**1. Introduction**

132 Applications of Digital Signal Processing

Ya Liu, Xiao-Hui Li, Yu-Lan Wang, *Multi-Channel Beat-Frequency Digital Measurement System* 

684

*for Frequency Standard*, 2009 IEEE International Frequency Control Symposium, 679-

Developing computationally efficient processing techniques for massive volumes of hyperspectral data is critical for space-based Earth science and planetary exploration (see for example, (Plaza & Chang, 2008), (Henderson & Lewis, 1998) and the references therein). With the availability of remotely sensed data from different sensors of various platforms with a wide range of spatiotemporal, radiometric and spectral resolutions has made remote sensing as, perhaps, the best source of data for large scale applications and study. Applications of Remote Sensing (RS) in hydrological modelling, watershed mapping, energy and water flux estimation, fractional vegetation cover, impervious surface area mapping, urban modelling and drought predictions based on soil water index derived from remotelysensed data have been reported (Melesse et al., 2007). Also, many RS imaging applications require a response in (near) real time in areas such as target detection for military and homeland defence/security purposes, and risk prevention and response. Hyperspectral imaging is a new technique in remote sensing that generates images with hundreds of spectral bands, at different wavelength channels, for the same area on the surface of the Earth. Although in recent years several efforts have been directed toward the incorporation of parallel and distributed computing in hyperspectral image analysis, there are no standardized architectures or Very Large Scale Integration (VLSI) circuits for this purpose in remote sensing applications.

Additionally, although the existing theory offers a manifold of statistical and descriptive regularization techniques for image enhancement/reconstruction, in many RS application areas there also remain some unsolved crucial theoretical and processing problems related to the computational cost due to the recently developed complex techniques (Melesse et al., 2007), (Shkvarko, 2010), (Yang et al., 2001). These descriptive-regularization techniques are associated with the unknown statistics of random perturbations of the signals in turbulent medium, imperfect array calibration, finite dimensionality of measurements, multiplicative signal-dependent speckle noise, uncontrolled antenna vibrations and random carrier trajectory deviations in the case of Synthetic Aperture Radar (SAR) systems (Henderson & Lewis, 1998), (Barrett & Myers, 2004). Furthermore, these techniques are not suitable for

High-Speed VLSI Architecture Based on Massively Parallel

optimization-based regularization.

of an operator form (Shkvarko, 2008):

products, [*u*1, *u*2]U = 1 2 () ()

*Y*

*X*

(Shkvarko, 2008) may be rewritten as

 *u*(**y**) = ( *Se*( ) **x** )(**y**) = ( , )

*uud*

**2.1 Problem statement** 

Processor Arrays for Real-Time Remote Sensing Applications 135

The problem of enhanced remote sensing (RS) imaging is stated and treated as an illposed nonlinear inverse problem with model uncertainties. The challenge is to perform high-resolution reconstruction of the power spatial spectrum pattern (SSP) of the wavefield scattered from the extended remotely sensed scene via space-time processing of finite recordings of the RS data distorted in a stochastic uncertain measurement channel. The SSP is defined as a spatial distribution of the power (i.e. the second-order statistics) of the random wavefield backscattered from the remotely sensed scene observed through the integral transform operator (Henderson & Lewis, 1998), (Shkvarko, 2008). Such an operator is explicitly specified by the employed radar signal modulation and is traditionally referred to as the signal formation operator (SFO) (Shkvarko, 2006). The classical imaging with an array radar or SAR implies application of the method called "matched spatial filtering" to process the recorded data signals (Franceschetti et al., 2006), (Shkvarko, 2008), (Greco & Gini, 2007). A number of approaches had been proposed to design the constrained regularization techniques for improving the resolution in the SSP obtained by ways different from the matched spatial filtering, e.g., (Franceschetti et al., 2006), (Shkvarko, 2006, 2008), (Greco & Gini, 2007), (Plaza, A. & Chang, 2008), (Castillo Atoche et al., 2010a, 2010b) but without aggregating the minimum risk descriptive estimation strategies and specialized hardware architectures via FPGA structures and VLSI components as accelerators units. In this study, we address a extended descriptive experiment design regularization (DEDR) approach to treat such uncertain SSP reconstruction problems that unifies the paradigms of minimum risk nonparametric spectral estimation, descriptive experiment design and worst-case statistical performance

