Single frame blind image deconvolution by non-negative sparse matrix factorization

Novel approach to single frame multichannel blind image deconvolution has been formulated recently as non-negative matrix factorization problem with sparseness constraints imposed on the unknown mixing vector that accounts for the case of non-sparse source image. Unlike most of the blind image deconvolution algorithms, the novel approach assumed no a priori knowledge about the blurring kernel and original image. Our contributions in this paper are: (i) we have formulated generalized non-negative matrix factorization approach to blind image deconvolution with sparseness constraints imposed on either unknown mixing vector or unknown source image; (ii) the criteria are established to distinguish whether unknown source image was sparse or not as well as to estimate appropriate sparseness constraint from degraded image itself, thus making the proposed approach completely unsupervised; (iii) an extensive experimental performance evaluation of the non-negative matrix factorization algorithm is presented on the images degraded by the blur caused by the photon sieve, out-of-focus blur with sparse and non-sparse images and blur caused by atmospheric turbulence. The algorithm is compared with the state-of-the-art single frame blind image deconvolution algorithms such as blind Richardson-Lucy algorithm and single frame multichannel independent component analysis based algorithm and non-blind image restoration algorithms such as multiplicative algebraic restoration technique and Van-Cittert algorithms. It has been experimentally demonstrated that proposed algorithm outperforms mentioned non-blind and blind image deconvolution methods.     

Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects.     

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.     

Evaluation of the residual birefringence of single-mode erbium-doped silica fibers

We present a nondestructive method that allows the spectral birefringence characterization of single-mode erbium-doped fibers within the amplification band. Using the same optical set up and the predicted polarization eigenmodes, the quality of the results has been verified. The results obtained for three commercial erbium-doped fibers with different erbium concentrations are shown. For two of them, the values measured for the elliptical birefringence shift, for different signal wavelengths, from having a dominant circular component to exhibit a dominant linear component.     

Instantaneous velocity measurement of dynamic deformation by digital holographic interferometry

A novel method for the instantaneous velocity measurement of dynamic deformation by digital holographic interferometry is proposed. During dynamic deformation, a series of digital holograms is recorded by a high-speed camera. At each pixel of the phase difference maps, phase and amplitude information are combined as complex phasor (CP). Each pixel can be then considered as an independent sensor and a sequence of complex phasors of such a sensor is analyzed by short time Fourier transform (STFT) along the time axis. A fast iterative algorithm is developed for the computation of instantaneous velocity. The displacement of each pixel can also be obtained by integration of the instantaneous velocity over time and phase unwrapping process is thus avoided. The performance of the proposed CP method is compared experimentally with the commonly used digital phase subtraction method.     

Advanced analysis concepts for terahertz time domain imaging

Imaging based on ultrashort terahertz (THz) pulses (100-3000 μm) is investigated. The measured pulses are analyzed and the resulting amplitude and time delay information are compared. An algorithm for discrimination of multiple pulses is presented, which can distinguish several layers inside an object. A new measurement concept is presented, which accelerates the measurement of samples with small optical path differences about two orders of magnitudes. Exemplarily different applications from the field of quality management are shown.     

A three-dimensional backward-wave network matched with free space

A backward-wave slab based on a capacitively and inductively loaded three-dimensional transmission-line network is designed in such a way that impedance-matching with free space is obtained. To enable field propagation from free space to the network and vice versa, the use of a transition layer is proposed. Matching of the designed network with free space and negative refraction occurring at the slab interfaces are confirmed with full-wave simulations.     

Image watermarking based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform domain

A novel digital image watermarking system based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform (DCT) domain is proposed. The original hidden image is first encrypted into two phase masks. Then the cosine and sine functions of one of the phase masks are introduced as a watermark to be embedded into an enlarged host image in the DCT domain. By extracting the watermark of the enlarged superposed image and decryption we can retrieve the hidden image. The feasibility of this method and its robustness against some attacks, such as occlusion, noise attacks, quantization have been verified by computer simulations. This approach can avoid the cross-talk noise due to direct information superposition and enhance the imperceptibility of hidden data.     

Distributed imaging using an array of compressive cameras

We describe a distributed computational imaging system that employs an array of feature specific sensors, also known as compressive imagers, to directly measure the linear projections of an object. Two different schemes for implementing these non-imaging sensors are discussed. We consider the task of object reconstruction and quantify the fidelity of reconstruction using the root mean squared error (RMSE) metric. We also study the lifetime of such a distributed sensor network. The sources of energy consumption in a distributed feature specific imaging (DFSI) system are discussed and compared with those in a distributed conventional imaging (DCI) system. A DFSI system consisting of 20 imagers collecting DCT, Hadamard, or PCA features has a lifetime of 4.8× that of the DCI system when the noise level is 20% and the reconstruction RMSE requirement is 6%. To validate the simulation results we emulate a distributed computational imaging system using an experimental setup consisting of an array of conventional cameras.     

