Hadamard imaging

R. Riesenberg, and U. Dillner, HADAMARD Imaging Spectrometers, SPIE s 44th Annual Meeting Exhibition, Optical Science, Engineering and Instrumentation, Denver, USA, Proceedings of SPIE, Vol. 3753, pp. 203-213, (18-23 July 1999). 

There is a number of alternative Raman imaging techniques these include using the Hadamard transform technique [25-27], and such as fibre-bundle image compression, which however is not yet commercially available [26-31]. However in the latter approach, the laser power on the sample could be high, since the beam is not defocused, and the possibility of sample damage increases. 

Hanley, Q. S., Verveer, P. J. and Jovin, T. M. (1999). Spectral imaging in a programmable array microscope by hadamard transform fluorescence spectroscopy. Appl. Spectrosc. 53, 1-10. 

Due to the fact that the first phase of manipulation of such data is usually a fast scanning of the entire collection, a highly compressed representation of uniformly coded data is essential in order to accelerate the handling. After the search reduces the collection to a smaller group in which the target object is supposed to be, the full (extended) representation of objects can be invoked if necessary for further manipulation. In the next sections we shall discuss the use of two methods, Fast Fourier Transformation (FFT) and Fast Hadamard Transformation (FHT), for the reduction of object representations and show by some examples in 1- and 2-dimensional patterns (spectra, images) how the explained procedures can be used... 

Hadamard transform spectroscopy existed long before Raman imaging, as a form of multiplex spectroscopy. A Hadamard mask is an array of clear and... 

Figure 11.27. Schematic of a Hadamard transform imaging Raman spectrometer. The mask is moved between CCD exposures by the stepping motor, and the cylindrical lens creates a line focus along the entrance slit to an imaging spectrograph. (Adapted from Reference 24.)...

R. A. DeVerse, R. M. Hammaker, and W.G. Fateley, An Improved Hadamard Encoding Mask for Multiplexed Raman Imaging Using Single Channel Detection, J. Mol. Struct, 521, 77-88 (2000). 

A. Wuttig, and R. Riesenberg, Sensitive Hadamard Transform Imaging Spectrometer with a simple MEMS,Prac. SPIE, 4881, pp. 167-178, (2003). 

C M. Wehlburg, J. C. Wehlburg, S. M. Gentry, and J. L Smith, Optimization and characterization of an imaging Hadamard spectrometer, Proc. SPIE, 4381, p. 506-515, Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VII, Sylvia S. Shen, Michael R. Descour, Eds., (2001). 

Stochastic excitation with m sequences and the use of the Hadamard transformation have been investigated in NMR spectroscopy [Kail, Zie2] as well as in NMR imaging [Chal]. Processing of the nonlinear response to m sequences by Hadamard and Fourier transformation results in signal distortions reminiscent of noise, which are caused by the nonlinear parts of the response [B1U2]. 

Shaped and composite pulses are devoid of free precession periods between periods of rf excitation. Pulse sequences combine both free precession and rf pulses. Clearly, given the manifold of shaped and composite pulses, there is an infinite number of pulse sequences which can be constructed from them. A variety of such sequences is used for volume localization. This topic is discussed in Section 10.2. Here two methods relevant to the acquisition of NMR images are reviewed. These are the DANTE technique for single-shot localization, and the Hadamard technique as an example of multi-shot localization. 

Fig. 5.3.13 Hadamard encoding and decoding for simultaneous four-slice imaging. The encoding is based on four experiments, A-D. In each experiment, all four slices are excited by a multi-frequency selective pulse. Its phase composition is determined by the rows of the Hadamard matrix H2. The image response is the sum of responses for each individual, frequency selective part of the pulse. Thus, addition and subtraction of the responses to the four experiments separates the information for each slice. This operation is equivalent to Hadamard transformation of the set of image responses. Adapted from [Miil21 with permission from Wiley-Liss. Inc., a division of John-Wiley Sons, Inc.

Hadamard spectroscopic imaging (HSI) is a technique to obtain localized spectroscopic information from n regions of interest in n scans [Boll, Hafl, Goel, Goe2, Goe4, MU14]. It is a straightforward extension of the multi-frequency selective-pulse technique... 

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