Comments on "Iterative procedures for reduction of blocking effects in transform image coding"

Because of the incomplete acquisition system, the irregularity appears in the observed seismic data. Besides, the observed seismic data contains random noise from the acquisition equipments and the surrounding environment. Both of them can affect the performances of multi-channel techniques, like Surface Related Multiple Elimination (SRME). Projection Onto Convex Sets (POCS) method, as an efficient interpolation method, is suitable for high Signal to Noise Ratio (SNR) situations, but the random noise in the observed seismic data may affect the final performance of the POCS method. Previously, we have deduced the POCS formula in the view of the Iterative Hard Threshold (IHT) method using a projection operator. In this abstract, a carton is provided to give more physical interpretation about the deduction. Then, the performances of the POCS and IHT methods are compared in noisy situations using seismogram comparisons, F-K spectrum comparisons and single trace comparisons. In which the performance of the POCS method is unsatisfactory because of the observed noisy data insertion, while the IHT performance is satisfactory because it uses a threshold operator to eliminate random noise. Numerical examples on noisy data tests prove the ability and superiority of the IHT method with the anti-noise property compared with the POCS method. Presentation Date: Tuesday, October 18, 2016 Start Time: 4:10:00 PM Location: Lobby D/C Presentation Type: POSTER

We propose a novel postprocessing technique, based on the theory of projections onto convex sets (POCS), to reduce the blocking artifacts in transform coded images. It is assumed, in our approach, that the original image is highly correlated. Thus, the global frequency characteristics in two adjacent blocks are similar to the local ones in each block. We consider the high-frequency components in the global characteristics of a decoded image, which are not found in the local ones, as the results from the blocking artifact. We employ an N-point discrete cosine transform (DCT) to obtain the local characteristics, and a 2N-point DCT to obtain the global ones, and then derive the relation between the N-point and 2N-point DCT coefficients. A careful comparison of the N-point with the 2N-point DCT coefficients makes it possible to detect the undesired high-frequency components, mainly caused by the blocking artifact. Then, we propose novel convex sets and their projection operators in the DCT domain. The performance of the proposed and conventional techniques are compared on the still images, decoded by JPEG. The results show that, regardless of the content of the input images, the proposed technique yields significantly better performance than the conventional techniques in terms of objective quality, subjective quality, and convergence behavior.

This paper proposes a clustering successive projections onto convex sets (CSPOCS) algorithm for enforcing two way constraints originated from point matching. Via point clustering, the problem of projection onto convex set (POCS) where the convex set is described by point correspondence's constraints is converted to the POCS problem where the convex set is described by cluster correspondence's constraints. Then the successive POCS (SPOCS) technique is employed to solve the POCS problem. The resulting algorithm can be viewed as a generalization of SPOCS by combining with clustering. Its precision and computational load are decided by the average radius of clusters. Experimental results demonstrate the effectiveness of the algorithm

Parallel imaging techniques for MRI use differences in spatial sensitivity of multiple receiver coils to achieve additional encoding effect and significantly reduce data acquisition time. Recently, a projection onto convex sets (POCS) based method for reconstruction from sensitivity-encoded data (POCSENSE) has been proposed. The main advantage of the POCSENCE in comparison with other iterative reconstruction techniques is that it offers a straightforward and computationally efficient way to incorporate non-linear constraints into the reconstruction that can lead to improved image quality and/or reliable reconstruction for underdetermined problems. However, POCSENSE algorithm demonstrates slow convergence in cases of badly conditioned problems. In this work, we propose a novel method for image reconstruction from sensitivity encoded MRI data that overcomes the limitation of the original POCSENSE technique. In the proposed method, the convex combination of projections onto convex sets is used to obtain an updated estimate of the solution via relaxation. The new method converges very efficiently due to the use of an iteration-dependent relaxation parameter that may extend far beyond the theoretical limits of POCS. The developed method was validated with phantom and volunteer MRI data and was demonstrated to have a much higher convergence rate than that of the original POCSENSE technique.

The limited-view angle problem is one of the difficulties in seismic diffraction tomography. In the configuration of seismic data acquisition systems, the exploring wave cannot probe the object from all directions. This limitation will lead to incomplete coverage in the wavenumber domain. If we ignore this incomplete data by assigning zero to the blind area and use the ordinary reconstruction algorithms, poor resolution will be introduced. Thus, it is important to estimate the missing data in the spectrum in order to improve the resolution. In this paper, POCS (Projections Onto Convex Sets) is applied to the cross-hole seismic diffraction tomography in order to solve the limited-view angle problem in this configuration. The algorithm that combines POCS with direct Fourier transform and bilinear interpolation in the wavenumber domain is proposed. POCS can incorporate many kinds of convex-type a priori knowledge about the object function as constraints and its estimate is superior to that of G-P extrapolation. INTRODUCTION In cross-hole seismic tomography, the sources and geophones are deployed in the two bore-holes respectively and it is very difficult to probe the object in the subsurface from all directions. This problem is known as the limited-view angle problem and it will lead to large patches of “blind area” in the wavenumber domain. Up to now, most seismic diffraction tomography methods have bypassed this problem by assigning zero to the “blind area” where data are not available. The reconstruction directly from the limited-view data is the so-called zero-order or “naive” solution and the image is often blured and distorted because the data in the blind area are not actually zero. In this paper, we combine the convex projections and direct Fourier transform to estimate the blind area data for cross-hole seismic diffraction tomography. The limited-view angle problem is an underdetermined problem in which only a small number of projections is available. Artifacts such as streaking and geometric distortion are inevitable in the reconstructed image. This lack of information, however, may be made up in part by adequate a priori knowledge about the image. Such knowledge may be used to impose constraints on the solutions or the reconstruction procedure in an attempt to regularize the ill-posed problem. POCS offers two note-worthy advantages: 1) it enables any number of a priori convex-type constraints to be incorporated in the algorithm; and 2) it guarantees convergence: weak in general, strong in practice. It is a recursive technique that finds a solution consistent with the measured data and a priori known constraints in both the space and Fourier domain. Because of these advantages, POCS has found applications in image restoration and X-ray CT image reconstruction, etc. In this paper, it is used in seismic diffraction tomography. BASIC EQUATIONS OF SEISMIC DIFFRACTION TOMOGRAPHY Consider the case of the acoustic wave equation with constant density. The object is described by the velocity distribution where is the position vector. The background medium has a velocity The wave equation in the source-free region is

