Alison E. Shortt

Compression of digital holograms of three-dimensional objects using wavelets.

We present the results of what we believe is the first application of wavelet analysis to the compression of complex-valued digital holograms of three-dimensional real-world objects. We achieve compression through thresholding and quantization of the wavelet coefficients, followed by lossless encoding of the quantized data.

Histogram Approaches for Lossy Compression of Digital Holograms of Three-Dimensional Objects

We present a novel nonuniform quantization compression technique-histogram quantization-for digital holograms of 3-D real-world objects. We exploit a priori knowledge of the distribution of the values in our data. We compare this technique to another histogram based approach: a modified version of Maxs algorithm that has been adapted in a straightforward manner to complex-valued 2-D signals. We conclude the compression procedure by applying lossless techniques to our quantized data. We demonstrate improvements over previous results obtained by applying uniform and nonuniform quantization techniques to the hologram data

A companding approach for nonuniform quantization of digital holograms of three-dimensional objects

We apply two novel nonuniform quantization techniques to digital holograms of three-dimensional real-world objects. Our companding approach, combines the efficiency of uniform quantization with the improved performance of nonuniform quantization. We show that the performance of companding techniques can be comparable with k-means clustering and a competitive neural network, while only requiring a single-pass processing step. The quantized holographic pixels are coded using lossless techniques for the calculation of compression ratio.

Compression of Optically Encrypted Digital Holograms Using Artificial Neural Networks

Compression and encryption/decryption are necessary for secure and efficient storage and transmission of image data. Optical encryption, as a promising application of display devices, takes advantage of both the massive parallelism inherent in optical systems and the flexibility offered by digital electronics. We encrypt real-world three-dimensional (3D) objects, captured using phase-shift interferometry, by combining a phase mask and Fresnel propagation. Compression is achieved by nonuniformly quantizing the complex-valued encrypted digital holograms using an artificial neural network. Decryption is performed by displaying the encrypted hologram and phase mask in an identical configuration. We achieved good quality decryption and reconstruction of 3D objects with as few as 2 bits in each real and imaginary value of the encrypted data

Optical implementation of the Kak neural network

We show that the Kak neural network is suitable for optical implementation using a bipolar matrix vector multiplier. We demonstrate how the CC4 algorithm, with suitable modifications to the structure and training algorithm, may be used to build an optical neural network implementing N-Parity.

Compression of Encrypted Digital Holograms Using Artificial Neural Networks

Some of the photos and figures here are available in color in the electronic version of the newsletter. To download, please go to An important aspect of security and defense is information gathering, dissemination, processing, and analysis. Central to this is the encryption and decryption of messages for storage and transmission. Although public-key cryptosystems are the state of the art currently, there is a place for private key systems in cases where hardware implementation permits very high throughputs. Optical implementation is a candidate for this. Optics has some very promising scalability advantages over purely electronic systems as, in principle, the size of the key can be increased without increasing the encryption or decryption time. Furthermore, optics is perfectly suited to scenarios where message distortion in the encryption/decryption process is permissible in order to increase efficiency. In such scenarios, the different processes involved in the secure transmission of image information—such Figure 1. Experimental setup for 3D object encryption using phase-shift digital holography.

Blockwise discrete Fourier transform analysis of digital hologram data of three-dimensional objects

We report on the results of a study into the characteristics of the blockwise discrete Fourier transform (DFT) coefficients of digital hologram data, with the aim of efficiently compressing the data. We captured digital holograms (whole Fresnel fields) of three-dimensional (3D) objects using phase-shift interferometry. The complex-valued fields were decomposed into nonoverlapping blocks of 8x8 pixels and transformed with the DFT. The inter-block distributions of the 64 Fourier coefficients were analyzed to determine the relative importance of each coefficient. Through techniques of selectively removing coefficients, or groups of coefficients, we were able to trace the relative importance of coefficients throughout a hologram, and over multiple holograms. We used rms error in the reconstructed image to quantify importance in the DFT domain. We have found that the positions of the most important coefficients are common throughout four of the five digital holograms in our test suite. These results will aid us in our aim of creating a general-purpose DFT quantization table that could be universally applied to digital hologram data of 3D objects as part of a JPEG-style compressor.

Vector quantisation compression of digital holograms of three-dimensional objects

Digital holograms of real-world three-dimensional objects have been captured using phase-shift digital holography. These holograms have complex-valued pixels and a white noise appearance. Uniform and nonuniform scalar quantisation compression have already been applied to the hologram data with some success. Although each complex-valued pixel can itself be treated as a vector of length two, we extend the analysis using a multidimensional vector quantisation technique based on k-means clustering. This involves an a-by-b blockwise decomposition of the data and mapping it to an ab-dimensional space. Degradation due to lossy compression is measured in the reconstruction domain.

Compression of digital holograms of three-dimensional objects using the wavelet transform

Wavelets are used extensively in image processing due to the localized frequency information that can be conveyed by the wavelet transform. This and other characteristics of wavelet transforms can be exploited very effectively for the compression of images. We apply the wavelet transform to digital holograms of three-dimensional objects. Our digital holograms are complex-valued signals captured using phase-shift interferometry. Speckle gives them a white noise-like appearance with little correlation between neighboring pixels. In our analyses we concentrate on the discrete wavelet transform and Haar dyadic bases. We achieve compression through quantization of the wavelet transform coefficients. We quantize the discrete wavelet coefficients in each of the subbands depending on the dynamic range of the coefficients in that subband. Finally, we losslessly encode these subbands to quantify the high compression ratios achieved. We outline the three issues that need to be dealt with in order to improve the compression ratio of wavelet based techniques for particular applications as (i) determining a good criterion for ascertaining the coefficients that have to be retained, (ii) determining a quantization strategy and quantization error appropriate to ones particular application, and (iii) compression of the bookkeeping data.

Nonuniform quantization compression techniques for digital holograms of three-dimensional objects

Digital holography is a successful technique for recording and reconstructing three-dimensional (3D) objects. The recent development of megapixel digital sensors with high spatial resolution and high dynamic range has benefited this area. We capture digital holograms (whole Fresnel fields) using phase-shift interferometry and compress then to enhance transmission and storage effciency. Lossy quantization techniques are applied to our complex-valued holograms as the initial stage in the compression procedure. Quantization reduces the number of different real and imaginary values required to describe each hologram. We outline the nonuniform quantization techniques that we have had some success with thus far, and present our latest results with two techniques based on companding and histogram approaches. Companding quantization attempts to combine the effciency of uniform quantization with the improved performance of nonuniform quantization. Our results show that companding techniques can be comparable with k-means and neural network clustering algorithms, while only requiring a single-pass processing step. In addition, we report on a novel lossy compression technique that utilizes histogram data to quantize digital holograms. Here, we use the results of a histogram analysis to inform our decision about the best choice for quantization values.