Improving the performance of DCT-based fragile watermarking using intelligent optimization algorithms

The performance of a fragile watermarking method based on discrete cosine transform (DCT) has been improved in this paper by using intelligent optimization algorithms (IOA), namely genetic algorithm, differential evolution algorithm, clonal selection algorithm and particle swarm optimization algorithm. In DCT based fragile watermarking techniques, watermark embedding can usually be achieved by modifying the least significant bits of the transformation coefficients. After the embedding process is completed, transforming the modified coefficients from the frequency domain to the spatial domain produces some rounding errors due to the conversion of real numbers to integers. The rounding errors caused by this transformation process were corrected by the use of intelligent optimization algorithms mentioned above. This paper gives experimental results which show the feasibility of using these optimization algorithms for the fragile watermarking and demonstrate the accuracy of these methods. The performance comparison of the algorithms was also realized.     

Wavefront reconstruction by two-step generalized phase-shifting interferometry

A wavefront reconstruction method by two-step generalized phase-shifting interferometry (GPSI) with blind phase shift extraction algorithm is verified by both the computer simulations and optical experiments. This method can retrieve complex object wave field by using two interferograms, the recorded object and reference wave intensities, and an unknown phase shift without additional processing. The simulations with irregular wavefronts have shown the effectiveness and high accuracy of this method for blind phase-shift extraction and wavefront reconstruction over a wide range of phase-shifts, while the optical experiments for both the direct and indirect objects have yielded satisfactory results with a higher resolution of reconstructed image than those reported recently.     

Cross-talk free image encryption and watermarking by digital holography and random composition

In previous image watermarking methods an encoded host image and a watermark image are usually directly added, consequently the two images have cross-talk in the decryption step. To eliminate this effect, we propose a novel method based on digital holography, in which all the image pixels of the two sets of holograms resulted from two hidden images are rearranged and integrated into one set of composite holograms with a random scattering matrix (RSM). In decryption the use of this matrix can ensure the exact retrieval of each hologram, and then the perfect reconstruction of each image without cross-talk noise can be achieved. The feasibility of this method and its robustness against occlusion and additional noise are verified by computer simulations with phase-shifting interferometry and double random-phase encoding technique. This approach is suitable for both two- and three-dimensional images, and the additional RSM as a key provides a much higher level of security.     

Non-interferometric transient quantitative phase microscopy for ultrafast engineering

Lead-free piezoelectric ceramics Bi_0.5(Na_1-x-yK_xAg_y)_0.5TiO₃ [BNKAT(x/y)] have been synthesized by the mixed oxide method. The effects of the amount of K⁺ and Ag⁺ on the electrical properties were examined. X-ray diffraction patterns indicate that K⁺ and Ag⁺ ions partially substitute for the Na⁺ ions in Bi_0.5Na_0.5TiO₃ and form a solid solution during sintering. At room temperature, the ceramics exhibit good performances with piezoelectric constant d₃₃=189 pC/N, electromechanical coupling factor k_p=35.0%, remanent polarization P_r=39.5 μC/cm², and coercive field E_c=3.3 kV/mm, respectively. The curves of the dielectric constant ε_r and loss tangent tan δ versus temperature show that the transition temperature from ferroelectric to anti-ferroelectric phase decreases with increasing the K⁺ content for the compositions researched. The dependencies of k_p and polarization versus electric (P–E) hysteresis loops on temperature reveal that the depolarization temperature T_d of BNKAT(0.15/0.015) ceramics, which have good piezoelectric properties (d₃₃=134 pC/N, k_p=32.5%) and strong ferroelectricity (P_r=39.5 μC/cm², E_c=4.1 kV/mm) at room temperature, is above 160 °C. PACS 77.22.-d; 77.65.Bn; 77.80.Bh; 77.80.Dj; 77.84.Dy     

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.     

Influence of the organism interface on the breast cancer detection by UWB

Ultra-wide band (UWB) imaging technique is very attractive for the early breast cancer detection based on the obvious contrast in the electrical properties of malignant tumor to the normal fatty breast tissue. The tumor can be detected by analyzing the reflecting and scattering behavior of the UWB microwaves propagating in the breast. In this study, the influence of the organism interfaces is investigated from different cases of breast configuration involving different gland shapes as well as the tumor locations. Results show that the gland structure and tumor status have large influences on the reconstructed images generated from the detected signals due to the interface varieties. The tumor information in the proposed configurations can be obtained by series signal processing including eliminating the early time response of the detected signals caused by the direct wave and the reflection from the interface between the skin and the breast fat, and compensating the path loss of the propagating signal due to the radial spreading and the attenuation in the lossy breast. The location and the number of emitters and detectors affect the quality of the reconstructed image.     

Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift

An iterative algorithm to extract the arbitrary unknown phase shift in two-frame phase-shifting interferometry and then reconstruct the complex object wave is proposed. In combination with the least square principle and some calculation formulae we developed, this algorithm allows us to find the value of unknown phase shift by using only two interferograms without additional knowledge or measurement. Computer simulations have shown that this algorithm works well for both the smooth and diffusing objects to a very high accuracy over a wide range of the phase shift from 0.4 to 2.5 rad.     

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.     

Phase-coded aperture for optical imaging

For the optical spectrum region, we describe a novel phase-coded aperture imaging system that can be used in a computational imaging camera. The optical design includes a phase-only screen followed by a detector array. A specific diffraction pattern forms at the detector array when the wavefront from a point source object passes through the phase screen. Since diffraction effects cannot be ignored in the optical regime, an iterative phase retrieval method is used to calculate the phase coded screen. Correlation type processing can be applied for the image recovery. Computer simulation results are presented to illustrate the excellent imaging performance of this camera.