HDL Implementation of OMP Based Compressed Sampled Reconstruction Algorithm

Nearly all signal acquisition techniques follow the much celebrated Shannon’s sampling theorem which specifies that the sampling rate of the signal must be at least two times the highest frequency present in the signal. The sampled data is then compressed to make it efficient for storage and transmission. Conventional approach to sampling is expensive in terms of data storage and transmission due to the large number of samples generated. Some cases increasing sampling rate is also very expensive like high speed ADCs, imaging systems, etc. It is also inefficient since lot of the data produced is redundant in nature since most naturally occurring signals are sparse in nature. Compressive sensing addresses these inefficiencies by directly acquiring a compressed signal representation without going through the intermediate stage of acquiring all samples. The sampled data can be reconstructed using computationally intensive algorithm. CS is also superior to conventional approaches in the following regard that the CS performs the time consuming processes at the recovery end rather than the sensing end. Reconstruction algorithms are complex and implementation of these algorithms in software is extremely slow and power consuming due to the reason that it is based on several layer of abstraction and shared resources between multiple processes. On the other hand hardware implementation takes advantage of hardware parallelism, custom datapath creation ability and dedicated hardware for each task. The hardware implementation in the project will be utilizing the OMP algorithm due to its less complexity and faster solution time. The algorithm will be implemented using VHDL. The objective of the project will be to implement the OMP algorithm using optimal resources so as to reduce the reconstruction time without compromising with accuracy intended

FPGA Implementation of Real-Time Compressive Sensing with Partial Fourier Dictionary

This paper presents a novel real-time compressive sensing (CS) reconstruction which employs high density field-programmable gate array (FPGA) for hardware acceleration. Traditionally, CS can be implemented using a high-level computer language in a personal computer (PC) or multicore platforms, such as graphics processing units (GPUs) and Digital Signal Processors (DSPs). However, reconstruction algorithms are computing demanding and software implementation of these algorithms is extremely slow and power consuming. In this paper, the orthogonal matching pursuit (OMP) algorithm is refined to solve the sparse decomposition optimization for partial Fourier dictionary, which is always adopted in radar imaging and detection application. OMP reconstruction can be divided into two main stages: optimization which finds the closely correlated vectors and least square problem. For large scale dictionary, the implementation of correlation is time consuming since it often requires a large number of matrix multiplications. Also solving the least square problem always needs a scalable matrix decomposition operation. To solve these problems efficiently, the correlation optimization is implemented by fast Fourier transform (FFT) and the large scale least square problem is implemented by Conjugate Gradient (CG) technique, respectively. The proposed method is verified by FPGA (Xilinx Virtex-7 XC7VX690T) realization, revealing its effectiveness in real-time applications

Vibrational Probe and Methods Development for Studying the Ultrafast Dynamics of Preferential Solvation of Biomolecules by 2D-IR.

Over the last decade two-dimensional infrared spectroscopy (2D-IR) has emerged as a powerful method for the investigation of biological samples and their dynamics. Through the implementation of state of the art signal processing methods we have demonstrated a significant, 20-fold, reduction in the acquisition time of traditional 2D-IR spectra. This new technique, utilizing compressed sensing, compliments our previously developed RASD method, allowing for the rapid acquisition of complete 2D-IR spectra as opposed to dynamical information at a single excitation-detection frequency pair. Additionally we have realized the first biocompatible, modular, metal-carbonyl probes for 2D-IR utilizing benzyl-chromium tribarbonyls. This has enabled ultrafast 2D-IR investigations of lipids and preferential solvation in solutions and at site-specific locations within enzyme scaffolds. In aqueous solutions we find that preferential solvation by a polar cosolvent causes a slowdown of the observed dynamics sensed by our probes. From modeling our system this slowdown is found to be consistent with arising from the slow, ca. 8 ps, exchange dynamics between the polar co-solute and water in the vicinity of our probe. This interpretation of preferential solvation in solution is further able to describe the observed dynamical differences found at the protein-solvent interface in a model system. By studying a series of protein mutants we find, spectroscopically and through simulations, that interactions between the side chains and the solution are sufficient to modulate the degree of preferential solvation and therefore dynamics, within specific sites of the protein. This information provides a foundation on how to modulate of the diffusion of substrates and products into and out-of the active sites of enzymes, through directed mutation of their protein sequence. The diffusional motion of the solvent and substrates is often the rate-limiting step in enzymatic catalysis. By controlling the local solvation dynamics of enzymes, sequence mutations offer a method to fine-tune the dynamics of enzymes. The ability to characterize the site-specific solvation dynamics of enzymes in response to primary structure mutations, positions 2D-IR and our chromium tricarbonyl probes as powerful tools for understanding protein and enzyme dynamics. This provides insight into controlling the catalytic rate of enzymes through directed mutation.PhDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111440/1/josefd_1.pd

Turbo Bayesian Compressed Sensing

Compressed sensing (CS) theory specifies a new signal acquisition approach, potentially allowing the acquisition of signals at a much lower data rate than the Nyquist sampling rate. In CS, the signal is not directly acquired but reconstructed from a few measurements. One of the key problems in CS is how to recover the original signal from measurements in the presence of noise. This dissertation addresses signal reconstruction problems in CS. First, a feedback structure and signal recovery algorithm, orthogonal pruning pursuit (OPP), is proposed to exploit the prior knowledge to reconstruct the signal in the noise-free situation. To handle the noise, a noise-aware signal reconstruction algorithm based on Bayesian Compressed Sensing (BCS) is developed. Moreover, a novel Turbo Bayesian Compressed Sensing (TBCS) algorithm is developed for joint signal reconstruction by exploiting both spatial and temporal redundancy. Then, the TBCS algorithm is applied to a UWB positioning system for achieving mm-accuracy with low sampling rate ADCs. Finally, hardware implementation of BCS signal reconstruction on FPGAs and GPUs is investigated. Implementation on GPUs and FPGAs of parallel Cholesky decomposition, which is a key component of BCS, is explored. Simulation results on software and hardware have demonstrated that OPP and TBCS outperform previous approaches, with UWB positioning accuracy improved by 12.8x. The accelerated computation helps enable real-time application of this work