MAP and regularized constrained total least-squares image restoration

Fast unbiased finite impulse response (UFIR) filtering of polynomial signals can be provided in the discrete Fourier transform (DFT) domain employing fast Fourier transform (FFT). We show that the computation time can further be reduced by utilizing properties of UFIR filters in the DFT domain. The transforms have been found and investigated in detail for low-degree FIRs most widely used in practice. As a special result, we address an explicit unbiasedness condition uniquely featured to UFIR filters in DFT domain. The noise power gain and estimation error bound have also been discussed. An application is given for state estimation in a crystal clock employing the Global Positioning System based measurement of time errors provided each second. Based upon it, it is shown that filtering in the time domain takes about 1 second, which is unacceptable for real-time applications. The Kalman-like algorithm reduces the computation time by the factor of about 8, the FFT-based algorithm by about 18, and FFT with the UFIR filter DFT properties by about 20.

LMMSE and MAP estimators for reduction of multiplicative noise in the nonsubsampled contourlet domain

This paper investigates turbo equalization (TE) with linear minimum mean squared error (LMMSE) equalizer, which has much lower complexity but much worse performance than TE with maximum a posteriori (MAP) equalizer because of inefficient information processing of LMMSE equalizer. Motivated by forward and backward recursions of MAP algorithm, three methods are presented to improve turbo equalization with LMMSE equalizer (TE-LMMSE). In the simulation, they all obtain more than 2.5-dB performance gain over TE-LMMSE with no or some complexity price.

The detection performance of coherent OFDM receiver significantly depends on the accuracy of channel estimation. The accuracy of channel estimation can be improved by properly post-processing the channel estimate using a so called channel estimation filter (CEF). Linear minimum mean-squared error (MMSE) filter is optimum as the CEF, but it may not practical due to implementation complexity. We consider the use of a reduced-complexity CEF whose tap coefficient is real valued and symmetrically weighted (RSW). The optimum RSW CEF is analytically designed using the multi-path intensity profile and SNR of the channel. We also propose a method to adapt the coefficient of the RSW CEF to the channel condition. Numerical results show that the proposed RSW CEF can provide channel estimation performance comparable to that of a linear MMSE filter, while significantly reducing the computational complexity. In addition, the proposed RSW CEF can provide performance robust to unknown timing offset with a fractional dB loss compared to the optimum one.

An iterative maximum a posteriori (MAP) algorithm is proposed for simultaneous signal-covariance estimation and restoration when only partial knowledge of the system response matrix (SRM) and the noisy-blurred sinogram of an image to be reconstructed are available. Convergence analysis is performed to ascertain that the proposed covariance estimator converges to the optimal one in the MAP sense. The superiority of the proposed algorithm, in comparison with the iterative linear minimum mean-squared-error (LMMSE) filter for incorrect SRM information, is experimentally verified.

In this paper, we propose a multi-bit watermarking technique for video sequences. An N-bit message is embedded in one unit of video fragment, in which a scene is employed as a watermarking unit. The proposed algorithm is fundamentally based on the three-dimensional discrete Fourier transform (DFT). In order to generate a watermark with optimum weighting factors, the perceptual properties for all the three-dimensional DFT coefficients should be computed, but this strategy seems to be undesirable due to the high computational complexity. So, we design a perceptual model of an image in the DFT domain, and apply it to the video watermarking. The proposed perceptual model is expected to give high fidelity and effective, compared to fully calculated visual masks, since it derives all the masks from one reference mask with a well-known estimation method. Through the computer simulations, it can be shown that the proposed watermarking algorithm with the perceptual model yields effective performance for fidelity. Moreover, it was also shown that the proposed scheme provides robustness against various attacks, such as compression, geometric attacks, and collusion attacks.

