OpenMS
SavitzkyGolayFilter Class Reference

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

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

Inheritance diagram for SavitzkyGolayFilter:
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Collaboration diagram for SavitzkyGolayFilter:
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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...
 
ProgressLoggeroperator= (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 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...
 
DefaultParamHandleroperator= (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 ParamgetParameters () const
 Non-mutable access to the parameters. More...
 
const ParamgetDefaults () const
 Non-mutable access to the default parameters. More...
 
const StringgetName () 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_
 
ProgressLoggerImplcurrent_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< Stringsubsections_
 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 Member Functions inherited from ProgressLogger
static String logTypeToFactoryName_ (LogType type)
 Return the name of the factory product used for this log type. 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:

NameTypeDefaultRestrictionsDescription
frame_length int11  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 int4  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()

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.