Methods, of deconvolution

The convolution theorem aided us in understanding a property of the spurious component 0(x). It also hints at a method of deconvolution when applied to Eq. (86). This method is developed in Section IV of Chapter 3. 

A linear deconvolution method is one whose output elements (the restoration) can be expressed as linear combinations of the input elements. Until recently, the only seriously considered methods of deconvolution were linear. These methods can be developed and analyzed in detail by use of long-standing mathematical tools. Analysis of linear methods tends to be simpler than that of nonlinear methods, and computations are shorter. This point is especially important, because deconvolution is inherently computation intensive. It is not surprising that linear methods have historically dominated deconvolution research and applications. 

Figure 1 Schematic representation of the positional scanning method of deconvolution.

Two methods of deconvolution can be employed the standard deconvolution called DCV where the image Pc is convolved by the matrix M which describes the aperture transmission, the deconvolution called PSF to which we add a convolution of a gaussian of which the sigma is adapted to the spatial resolution (2.61 pixels SI in 40-75 keV energy band). This new convolution allows to obtain the most significant flux and to eliminate the high frequency noise [5]. 

Band intensities, if available, were taken from the references. Usually the intensities are summarized as weak, medium and strong bands. Shoulders arise from overlapping bands. Several references used the term shoulder together with the term weak. Overlapping bands may be separated by sophisticated methods of deconvolution or curve fitting. Fig. 13 shows the IR spectrum of LDPE in the range of the C-H deformation vibrations. The registrated absorption band (black curve) consists of three individual bands (dotted... 

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