This paper presents a comparative study of single-carrier (SC)-frequency division multiple access (FDMA) and OFDMA using turbo soft interference cancellation (SIC) from the viewpoint of throughput for multiple-input multiple-output (MIMO) spatial division multiplexing (SDM). In turbo SIC, interference from other transmission streams is generated based on the log-likelihood ratio (LLR) at the turbo decoder output and subtracted from the received signal iteratively associated with a linear minimum mean-square error (LMMSE) filter. Hence, we compare the throughput performance levels of methods for generating soft-symbol estimates of other streams based on the extrinsic LLR and the a posteriori LLR at the Max-Log-MAP decoder output. We show by computer simulation the difference in performance of turbo SIC based on the a posteriori LLR and extrinsic LLR from the viewpoints of the average block error rate and throughput. We also show that the OFDMA yields superior throughput performance compared to SC-FDMA with 16QAM and 64QAM schemes when using turbo SIC for 2-by-2 to 8-by-8 MIMO SDM.

The stereo image pair taken from different positions, theoretically the redundant information and disparity allows to reconstruction higher resolution images and reduces the aliasing artifacts. We present an improved hybrid MAP (Maximum a Posteriori) restoration algorithm for stereo image pair combined PSF (Point Spread Function) measurement and iterative registration parameters updated scheme. With the regularity parameter choice based on L-curve, this method preserves discontinuity efficiently. The reconstruction images quality lies on the accurate registration, the PSF non-bias estimation and regulation parameters choice. In this paper, an MTF (Modulation Transfer Function) measure and spatial profile methods are presented for reconstruction images quality estimation. A simulation and a real-data experiment demonstrate the performance of the algorithm.

Multiple transmit (Tx) and multiple receive (Rx) antenna systems, referred to as multiple input multiple output (MIMO) systems, have been proposed to achieve higher data rates in wireless communication systems. In this paper, we investigate joint optimization of transmitter and receiver for MIMO system when the channel information is available at both transmitter and receiver. We discuss the problem of designing Tx and Rx filter based on minimum bit error probability criterion. We first derive the optimum Tx and Rx filters for the special case of two input data symbols. Based on this optimum filter, we propose a Tx and Rx filter optimization for the general case of input data symbols. The performance of the proposed Tx and Rx filters is compared with that of the conventional minimum mean-squared error (MMSE) filter. Performance analysis shows that the proposed filter provides significant improvement over the MMSE filter in bit error probability.

Backscatter communication (BC) has emerged as a promising paradigm for enabling energy-efficient and low-cost Internet of Things (IoT) systems. However, one practical constraint that is often neglected in BC studies is the circuit sensitivity of the backscatter device (BD), which sets the minimum signal strength required to activate it for signal reflection. In this paper, we address the channel estimation (CE) problem in the BC system with a circuit sensitivity constraint. Specifically, we propose three channel estimators for the receiver in the BC system that is unaware of the activation states of the BD, namely the maximum likelihood (ML), linear minimum mean square error (LMMSE), and maximum a posteriori (MAP) estimators. We derive both the Cramér-Rao bound (CRB) and Bayesian Cramér-Rao bound (BCRB) to evaluate the performance of the proposed estimators. Finally, we provide simulations to validate our analysis. Our results demonstrate that the proposed LMMSE and MAP estimators outperform traditional estimators that neglect the circuit sensitivity constraint.

Orthogonal frequency division multiplexing (OFDM) system suffers extra performance degradation in fast fading channels due to intercarrier interference (ICI). Combining frequency domain equalization and bit-interleaved coded modulation (BICM), the iterative receiver is able to harvest both temporal and frequency diversity. Realizing that ICI channels are intrinsically ISI channels, this paper proposes a soft-in soft-out (SISO) maximum a posteriori (MAP) equalizer by extending Ungerboeck's maximum likelihood sequence estimator (MLSE) formulation to ICI channels. The SISO MAP equalizer employs BCJR algorithm and computes the bit log-likelihood ratios (LLR) for the entire received sequence by efficiently constructing a trellis that takes into account of the ICI channel structure. A reduced state (RS) formulation of the SISO MAP equalizer which provides good performance/complexity tradeoff is also described. Utilizing the fact that ICI energy is clustered in adjacent subcarriers, frequency domain equalization is made localized. This paper further proposes two computational efficient linear minimum mean square error (LMMSE) based equalization methods: recursive q-tap SIC-LMMSE equalizer and recursive Sliding-Window (SW) SIC-LMMSE equalizer respectively. Simulations results demonstrate that the iterative SISO RS-MAP equalizer achieves the performance of no ICI with normalized Doppler frequency f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> up to 20.46% in realistic mobile WiMAX environment.

