Singular value decomposition and information theoretic criterion-based image enhancement is proposed for through-wall imaging. The scheme is capable of discriminating target, clutter, and noise subspaces. Information theoretic criterion is used with conventional singular value decomposition to find number of target singular values. Furthermore, wavelet transform-based denoising is performed (to further suppress noise signals) by estimating noise variance. Proposed scheme works also for extracting multiple targets in heavy cluttered through-wall images. Simulation results are compared on the basis of mean square error, peak signal to noise ratio, and visual inspection.

Through-wall imaging (TWI) is an active research area [

TWI system works on RADAR principle [

Image enhancement in TWI, has enjoyed an increasing interest over last few years [

Techniques for image enhancement in TWI includes, background subtraction [

Main drawback of background subtraction technique is that it requires a surveillance mode of operation in which there is an access to the background (image scene that is free from targets) or reference [

Statistical methods for TWI enhancement include: singular value decomposition (SVD), factor analysis (FA), principal component analysis (PCA) and independent Component Analysis (ICA) [

Information theoretic criterion (ITC) is a scheme used in array signal processing for determining number of target eigenvalues [

TWI setup is shown in Figure

Geometrical representation of TWI.

2D wavelet transform.

Image enhancement in TWI can be performed by decomposing

Image

WT (multiresolution analysis) localize image (in both space and scale) using scaled and translated copies of a finite-length waveform (mother wavelet). Image on larger scales provide gross features while small scales provide detail features. WT have advantages over other (spatial and fourier) transforms for: accurate representation of functions (having discontinuities and sharp peaks); data compression; noise reduction; probability density function estimation [

WT for image

Figure

2D wavelet decomposition.

Various mother wavelet functions (Daubechies, Haar, Maxican Hat, Symlets, Morlet, etc.) may be used to calculate WT. These wavelets are different due to their complexity, accuracy, and time frequency analysis. Wavelet and scaling coefficients of Daubechies wavelet is shown in Figure

Daubechies wavelet and scaling coefficients.

Wavelet coefficients

Scaling coefficients

Thresholding techniques are broadly classified into soft and hard [

ITC (AIC and MDL) is applied on singular values of

Experimental setup (constructed using [

TWI setup.

Physical elements of experimental setup at Microwave Engineering Laboratory, College of Signals, NUST.

Image enhancement algorithms based on conventional SVD and proposed schemes are simulated in MATLAB. For wavelet denoising we have used Daubechies wavelet, fourth order filter, third level decomposition and soft thresholding technique. Background subtracted image

A single metallic target is placed approximately

Example

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Three metallic targets are placed approximately

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Five metallic targets are placed approximately

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Five metallic targets are placed approximately

Note that, proposed (AIC based SVD, MDL based SVD and WT MDL based SVD) schemes successfully detects all targets and cause some target spread in cross-range direction. This is due to the fact that we are only considering

Figure

Example

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Example

MSE and PSNR comparison of conventional and proposed schemes against number of targets.

MSE Comparison

PSNR Comparison

SVD-based image enhancement for TWI using ITC and WT is proposed. The scheme is capable of discriminating between target and noise subspaces. The limitation of subjective threshold setting in conventional SVD is overcome using ITC scheme. Furthermore, noise is suppressed using WT-based denoising. Proposed method increases accuracy of conventional SVD-based TWI image enhancement scheme. Both AIC and MDL technique detect multiple targets (so one can use either of these). Proposed scheme can easily be modified for PCA, FA, and ICA methods to get better accuracy.