Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample

This study demonstrates a simple method for attenuating the speckle noise generated by coherent multiple-scattered photons in optical-coherence tomography images. The method could be included among the space-diversity techniques used for speckle reduction. It relies on displacing the sample along a weakly focused beam in the sample arm of the interferometer, acquiring a coherent image for each sample position and adding the individual images to form a compounded image. It is proven that the compounded image displays a reduction in the speckle noise generated by multiple scattered photons and an enhancement in the intensity signal caused by single-backscattered photons. To evaluate its potential biomedical applications, the method is used to investigate in vitro a caries lesion affecting the enamel layer of a wisdom tooth. Because of the uncorrelated nature of the speckle noise the compounded image provides a better mapping of the lesion compared to a single (coherent) image.     

Precision of degree of polarization estimation in the presence of additive Gaussian detector noise

We address the problem of degree of polarization (DOP) estimation in images limited by additive Gaussian detector noise. We derive and analyze the probability density function (PDF) of the pixelwise DOP estimate, which is shown to have significantly different statistical properties than when noise is Gamma distributed (speckle). We then determine the Cramer-Rao Lower Bound and the maximum likelihood estimator of the DOP. We deduce from this study practical solutions for characterizing and reducing the noise in these images.     

Analysis of speckle in ultrasound images using fractional order statistics and the homodyned k-distribution

It is necessary to identify speckled regions in ultrasound images to control adaptive speckle suppression algorithms, for tissue characterisation, and to estimate the elevational separation of B-scans by speckle decorrelation. Previous authors have proposed classification techniques based on second order powers of the homodyned k-distribution, or lower order powers of the more limited k-distribution. In this paper we explore the speckle discrimination properties of statistics based on arbitrary powers of the ultrasound echo envelope signal using a combination of simulations and theoretical results from the homodyned k-distribution. We conclude that statistics based on powers less than one are surprisingly less effective than some higher powers. A simple discriminant function for speckle is evaluated quantitatively in simulation and qualitatively on sample B-scan images.     

Multiplexing encryption-decryption via lateral shifting of a random phase mask

We present an holographic memory optical arrangement based on the successive shifting of a random pure-phase mask to achieve encrypted images multiplexing. The input images are encrypted to a stationary white noise using the usual double random encoding in the Fresnel domain. The encrypted information is imaged in a photorefractive crystal where also a reference beam impinges. In the holographic memory, a BSO crystal is used to provide both a recording medium and a phase conjugate mirror. The combination of these two features supplies at the same time the necessary exact cancellation of the random pure-phase mask as well as allows a real-time decryption process. Successive images are encrypted and position-encoded by speckle patterns arising from the random pure-phase mask in-plane shifting between exposures. We include experimental results to corroborate the multiplexing capability and the read-out fidelity of the proposed arrangement.     

Multiple image encryption using an aperture-modulated optical system

A multiple image cryptosystem based on different apertures in an optical set-up under a holographic arrangement is proposed. The system is a security architecture that uses different pupil aperture mask in the encoding lens to encrypt different images. Based on this approach multiple encryption is achieved by changing the pupil aperture arrangement of the optical system among exposures. In addition to the classical speckle phase mask, the geometrical parameters characterizing the apertures are introduced to increase the system security. Even when an illegal user steals the speckle phase mask, the system cannot be broken into without the correct pupil geometrical parameters. The experimental set-up is based on a volume photorefractive BSO crystal as storing device. Information retrieval is done via a phase conjugation operation. We also have to stress that the multiple storage under this scheme, is only possible with the help of the aperture mask. Simulation and experimental results are further introduced to verify the proposed method.     

Mechanism of speckle reduction in laser-microscope images using a rotating optical fiber

The reduction mechanism of speckles appearing in laser-microscope images is studied theoretically and experimentally when an object is illuminated by laser light through a rotating multimode optical fiber. The principle of the speckle reduction is based on independent addition of microscope images with boiling-like speckles as a result of the rotational motion of the optical fiber used for illumination. Especially, the speckle reduction is evaluated from first-order statistics of the speckle intensity in which its saturation effect is taken into consideration.     