Consider a coherent RS experiment in a random medium and the narrowband assumption (Henderson & Lewis, 1998), (Shkvarko, 2006) that enables us to model the extended object backscattered field by imposing its time invariant complex scattering (backscattering)

wavefield *u*(**y**) = *s*(**y**) + *n*(**y**)consists of the echo signals *s* and additive noise *n* and is available for observations and recordings within the prescribed time-space observation domain *Y* = *T*u*P*, where **y** = (*t*, **p**)T defines the time-space points in *Y*. The model of the observation wavefield *u* is defined by specifying the stochastic equation of observation (EO)

in the Hilbert signal spaces E and U with the metric structures induced by the inner

model of the stochastic EO in the conventional integral form (Henderson & Lewis, 1998),

*X*

*X*

*eed*

*<sup>S</sup>*³ **y x** *<sup>e</sup>*(**x**)*d***<sup>x</sup>** + (,)

*X* G

*u* = *Se + n*; *e* E; *u, n* U; *S*

³ **y yy** , and [*e*1, *e*2]E = 1 2 () ()

*<sup>S</sup>*³ **y x** *<sup>e</sup>*(**x**)*d***x** +4 *n*(**y**) = ( , )

**x**. The measurement data

: E o U , (1)

*<sup>S</sup>* ³ **y x** *<sup>e</sup>*(**x**)*d***<sup>x</sup>** <sup>+</sup> *n*(**y**) . (2)

³ **x xx** , respectively. The operator

function *e*(**x**) in the scene domain (scattering surface) *X*

(near) real time implementation with existing Digital Signal Processors (DSP) or Personal Computers (PC).

To treat such class of real time implementation, the use of specialized arrays of processors in VLSI architectures as coprocessors or stand alone chips in aggregation with Field Programmable Gate Array (FPGA) devices via the hardware/software (HW/SW) co-design, will become a real possibility for high-speed Signal Processing (SP) in order to achieve the expected data processing performance (Plaza, A. & Chang, 2008), (Castillo Atoche et al., 2010a, 2010b). Also, it is important to mention that cluster-based computing is the most widely used platform on ground stations, however several factors, like space, cost and power make them impractical for on-board processing. FPGA-based reconfigurable systems in aggregation with custom VLSI architectures are emerging as newer solutions which offer enormous computation potential in both cluster-based systems and embedded systems area. In this work, we address two particular contributions related to the substantial reduction of the computational load of the Descriptive-Regularized RS image reconstruction technique based on its implementation with massively processor arrays via the aggregation of highspeed low-power VLSI architectures with a FPGA platform.

First, at the algorithmic-level, we address the design of a family of Descriptive-Regularization techniques over the range and azimuth coordinates in the uncertain RS environment, and provide the relevant computational recipes for their application to imaging array radars and fractional imaging SAR operating in different uncertain scenarios. Such descriptive-regularized family algorithms are computationally adapted for their HWlevel implementation in an efficient mode using parallel computing techniques in order to achieve the maximum possible parallelism.

Second, at the systematic-level, the family of Descriptive-Regularization techniques based on reconstructive digital SP operations are conceptualized and employed with massively parallel processor arrays (MPPAs) in context of the real time SP requirements. Next, the array of processors of the selected reconstructive SP operations are efficiently optimized in fixed-point bit-level architectures for their implementation in a high-speed low-power VLSI architecture using 0.5um CMOS technology with low power standard cells libraries. The achieved VLSI accelerator is aggregated with a FPGA platform via HW/SW co-design paradigm.

Alternatives propositions related to parallel computing, systolic arrays and HW/SW codesign techniques in order to achieve the near real time implementation of the regularizedbased procedures for the reconstruction of RS applications have been previously developed in (Plaza, A. & Chang, 2008), (Castillo Atoche et al., 2010a, 2010b). However, it should be noted that the design in hardware (HW) of a family of reconstructive signal processing operations have never been implemented in a high-speed low-power VLSI architecture based on massively parallel processor arrays in the past.

Finally, it is reported and discussed the implementation and performance issues related to real time enhancement of large-scale real-world RS imagery indicative of the significantly increased processing efficiency gained with the proposed implementation of high-speed low-power VLSI architectures of the descriptive-regularized algorithms.