For the orthogonal frequency-division multiplexing (OFDM) system, one can estimate the channel responses (CRs) based on frequency-domain (FD) pilot symbols. On the other hand, one can also estimate the time-domain (TD) channel impulse response by inserting a unit pulse ahead of each OFDM block. However, there is no analytical comparison between the CR estimation based on FD pilot symbols and TD unit pulses. In this paper, we give the analytical comparison of the mean-squares errors (MSEs) for the CR estimation based on TD and FD pilot signals. For the CR estimation based on FD pilot symbols, the linear minimum mean-squares error (LMMSE) algorithm is optimal. We derive an MSE lower bound for the LMMSE algorithm among all possible distribution of pilot symbols. This MSE lower bound coincides with the MSE attained by the optimal CR estimation based on TD unit pulses. We also show that with the uniform distribution of pilot symbols, the resulted MSE is very close to the MSE lower bound for the LMMSE algorithm. Our results conclude that the optimal CR estimation based on TD and FD pilot signals attain almost the same MSEs.

The performances of various estimators for wavefront sensing applications such as adaptive optics (AO) are compared. Analytical expressions for the bias and variance terms in the mean squared error (MSE) are derived for the minimum-norm maximum likelihood (MNML) and the maximum a posteriori (MAP) reconstructors. The MAP estimator is analytically demonstrated to yield an optimal trade-off that reduces the MSE, hence leading to a better Strehl ratio. The implications for AO applications are quantified thanks to simulations on 8-m- and 42-m-class telescopes. We show that the MAP estimator can achieve twice as low MSE as MNML methods do. Large AO systems can thus benefit from the high quality of MAP reconstruction in O(n) operations, thanks to the fast fractal iterative method (FrIM) algorithm (Thiébaut and Tallon, submitted to J. Opt. Soc. Am. A).

Retinal images are often degraded with a blur that varies across the field view. Because traditional deblurring algorithms assume the blur to be space-invariant they typically fail in the presence of space-variant blur. In this work we consider the blur to be both unknown and space-variant. To carry out the restoration, we assume that in small regions the space-variant blur can be approximated by a space-invariant point-spread function (PSF). However, instead of deblurring the image on a per-patch basis, we extend individual PSFs by linear interpolation and perform a global restoration. Because the blind estimation of local PSFs may fail we propose a strategy for the identification of valid local PSFs and perform interpolation to obtain the space-variant PSF. The method was tested on artificial and real degraded retinal images. Results show significant improvement in the visibility of subtle details like small blood vessels.

Hyperspectral images acquired by remote sensing systems are generally degraded by noise and can be sometimes more severely degraded by blur. When no knowledge is available about the degradations present on the original image, blind restoration methods can only be considered. By blind, we mean absolutely no knowledge neither of the blur point spread function (PSF) nor the original latent channel and the noise level. In this study, we address the blind restoration of the degraded channels component-wise, according to a sequential scheme. For each degraded channel, the sequential scheme estimates the blur point spread function (PSF) in a first stage and deconvolves the degraded channel in a second and final stage by means of using the PSF previously estimated. We propose a new component-wise blind method for estimating effectively and accurately the blur point spread function. This method follows recent approaches suggesting the detection, selection and use of sufficiently salient edges in the current processed channel for supporting the regularized blur PSF estimation. Several modifications are beneficially introduced in our work. A new selection of salient edges through thresholding adequately the cumulative distribution of their corresponding gradient magnitudes is introduced. Besides, quasi-automatic and spatially adaptive tuning of the involved regularization parameters is considered. To prove applicability and higher efficiency of the proposed method, we compare it against the method it originates from and four representative edge-sparsifying regularized methods of the literature already assessed in a previous work. Our attention is mainly paid to the objective analysis (via l1-norm) of the blur PSF error estimation accuracy. The tests are performed on a synthetic hyperspectral image. This synthetic hyperspectral image has been built from various samples from classified areas of a real-life hyperspectral image, in order to benefit from realistic spatial distribution of reference spectral signatures to recover after synthetic degradation. The synthetic hyperspectral image has been successively degraded with eight real blurs taken from the literature, each of a different support size. Conclusions, practical recommendations and perspectives are drawn from the results experimentally obtained.