SavitzkyGolayFilter Class Reference

Computes the Savitzky-Golay filter coefficients using QR decomposition. More...

#include <OpenMS/PROCESSING/SMOOTHING/SavitzkyGolayFilter.h>

Inheritance diagram for SavitzkyGolayFilter:

Collaboration diagram for SavitzkyGolayFilter:

Public Member Functions
	SavitzkyGolayFilter ()
	Constructor. More...
	~SavitzkyGolayFilter () override
	Destructor. More...
template<class InputIt , class OutputIt >
void	filter (InputIt first, InputIt last, OutputIt d_first)
void	filter (MSSpectrum &spectrum)
	Removed the noise from an MSSpectrum containing profile data. More...
void	filter (MSChromatogram &chromatogram)
	Removed the noise from an MSChromatogram. More...
void	filterExperiment (PeakMap &map)
	Removed the noise from an MSExperiment containing profile data. More...
Public Member Functions inherited from ProgressLogger
	ProgressLogger ()
	Constructor. More...
virtual	~ProgressLogger ()
	Destructor. More...
	ProgressLogger (const ProgressLogger &other)
	Copy constructor. More...
ProgressLogger &	operator= (const ProgressLogger &other)
	Assignment Operator. More...
void	setLogType (LogType type) const
	Sets the progress log that should be used. The default type is NONE! More...
LogType	getLogType () const
	Returns the type of progress log being used. More...
void	setLogger (ProgressLoggerImpl *logger)
	Sets the logger to be used for progress logging. More...
void	startProgress (SignedSize begin, SignedSize end, const String &label) const
	Initializes the progress display. More...
void	setProgress (SignedSize value) const
	Sets the current progress. More...
void	endProgress (UInt64 bytes_processed=0) const
void	nextProgress () const
	increment progress by 1 (according to range begin-end) More...
Public Member Functions inherited from DefaultParamHandler
	DefaultParamHandler (const String &name)
	Constructor with name that is displayed in error messages. More...
	DefaultParamHandler (const DefaultParamHandler &rhs)
	Copy constructor. More...
virtual	~DefaultParamHandler ()
	Destructor. More...
DefaultParamHandler &	operator= (const DefaultParamHandler &rhs)
	Assignment operator. More...
virtual bool	operator== (const DefaultParamHandler &rhs) const
	Equality operator. More...
void	setParameters (const Param &param)
	Sets the parameters. More...
const Param &	getParameters () const
	Non-mutable access to the parameters. More...
const Param &	getDefaults () const
	Non-mutable access to the default parameters. More...
const String &	getName () const
	Non-mutable access to the name. More...
void	setName (const String &name)
	Mutable access to the name. More...
const std::vector< String > &	getSubsections () const
	Non-mutable access to the registered subsections. More...

Protected Member Functions
void	updateMembers_ () override
	This method is used to update extra member variables at the end of the setParameters() method. More...
Protected Member Functions inherited from DefaultParamHandler
void	defaultsToParam_ ()
	Updates the parameters after the defaults have been set in the constructor. More...

Protected Attributes
std::vector< double >	coeffs_
	Coefficients. More...
UInt	frame_size_
	UInt of the filter kernel (number of pre-tabulated coefficients) More...
UInt	order_
	The order of the smoothing polynomial. More...
Protected Attributes inherited from ProgressLogger
LogType	type_
time_t	last_invoke_
ProgressLoggerImpl *	current_logger_
Protected Attributes inherited from DefaultParamHandler
Param	param_
	Container for current parameters. More...
Param	defaults_
	Container for default parameters. This member should be filled in the constructor of derived classes! More...
std::vector< String >	subsections_
	Container for registered subsections. This member should be filled in the constructor of derived classes! More...
String	error_name_
	Name that is displayed in error messages during the parameter checking. More...
bool	check_defaults_
	If this member is set to false no checking if parameters in done;. More...
bool	warn_empty_defaults_
	If this member is set to false no warning is emitted when defaults are empty;. More...

Additional Inherited Members
Public Types inherited from ProgressLogger
enum	LogType { CMD , GUI , NONE }
	Possible log types. More...
Static Public Member Functions inherited from DefaultParamHandler
static void	writeParametersToMetaValues (const Param &write_this, MetaInfoInterface &write_here, const String &key_prefix="")
	Writes all parameters to meta values. More...
Static Protected Attributes inherited from ProgressLogger
static int	recursion_depth_

Detailed Description

Computes the Savitzky-Golay filter coefficients using QR decomposition.

This class represents a Savitzky-Golay lowpass-filter. The idea of the Savitzky-Golay filter is to find filtercoefficients that preserve higher moments, which means to approximate the underlying function within the moving window by a polynomial of higher order (typically quadratic or quartic). Therefore we least-squares fit for each data point a polynomial to all points \( f_i \) in the window and set \(g_i\) to be the value of that polynomial at position \( i \). This method is superior to adjacent averaging because it tends to preserve features of the data such as peak height and width, which are usually 'washed out' by adjacent averaging.

