crop
interpolate/binning
replace NaNs
filter images
edge preserving denoising
3D-FSD

Lasch P. Spectral pre-processing for biomedical vibrational spectroscopy and microspectroscopic imaging. Chem Intell Lab Syst 2012 117:100-114
 
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• Cut spectra, i.e. cutting in the spectral domain, and
• Crop images in the spatial domains.

	Cropping in the spatial (x,y) dimensions reduces the number of pixel spectra. Select the 'crop images' radiobutton and enter the respective values for the x- and y-spatial regions (in pixels) which should be retained. Then press 'crop' to proceed.
Note that the 'cut/crop' function overwrites all existing data blocks (see also Internal Data Organization, Table IV).   The parameter used for 'cut' are stored within the program workspace and are accessible through the File Info menu bar (File Info → File Manipulations → type of data block).

• interpolation in the spectral domain, and
• interpolation in the spatial domains.

 

Interpolation in the spatial [x,y] dimensions changes the number of pixel spectra. The number of pixel spectra can be increased, or decreased (binning). For example, if the actual number of pixel spectra is 64 × 64 (cf. edit field '# of pixel in x/y') and the settings for 'new xdim/ydim' are 32 × 32, the program performs a two-dimensional interpolation in the spatial domains which will reduce the map size by a factor of 2 × 2. Note that spatial HSI dimensions can be changed to any sizes, e.g. spatial interpolation from an initial HSI size of 64 × 64 to a size of 30 × 32 will be possible. Note also that enlarged images may require a lot of memory resources (RAM)   Select the 'interpolate in the spatial dimensions' radiobutton and enter the desired image size in x-direction. Then press 'enter' - the value in the field 'new ydim' will be automatically updated. To change the aspect ratio between the x- and y-dimensions uncheck the checkbox 'fix aspect ratio'. Then press 'interpolate' to proceed.

The 'interpolate / pixel binning' function overwrites all existing data blocks (see also Internal Data Organization, Table III).   The parameter used for interpolate are stored within the program workspace and are accessible through File Info menu (File Info → File Manipulations → type of data block). These parameters are also provided in the report window of CytoSpec.

quality test

edge preserving denoising

3D Fourier-self deconvolution

• The [x,y] coordinates of all NaN pixel spectra are identified. CytoSpec returns a warning message in cases where more than 15% of the pixel spectra are NaN spectra.
• CytoSpec determines whether the NaN spectra are located (i) at the the corners of the image, (ii) at the margins of the image, or (iii) in the center of the image.
• The coordinates of the pixel neighbors are obtained and the number of non-NaN neighbors is determined.
• Mean spectra are obtained from non-NaN neighbors if the number of non-NaN neighbor spectra is larger than zero (corner case i), one (edge case, ii), or two (center case, iii).
• Mean spectra are used to replace the NaN spectra.
• The algorithm is repeated until all NaN spectra are replaced by non-NaN mean spectra.

1. This function should only be used to preprocess data prior to edge preserving denoising, 3D Fourier-self deconvolution, or spatial filtering.
2. The function 'replace NaN' should ideally only be employed in cases were single NaN spectra prevent application of the above mentioned functions.
3. Try to avoid replacing NaN spectra from large image regions.
4. Do not interpret spectra from regions with interpolated data.
5. Replacing NaN spectra is not possible in cases where more than one third (34%) of pixel spectra are NaN spectra.

