The Fast Fourier Transform (FFT) is an efficient algorithm widely used in digital signal processing to transform between the time domain and the frequency domain. For fixed-point VLSI implementations, dynamic range growth inevitably occurs at each stage of the FFT operation. However, current methods either waste bitwidth or consume excessive resources when dealing with the dynamic range growth issue. To address this issue, we propose an efficient scaling method called Scaling Information Propagation (SIP) to alleviate the problem of dynamic range growth, which makes full use of bitwidth with much less extra area consumed than the state-of-the-art solutions. In two consecutive transform operations, the SIP method extracts scaling information and makes scaling decisions in the former transform, then executes those in the latter one. We implement the FFT’s VLSI architecture in the orthogonal frequency division multiplexing (OFDM) and the holographic video compression (HVC) systems to verify the SIP method. Compared to the state-of-the-art, experimental results after VLSI synthesis show that our method achieves 9.38% energy reduction and 8.36% area savings when requiring 1.02 × 10-7bit error ratio (BER) of the OFDM system, and 33.47% energy reduction and 30.98% area savings when requiring 20dB signal-to-noise ratio (SNR) of the HVC system, respectively.

Computer-Generated Holography (CGH) algorithms simulate numerical diffraction, being applied in particular for holographic display technology. Due to the wave-based nature of diffraction, CGH is highly computationally intensive, making it especially challenging for driving high-resolution displays in real-time. To this end, we propose a technique for efficiently calculating holograms of 3D line segments. We express the solutions analytically and devise an efficiently computable approximation suitable for massively parallel computing architectures. The algorithms are implemented on a GPU (with CUDA), and we obtain a 70-fold speedup over the reference point-wise algorithm with almost imperceptible quality loss. We report real-time frame rates for CGH of complex 3D line-drawn objects, and validate the algorithm in both a simulation environment as well as on a holographic display setup.

Compression of digital holograms is a major challenge that needs to be resolved to enable the efficient storage, transmission and rendering of macroscopic holographic signals. In this work, we propose to deploy the wave atom transform that has been utilized before for interferometric modalities such as acoustic and seismic signals. This non-adaptive multiresolution transform has good space-frequency localization and its orthonormal basis is suitable for sparsifying holographic signals. By replacing the CDF 9/7 wavelet transform stage in a JPEG 2000 codec with the proposed wave atom transform, we did assess its suitability for coding complex amplitude wavefronts. Experimental results demonstrate improved rate-distortion performance with respect to JPEG 2000 and H.265/HEVC for a set of computer-generated, diffuse, macroscopic holograms.

Digital holograms fully encode the wavefield of light, thereby having many applications both for 3D object measurements as well as for display purposes, accounting for all human visual cues. Because the statistics and properties of holographic signals differ considerably from natural imagery such as photographs, conventional coding solutions will be sub-optimal. In this paper, we propose the integer Fresnel transform, which is - to our knowledge - the first lossless transform tailored for hologram coding. By combining the proposed transform with JPEG 2000, we report bit-rate savings from 0.12 up to 2.83 bits per channel on a collection of 8 digital holograms obtained from 3 different databases.

Holography is considered to be the ultimate display technology since it can account for all human visual cues such as stereopsis and eye focusing. Aside from hardware constraints for building holographic displays, there are still many research challenges regarding holographic signal processing that need to be tackled. In this overview, we delineate the steps needed to realize an end-to-end chain from digital content acquisition to display, involving the efficient generation, representation, coding and quality assessment of digital holograms. We discuss the current state-of-the-art and what hurdles remain to be taken to pave the way towards realistic visualization of dynamic holographic content.

Advanced sparse sampling acquisition systems capture only scattered information from the continuous image domain. Unfortunately, conventional image encoders are not yet able to properly compress arbitrarily subsampled image data. This work introduces a system leveraging the JPEG 2000 image compression framework by enabling scalable compression of the selected image samples. Using a complete dictionary of CDF 9/7 wavelets, a minimum l1-norm compressed sensing solution is recovered which can be fed directly into the encoder, producing a bitstream that can be decoded with existing JPEG 2000-compliant implementations. Experiments on standard images with quasi-random subsampling demonstrate that the proposed system outperforms regular JPEG 2000 compression of stacked sample images and quad-tree based compression for point-clouds. We also demonstrate the robustness of the technique for images that infringe the sparsity prior of compressed sensing.

Compressive sensing is a mathematical framework, which seeks to capture the information of an object using as few measurements as possible. Recently, it has been applied to holography, where the most frequently used reconstruction method is l1-norm minimization with the Haar wavelet as the sparsifying operator. In this work, we promote the CDF 9/7 wavelet as the sparsifying operator. We demonstrate that the CDF 9/7 wavelet performs better than the Haar wavelet.