Because of the linearity of the problem, we can reduce the work computing by fitting in advance, for fictious data consisting of all zeros except for a singe 1 and then do the fits on the real data just by taking linear combinations. There are a particular sets of filter coefficients \( c_n \) which accomplish the process of polynomial least-squares fit inside a moving window. To get the symmetric coefficient-matrix \(C \in R^{frameSize \times frameSize}\) with

\[ C= \left[ \begin{array}{cccc} c_{0,0} & c_{0,1} & \cdots & c_{0,frameSize-1} \\ \vdots & & & \vdots \\ c_{frameSize-1,0} & c_{frameSize-1,2} & \ldots & c_{frameSize-1,frameSize-1} \end{array} \right]\]

The first (last) \( \frac{frameSize}{2} \) rows of \( C \) we need to smooth the first (last) \( frameSize \) data points of the signal. So we use for the smoothing of the first data point the data point itself and the next \( frameSize-1 \) future points. For the second point we take the first datapoint, the data point itself and \( frameSize-2 \) of rightward data points... . We compute the Matrix \( C \) by solving the underlying least-squares problems with the singular value decomposition. Here we demonstrate the computation of the first row of a coefficient-matrix \( C \) for a Savitzky-Golay Filter of order=3 and frameSize=5: The design-matrix for the least-squares fit of a linear combination of 3 basis functions to 5 data points is:

\[ A=\left[ \begin{array}{ccc} x_0^0 & x_0^1 & x_0^2 \\ \\ x_1^0 & x_1^1 & x_1^2 \\ \\ x_2^0 & x_2^1 & x_2^2 \\ \\ x_3^0 & x_3^1 & x_3^2 \\ \\ x_4^0 & x_4^1 & x_4^2 \end{array} \right]. \]

To smooth the first data point we have to create a design-matrix with \( x=[0,\ldots, frameSize-1] \). Now we have to solve the over-determined set of \( frameSize \) linear equations

\[ Ac=b \]

where \( b=[1,0,\ldots,0] \) represents the fictious data. Therefore we solve the normal equations of the least-squares problem

\[ A^TAc=A^Tb. \]

Now, it is possible to get

\[ c_n=\sum_{m=0}^8 \{(A^TA)^{-1}\}_{0,m} n^m, \]

with \( 0\le n \le 8\). Because we only need one row of the inverse matrix, it is possible to use LU decomposition with only a single backsubstitution. The vector \(c=[c_0,\ldots,c_8] \) represents the wanted coefficients. Note that the solution of a least-squares problem directly from the normal equations is faster than the singular value decomposition but rather susceptible to roundoff error!

Note

This filter works only for uniform profile data! A polynomial order of 4 is recommended. The bigger the frame size the smoother the signal (the more detail information get lost!). The frame size corresponds to the number of filter coefficients, so the width of the smoothing interval is given by frame_size*spacing of the profile data.

The data must be sorted according to ascending m/z!

Parameters of this class are:

Name	Type	Default	Restrictions	Description
frame_length	int	11		The number of subsequent data points used for smoothing. This number has to be uneven. If it is not, 1 will be added.
polynomial_order	int	4		Order or the polynomial that is fitted.

Note:

• If a section name is documented, the documentation is displayed as tooltip.
• Advanced parameter names are italic.

Constructor & Destructor Documentation

SavitzkyGolayFilter()

SavitzkyGolayFilter

(

)

Constructor.

~SavitzkyGolayFilter()

~SavitzkyGolayFilter ( )

override

Destructor.

Member Function Documentation

filter() [1/3]

void filter ( InputIt  first, InputIt  last, OutputIt  d_first  )

inline

filter() [2/3]

void filter ( MSChromatogram &  chromatogram )

inline

Removed the noise from an MSChromatogram.

filter() [3/3]

void filter ( MSSpectrum &  spectrum )

inline

Removed the noise from an MSSpectrum containing profile data.

filterExperiment()

void filterExperiment ( PeakMap &  map )

inline

Removed the noise from an MSExperiment containing profile data.

References MSExperiment::getChromatogram(), MSExperiment::getChromatograms(), and MSExperiment::size().

updateMembers_()

void updateMembers_ ( )

overrideprotectedvirtual

This method is used to update extra member variables at the end of the setParameters() method.

Also call it at the end of the derived classes' copy constructor and assignment operator.

The default implementation is empty.

Reimplemented from DefaultParamHandler.

Member Data Documentation

coeffs_

std::vector<double> coeffs_

protected

Coefficients.

frame_size_

UInt frame_size_

protected

UInt of the filter kernel (number of pre-tabulated coefficients)

order_

UInt order_

protected

The order of the smoothing polynomial.