Speckle detection for 3D ultrasound

Positioning accuracy of 3D ultrasound slice planes can be enhanced by speckle decorrelation of the B-scans. A suitable method requires accurate identification of zones of non-specular reflection in the image, a feature of parenchymal tissue. This has traditionally been achieved with statistics such as signal-to-noise ratios and measures of autocorrelation curves. Co-occurrence matrices and structural approaches have also been applied to ultrasound images. In this paper we assess the performance of these methods when only B-scan display data is available. We also report improved results with in vivo images using a proposed structural algorithm that detects speckle kernels. All detection algorithms yielded detection error rates between 28% and 38%, suggesting that user intervention may be required for clinically useful performance.     

Double-image encryption based on iterative gyrator transform

A novel double-image encryption algorithm is proposed, which can simultaneously encrypt two images into a single one as the amplitude of gyrator transform with two different groups of angles. The two original images can be retrieved independently by gyrator transforms with two different groups of angles, one common phase mask, and two different private phase masks. The proposed approach can enlarge the key space, achieve faster convergence in iterative process, and avoid cross-talk between two images in reconstruction. Numerical simulations are presented to verify its validity and efficiency.     

Evaluation of dynamic speckle activity using the empirical mode decomposition method

The empirical mode decomposition (EMD) method is used to process sequences of dynamic speckle patterns to segment the differential activity that presents a sample as a function of the spatial coordinates and time. The application of the method is illustrated by segmenting bruised regions in fruits. A discussion of the obtained results and a comparison with the use of the filter bank technique are also presented.     

Color image encoding in dual fractional Fourier-wavelet domain with random phases

A new cryptology in dual fractional Fourier-wavelet domain is proposed in this paper, which is calculated by discrete fractional Fourier transform and wavelet decomposition. Different random phases are used in different wavelet subbands in encryption. A new color image encoding method is also presented with basic color decomposition and encryption respectively. All the keys, including random phases and fractional orders in R, G and B three channels, should be correctly used in decryption, otherwise people cannot obtain the totally correct information. Some numerical simulations are presented to demonstrate the possibility of the method. It would have widely potential applications in digital color image processing and protection.     

Theory of speckle displacement and decorrelation with electronic correlation

The paper deals with the determination of small deformation tensor components by means of an optical experimental method, which utilizes statistical properties of the speckle field in optically free space. The term “deformation tensor” is introduced and the relationship between the small deformation tensor components and the cross-correlation function of two intensity speckle patterns in free-space is analyzed. Furthermore, experimental arrangements for measurement of rotation, deformation, and translation, and their sensitivity and accuracy analyses are also presented.     

Refractive and geometric lens characterization through multi-wavelength digital speckle pattern interferometry

Physical parameters of different types of lenses were measured through digital speckle pattern interferometry (DSPI) using a multimode diode laser as light source. When such lasers emit two or more longitudinal modes simultaneously the speckle image of an object appears covered of contour fringes. By performing the quantitative fringe evaluation the radii of curvature as well as the refractive indexes of the lenses were determined. The fringe quantitative evaluation was carried out through the four- and the eight-stepping techniques and the branch-cut method was employed for phase unwrapping. With all these parameters the focal length was calculated. This whole-field multi-wavelength method does enable the characterization of spherical and aspherical lenses and of positive and negative ones as well.     

Ultrasound speckle and equivalent scatterers

B-mode ultrasound images are characterised by the speckle artefact, which introduces fine-false structures whose apparent resolution is beyond the imaging system capabilities. Speckle presence is due to interference effects between overlapping echoes and its occurrence is related to a great number of randomly distributed structure scatterers within a resolution cell. Basing our analysis on linear system theory, we show that a dense random set of scatterers can be substituted by an equivalent one with a much smaller number of periodic scatterers. This new structure with regularly distributed scatterers is able to give rise to the same B-mode image and the same speckle pattern, for a given ultrasound pulse. This new approach helps the understanding of the deterministic nature of speckle and may reduce drastically the computing time in numerical simulations. Additionally, it can contribute to periodicity analysis used in tissue characterisation.     

