimited, like sequences of Dirac pulses,

Ranjelin: /* History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling */

Ranjelin — Tue, 23 Nov 2010 07:32:23 GMT

History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling

←Older revision		Revision as of 07:32, 23 November 2010
Line 16:		Line 16:
	to spectral estimation methods, and the annihilation filter, also known		to spectral estimation methods, and the annihilation filter, also known
	in error control coding. This lead to a complete report in 2001 [2],		in error control coding. This lead to a complete report in 2001 [2],
-	published in part as conference papers in [3,4],	+	published in part as conference papers in [3] [4],
	and to a patent application [5], all in 2001.		and to a patent application [5], all in 2001.

Line 35:		Line 35:

	'''(1)''' FRI sampling is a continuous-time to discrete-time sampling result,		'''(1)''' FRI sampling is a continuous-time to discrete-time sampling result,
-	whereas CS is a map from R^N to R^M.	+	whereas CS is a map from <math>\mathbb{R}^N</math> to <math>\mathbb{R}^M</math>.
	Thus, FRI is in the ''classic'' sampling tradition of Shannon and the likes.		Thus, FRI is in the ''classic'' sampling tradition of Shannon and the likes.
	To be more precise,		To be more precise,

Ranjelin: /* References */

Ranjelin — Tue, 23 Nov 2010 07:27:33 GMT

References

←Older revision		Revision as of 07:27, 23 November 2010
Line 77:		Line 77:
	[6] M. Vetterli, P. Marziliano and T. Blu, [http://bigwww.epfl.ch/publications/vetterli0201.pdf Sampling Signals with Finite Rate of Innovation], IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.		[6] M. Vetterli, P. Marziliano and T. Blu, [http://bigwww.epfl.ch/publications/vetterli0201.pdf Sampling Signals with Finite Rate of Innovation], IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.

-	[7] Pina Marziliano, [http://biblion.epfl.ch/EPFL/theses/2001/2369/EPFL_TH2369.pdf Sampling ~~Innovation~~], PhD Thesis, EPFL, Mar. 2001.	+	[7] Pina Marziliano, [http://biblion.epfl.ch/EPFL/theses/2001/2369/EPFL_TH2369.pdf Sampling Innovations], PhD Thesis, EPFL, Mar. 2001.

	[8] I. Maravic and M. Vetterli, [http://lcavwww.epfl.ch/~vetterli/SP-8-2005.pdf Sampling and Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise], IEEE Transactions on Signal Processing, Vol.53, Nr.8, pp.2788-2805, 2005.		[8] I. Maravic and M. Vetterli, [http://lcavwww.epfl.ch/~vetterli/SP-8-2005.pdf Sampling and Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise], IEEE Transactions on Signal Processing, Vol.53, Nr.8, pp.2788-2805, 2005.

Ranjelin: /* References */

Ranjelin — Tue, 23 Nov 2010 07:27:05 GMT

References

←Older revision		Revision as of 07:27, 23 November 2010
Line 77:		Line 77:
	[6] M. Vetterli, P. Marziliano and T. Blu, [http://bigwww.epfl.ch/publications/vetterli0201.pdf Sampling Signals with Finite Rate of Innovation], IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.		[6] M. Vetterli, P. Marziliano and T. Blu, [http://bigwww.epfl.ch/publications/vetterli0201.pdf Sampling Signals with Finite Rate of Innovation], IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.

-	[7] Pina Marziliano, [http://~~infoscience~~.epfl.ch/~~record~~/~~32845~~ Sampling Innovation], PhD Thesis, EPFL, Mar. 2001.	+	[7] Pina Marziliano, [http://biblion.epfl.ch/EPFL/theses/2001/2369/EPFL_TH2369.pdf Sampling Innovation], PhD Thesis, EPFL, Mar. 2001.

	[8] I. Maravic and M. Vetterli, [http://lcavwww.epfl.ch/~vetterli/SP-8-2005.pdf Sampling and Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise], IEEE Transactions on Signal Processing, Vol.53, Nr.8, pp.2788-2805, 2005.		[8] I. Maravic and M. Vetterli, [http://lcavwww.epfl.ch/~vetterli/SP-8-2005.pdf Sampling and Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise], IEEE Transactions on Signal Processing, Vol.53, Nr.8, pp.2788-2805, 2005.

Ranjelin: /* References */

Ranjelin — Tue, 23 Nov 2010 07:25:28 GMT

References

←Older revision		Revision as of 07:25, 23 November 2010
Line 60:		Line 60:

	===References===		===References===
-	All these papers are online at  http://lcavwww.epfl.ch/~vetterli/publications~~/index.html~~	+	All these papers are online:  http://lcavwww.epfl.ch/~vetterli/publications

	[1] M. Vetterli, Sampling of Piecewise Polynomial Signals, Swiss Fed.		[1] M. Vetterli, Sampling of Piecewise Polynomial Signals, Swiss Fed.