Wikipedia, Total variation denoising

filter images

Wikipedia, Total variation denoising

source block: allows selecting the type of source data (original, preprocessed, derivative or deconvolution data).   lambda: initial value of the regularization parameter λ defining the strength of smoothing. When λ = 0 there will be no smoothing. As λ → ∞ however, the output data is forced to have smaller total variation (TV) which means that the output is less like the input data. In this way noise (but also parts of the signal) are removed. The choice of the regularization parameter λ thus defines the amount of noise removal. Note that the parameter λ represents in fact λ(0) - an initialization parameter which will be adapted at each iteration step.   error tol. (error tolerance): the central parameter of the iterative procedure. The error tolerance value and the noise in the image data are employed to adapt the parameter λ at each iteration cycle. The higher the value of the error tolerance, the shorter the runtime of the routine and the lower the power of edge-preserving denoising.   # iterations (number of iterations, n): EPD uses a fast iterative procedure to minimize the total variation of the image plane data. This popupmenu allows defining the maximum number of allowed iterations which might be useful to reduce computational efforts in case of large HSI data sets. Note that the iterative procedure of EPD is executed for each individual image of the HSI. Large values of n may thus result in long EPD computation times.

exit criter. the exit criterion defines the conditions for exiting the iterative cycle and serves as a threshold of the 'change' observed between two consecutive iterations, whereby 'change' is determined on the basis of the following expression: change = norm(x2-x1,'fro')/sqrt(numel(x1)), with x2 being the image data of the actual iteration cycle and x1 being the image data at the previous iteration cycle. If the exit criterion chosen is reached within the given number of iterations, then the iterative loop will be left immediately. If the criterion has not been reached after n iterations, the loop will be left in cases where the error value is less than 10 × the exit criterion. Otherwise, the iterative cycle will be continued until a maximum of 10 × n iterations. The iteration loop will be unconditionally left after this regardless of the change value and CytoSpec displays warning messages in the report window. In such cases it is recommended to modify EPD parameters accordingly and re-run EPD.   verbose mode: provides additional details of the EPD procedure in CytoSpec's report window.

Rudin, L. I.; Osher, S.; Fatemi, E. Nonlinear total variation based noise removal algorithms. Physica D 1992 60 (1–4): 259–268.
 
Chambolle, A. An Algorithm for Total Variation Minimization and Applications. J Math Imag 2004 Vis 20:89–97.
 
Alexandrov T, Lasch P, Segmentation of confocal Raman microspectroscopic imaging data using edge-preserving denoising and clustering. Anal Chem. 2013 18;85(12):5676-83.
(An example of EPD based on Raman microspectroscopy data; note that an alternative EPD method has been used)

blind deconvolution

J.K. Kauppinen, D.J. Moffat, H.H. Mantsch, D.G. Cameron, Fourier Self-Deconvolution: a method for resolving intrinsically overlapped bands. Appl Spectrosc. 35(3) 1981. 271-276.
J.K. Kauppinen, D.J. Moffat, H.H. Mantsch, D.G. Cameron, Self-deconvolution and first order derivatives using Fourier transforms. Anal Chem. 53(9) 1981. 1454-1457.
J.K. Kauppinen, D.J. Moffat, H.H. Mantsch, D.G. Cameron, Noise in Fourier self-deconvolution. Appl. Opt. 20(3) 1981. 1866-.
 

• Exponential functions of the form f(i) = exp(2 × π × γ × |i|) are defined in the x-,y- (spatial) and λ- (spectral) dimensions.
• These exponential functions f(x), f(y) and f(λ) are in the following multiplied to form a 3D exponential function E(x,y,λ)
• A 3D damping function is generated in the same way: Damping functions are defined for the x-,y- and λ-dimensions according to D(i) = [1-(|i|/k(i))]², for |i| ≤ k(i) and D(i) = 0 for |i| > k(i). The 3D-damping D(x,y,λ) function is produced by multiplication of D(x), D(y) and D(λ).
• The deconvolution function F(x,y,λ) is obtained as the product of the 3D exponential E(x,y,λ) and 3D damping D(x,y,λ) function
• The 3D HSI data cube C(x,y,λ) is Fourier transformed.
• The Fourier transformed data is multiplied by the deconvolution function F(x,y,λ)
• Finally, the product is inversely Fourier transformed to get the resolution-enhanced (deconvoluted) HSI data.

Lasch P. Naumann D. Spatial Resolution in Infrared Microspectroscopic Imaging of Tissues. Biochim Biophys Acta (BBA) - Biomembranes 2006 1758(7):814-29.