Adaptive correlation filters for speckle patterns in photorefractive crystals

The experimental study of the in-plain vibration of the speckle pattern in photorefractive GaP and BTO crystals using the polarization self-modulation effect are presented. The simple model based on the propagation of the Gaussian beam through the crystal with recorded space-charge field is proposed to explain main features of the experiment. It is shown that these results allow designing a linear sensor of the speckle-pattern displacement in an effective way. The optical system is very simple and does not include any reference or readout beam. The sensitivity of this system is the same as that of an interferometer. Received: 27 November 1998 / Revised version: 26 January 1999 / Published online: 12 April 1999     

Multiple-scattering speckle in holographic optical coherence imaging

We investigate the effect of multiple scattering on the image quality of holographic optical coherence imaging, which is a full-field coherence-domain imaging form of optical coherence tomography. The speckle holograms from turbid media and from multicellular tumor spheroids are characterized by high-contrast speckle on a multiply-scattered background caused by channel cross-talk. We quantify the multiple-scattered light that is accepted by the holographic coherence gate, and identify a cross-over from single-scattered to multiple-scattered light beyond 15 to 20 optical thicknesses. Speckle reduction relies on vibrating diffusers and on fast adaptive holograms in photorefractive quantum well devices. The high anisotropy factor for tumor tissue reduces multiply-scattered light contributions for biomedical tumor imaging.     

A combined method for obtaining fringe orientations of ESPI

Fringe orientation can direct the processing of fringe patterns and provide basic information for understanding the fringe patterns. The gradient method is popularly used for its convenience but it is easily affected by noise. The plane-fit method is capable of obtaining precise local fringe orientation despite the high speckle noise but it is strict with the calculating window size. In this paper, a combined method is proposed. This method uses the plane-fit algorithm to get local gradients and uses the gradient method to get the orientation results from these gradients. It can be seen that this new method can get more accurate orientations for ESPI than both the gradient method and the plane-fit method.     

Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform

In this paper, a filtering technique based upon two-dimensional continuous wavelet transform (2D-CWT) is used to eliminate the low frequency components of fringe patterns. The filtered fringe patterns are subsequently demodulated using a standard Fourier transform profilometry (FTP) algorithm. This image pre-filtering stage improves the noise performance of the FTP algorithm and enables the FTP method to demodulate fringe patterns with larger bandwidths. Also, the 2D-CWT technique reduces speckle noise significantly. Moreover, only a single fringe pattern is required in this technique. The 2D-CWT algorithm is capable of separating low frequency terms from the high frequency terms that contain phase-modulated fringe information, even when both interfere, greatly, in the frequency domain. The proposed algorithm is tested, both via computer simulation and using real fringe patterns. This revealed the robustness of this algorithm and also demonstrably enables the demodulation of a wider range of fringe patterns using the FTP technique.     

Multiplexing encrypted data by using polarized light

We investigate the feasibility of multiplexing, employing polarized light, a set of security encrypted data. The encryption approach is based on the double random pure-phase enciphering method. Phase conjugation operation is conducted in the reconstruction stage with the aid of a photorefractive crystal which stores the encrypted information. When storing each encrypted image, a polarization change is introduced in the system. This induces decorrelation on the speckle patterns inside the storing medium. We apply this approach for multiple image encryption. We show experimental results that confirm our approach.     

Anisotropic partial differential equation noise-reduction algorithm based on fringe feature for ESPI

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a new anisotropic partial differential equation noise-reduction algorithm based on fringe orientation for interferometric fringe patterns. The proposed equation performs diffusion along the two directions of fringe gradient and isophote line, which are extracted accurately according to fringe feature. By restriction of diffusion in the gradient direction of fringe patterns, this method can provide optimal results in denoising but does not destroy fringe edges. The experimental results show that this technique is more capable of significantly improving the quality of the fringe patterns than the classical anisotropic diffusion equation proposed by Perona and Malik. Based on our filtered fringe patterns, the phase map obtained by phase-shifting technique can be extracted more accurately. It is an effective pre-processing method for electronic speckle pattern interferometry.