Ranjelin: /* References */

Ranjelin — Tue, 23 Nov 2010 07:24:47 GMT

References

←Older revision		Revision as of 07:24, 23 November 2010
Line 83:		Line 83:
	[9] T. Blu, P.L. Dragotti, M. Vetterli, P. Marziliano and L. Coulot, [http://bigwww.epfl.ch/publications/blu0801.pdf Sparse Sampling of Signal Innovations], IEEE Signal Processing Magazine, Vol.25, Nr.2, pp.31-40, 2008.		[9] T. Blu, P.L. Dragotti, M. Vetterli, P. Marziliano and L. Coulot, [http://bigwww.epfl.ch/publications/blu0801.pdf Sparse Sampling of Signal Innovations], IEEE Signal Processing Magazine, Vol.25, Nr.2, pp.31-40, 2008.

-	[10] P.L. Dragotti, M. Vetterli and T. Blu, [http://bigwww.epfl.ch/publications/dragotti0701.pdf Sampling Moments and Reconstructing	+	[10] P.L. Dragotti, M. Vetterli and T. Blu, [http://bigwww.epfl.ch/publications/dragotti0701.pdf Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix], IEEE Transactions on Signal Processing, Vol.55, Nr.5, Part 1, pp.1741-1757, 2007.
-	Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix], IEEE Transactions on Signal Processing, Vol.55, Nr.5, Part 1, pp.1741-1757, 2007.	+

Ranjelin at 07:22, 23 November 2010

Ranjelin — Tue, 23 Nov 2010 07:22:13 GMT

←Older revision		Revision as of 07:22, 23 November 2010
Line 65:		Line 65:
	Inst. Technol., Lausanne, Switzerland, LCAV, 1999.		Inst. Technol., Lausanne, Switzerland, LCAV, 1999.

-	[2] M. Vetterli, P. Marziliano, and T. Blu, ~~[http://bigwww.epfl.ch/publications/vetterli0201.pdf~~ Sampling Signals with Finite Rate of Innovation], Swiss Fed. Inst. Technol., Lausanne, Switzerland, DSC-017, 2001.	+	[2] M. Vetterli, P. Marziliano, and T. Blu, Sampling Signals with Finite Rate of Innovation, Swiss Fed. Inst. Technol., Lausanne, Switzerland, DSC-017, 2001.

	[3] M. Vetterli, P. Marziliano, and T. Blu, [http://infoscience.epfl.ch/record/34051/files/VetterliMB01b.pdf Sampling Discrete-Time Piecewise Bandlimited Signals], in Proc. Sampling Theory and Applications Workshop, Orlando, FL, May 2001, pp.97–102.		[3] M. Vetterli, P. Marziliano, and T. Blu, [http://infoscience.epfl.ch/record/34051/files/VetterliMB01b.pdf Sampling Discrete-Time Piecewise Bandlimited Signals], in Proc. Sampling Theory and Applications Workshop, Orlando, FL, May 2001, pp.97–102.
Line 75:		Line 75:
	Sampling Method, Reconstruction Method, and Device for Sampling and/or Reconstructing Signals, Patent application, filed March 26 2001.		Sampling Method, Reconstruction Method, and Device for Sampling and/or Reconstructing Signals, Patent application, filed March 26 2001.

-	[6] M. Vetterli, P. Marziliano and T. Blu, ~~Sampling Signals~~ with Finite Rate of Innovation, IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.	+	[6] M. Vetterli, P. Marziliano and T. Blu, [http://bigwww.epfl.ch/publications/vetterli0201.pdf Sampling Signals with Finite Rate of Innovation], IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.

-	[7] Pina Marziliano, ~~Sampling Innovation, PhD Thesis, EPFL, Mar. 2001. ~~	+	[7] Pina Marziliano, [http://infoscience.epfl.ch/record/32845 Sampling Innovation], PhD Thesis, EPFL, Mar. 2001.
-	http://infoscience.epfl.ch/record/32845	+

-	[8] I. Maravic and M. Vetterli, ~~Sampling and~~ Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise, IEEE Transactions on Signal Processing, Vol.53, Nr.8, pp.2788-2805, 2005.	+	[8] I. Maravic and M. Vetterli, [http://lcavwww.epfl.ch/~vetterli/SP-8-2005.pdf Sampling and Reconstruction of Signals with Finite Rate of Innovation in the Presence of Noise], IEEE Transactions on Signal Processing, Vol.53, Nr.8, pp.2788-2805, 2005.

-	[9] T. Blu, P.L. Dragotti, M. Vetterli, P. Marziliano and L. Coulot, ~~Sparse Sampling~~ of Signal Innovations, IEEE Signal Processing Magazine, Vol.25, Nr.2, pp.31-40, 2008.	+	[9] T. Blu, P.L. Dragotti, M. Vetterli, P. Marziliano and L. Coulot, [http://bigwww.epfl.ch/publications/blu0801.pdf Sparse Sampling of Signal Innovations], IEEE Signal Processing Magazine, Vol.25, Nr.2, pp.31-40, 2008.

-	[10] P.L. Dragotti, M. Vetterli and T. Blu, ~~Sampling Moments~~ and Reconstructing	+	[10] P.L. Dragotti, M. Vetterli and T. Blu, [http://bigwww.epfl.ch/publications/dragotti0701.pdf Sampling Moments and Reconstructing
-	Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix, IEEE Transactions on Signal Processing, Vol.55, Nr.5, Part 1, pp.1741-1757, 2007.	+	Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix], IEEE Transactions on Signal Processing, Vol.55, Nr.5, Part 1, pp.1741-1757, 2007.

Ranjelin: /* References */

Ranjelin — Tue, 23 Nov 2010 07:10:56 GMT

References

←Older revision		Revision as of 07:10, 23 November 2010
Line 65:		Line 65:
	Inst. Technol., Lausanne, Switzerland, LCAV, 1999.		Inst. Technol., Lausanne, Switzerland, LCAV, 1999.

-	[2] M. Vetterli, P. Marziliano, and T. Blu, Sampling Signals with Finite Rate of Innovation, Swiss Fed. Inst. Technol., Lausanne, Switzerland, DSC-017, 2001.	+	[2] M. Vetterli, P. Marziliano, and T. Blu, [http://bigwww.epfl.ch/publications/vetterli0201.pdf Sampling Signals with Finite Rate of Innovation], Swiss Fed. Inst. Technol., Lausanne, Switzerland, DSC-017, 2001.

-	[3] M. Vetterli, P. Marziliano, and T. Blu, Sampling Discrete-Time Piecewise	+	[3] M. Vetterli, P. Marziliano, and T. Blu, [http://infoscience.epfl.ch/record/34051/files/VetterliMB01b.pdf Sampling Discrete-Time Piecewise Bandlimited Signals], in Proc. Sampling Theory and Applications Workshop, Orlando, FL, May 2001, pp.97–102.
-	Bandlimited Signals, in Proc. Sampling Theory and Applications Workshop, Orlando, FL, May 2001, pp.97–102.	+

-	[4] M. Vetterli, P. Marziliano, and T. Blu, A Sampling Theorem for Periodic Piecewise Polynomial Signals,	+	[4] M. Vetterli, P. Marziliano, and T. Blu, [http://infoscience.epfl.ch/record/34050/files/VetterliMB01a.pdf A Sampling Theorem for Periodic Piecewise Polynomial Signals],
	in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Salt Lake City, UT, May 2001.		in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Salt Lake City, UT, May 2001.

	[5] M. Vetterli, P. Marziliano, and T. Blu,		[5] M. Vetterli, P. Marziliano, and T. Blu,
-	Sampling Method, Reconstruction Method, and Device for Sampling and/or Reconstructing Signals,	+	Sampling Method, Reconstruction Method, and Device for Sampling and/or Reconstructing Signals, Patent application, filed March 26 2001.
-	Patent application, filed March 26 2001.	+

	[6] M. Vetterli, P. Marziliano and T. Blu, Sampling Signals with Finite Rate of Innovation, IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.		[6] M. Vetterli, P. Marziliano and T. Blu, Sampling Signals with Finite Rate of Innovation, IEEE Transactions on Signal Processing, Vol.50, Nr.6, pp.1417-1428, 2002.

Dattorro: /* History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling */

Dattorro — Tue, 23 Nov 2010 05:51:44 GMT

History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling

←Older revision		Revision as of 05:51, 23 November 2010
Line 1:		Line 1:
	==History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling==		==History of Finite Rate of Innovation (FRI) Sampling, or Sparse Sampling==
		+	Martin Vetterli

	In the late 1990's, we got interested to see if signals which are far		In the late 1990's, we got interested to see if signals which are far
Line 18:		Line 19:
	and to a patent application [5], all in 2001.		and to a patent application [5], all in 2001.

-	This all went into a journal paper [6] (published in 2002, and which got the	+	This all went into a journal paper [6] '''('''published in 2002, and which got the
-	IEEE Signal Processing Society best paper award in 2008),	+	IEEE Signal Processing Society best paper award in 2008''')''',
	which basically shows how to sample continuous-time parametric classes of		which basically shows how to sample continuous-time parametric classes of
	signals that are very far from being bandlimited, like sequences of Dirac pulses,		signals that are very far from being bandlimited, like sequences of Dirac pulses,
Line 42:		Line 43:
	for certain mapping matrices and sparsities.		for certain mapping matrices and sparsities.
	FRI can be done in a discrete set-up, and then, it is a version of compressed		FRI can be done in a discrete set-up, and then, it is a version of compressed
-	sensing with particular matrices (convolution matrices, Fourier matrices, because	+	sensing with particular matrices '''('''convolution matrices, Fourier matrices, because
-	the sampling is uniform and shift-invariant).	+	the sampling is uniform and shift-invariant''')'''.
	But FRI on a real interval is like CS with an infinite matrix.		But FRI on a real interval is like CS with an infinite matrix.