We consider the problem of locating a signal-source node, using characteristic signals emitted by the node that are captured by a set of sensor nodes. This estimation problem has often been formulated as a weighted least-squares problem in the literature. Received signal strength and asynchronous time-of-arrival measurements, however, give rise to objective functions with multiple local minima and saddle-points, complicating the optimization process. Recently, the method of projection onto convex sets (POCS) was suggested as a means to estimate source position, when received signal strength measurements are available. POCS has been shown to be robust to local minima in the objective function, is of low complexity, and is possible to distribute over the sensor nodes in the network. The drawback of POCS, when convex sets bounded by circles are used, is its poor performance in locating source nodes outside the outer perimeter of sensor nodes. We propose an extension to the presented POCS algorithm, called hyperbolic POCS, that increases the performance of circular POCS, allows for positioning of source nodes outside the outer perimeter of sensor nodes, and is applicable also for the case of asynchronous time-of-arrival measurements

In this paper, we present a novel postprocessing technique based on the theory of the projection onto convex sets (POCS) in order to reduce the blocking artifacts in digital high definition television (HDTV) images. By detecting and eliminating the undesired high-frequency components, mainly caused by blocking artifacts, we propose a new smoothness constraint set (SCS) and its projection operator in the DCT domain. In addition, we propose an improved quantization constraint set (QCS) using the correlation of DCT coefficients between adjacent blocks. In the proposed technique, the range of the QCS is efficiently reduced as close to the original DCT coefficient as possible to yield better performance of the projection onto the QCS. Computer simulation results indicate that the proposed schemes perform better than conventional algorithms. Furthermore, we introduce a fast implementation method of the proposed algorithm. The conventional POCS-based postprocessing techniques require the forward/inverse discrete cosine transform (DCT/IDCT) operations with a heavy computational burden. To reduce the computational complexity we introduce a fast implementation method of the proposed algorithm that does not perform DCT/IDCT operations. Estimates of computation savings vary between 41% and 64% depending on the task.

Improved POCS reconstruction of stereoscopic views

An image recovery algorithm based on alternating projections onto convex sets (POCS) is proposed for block-based coding. In the proposed algorithm, vectors are extracted from the surrounding neighborhood of a missing block to make a convex hull for the reference of recovery. The recovery vectors including both known and lost pixels are used for the projections to find optimal spectrum coefficients for the missing pixels. The convex hull and two other convex sets are formulated for application of POCS. Simulation results show that the proposed algorithm recovers spatial structure both at low and high frequencies.

Rotational motion artifacts in magnetic resonance (MR) images can have a significantly adverse effect on the diagnostic value of the image. Post-processing techniques for the suppression of such artifacts often involve re-gridding of the acquired k-space data. This technique creates significant data void regions in the corrected k-space. Projection onto convex sets (POCS) proved to be successful in estimating the missing k-space values. However, the available data are often subjected to noise and interpolation errors which cause the k-space constraints to form an ill defined convex set, inconsistent with the spatial constraints. Inconsistent constraints often lead to divergence of POCS from the desired solution, within a finite number of iterations. Here, the authors propose a fuzzy model for representing the available k-space values to avoid such divergence. They also present a set of fuzzy rules, to impose soft k-space constraints. Simulation results indicate that the proposed algorithm avoids divergence, producing a superior quality final image.

Summary form only given, as follows. The tomographic reconstruction of multidimensional waveforms from limited data is considered. The particular case treated is when there is access to projections over only a limited view of an object. The algorithm that has been developed can be considered to be an enhanced version of the projection onto convex sets (POCS) technique. Two problems with the original algorithm, dependence of the final answer upon the starting guess and the question of when to terminate the procedure, are addressed. An enhanced version computes an ensemble of inverses that are consistent with both the observed data and the a priori knowledge by executing the POCS algorithm a multiplicity of times with measured data plus random noise as a starting guess. The resulting ensemble of inverses is analyzed in order to create an a posteriori filter. This filter is applied to the restored image, the result of executing the POCS algorithm on the measured data. The resulting image exhibits less noise amplification in the final result than is the case with the original procedure. The enhanced algorithm seems to perform well in the presence of moderate noise and is less dependent on both starting data and the number of iterations. >

Super-resolution (SR) reconstruction, particularly on face images, can be widely used in forensic analysis and video surveillance. In this paper, we investigate the statistical characteristics of face images and incorporate them into SR reconstruction in terms of deterministic sets. Based on the set theoretic formulation, the projection onto convex sets (POCS) algorithm is applied to find the solution to face image reconstruction. Compared with the traditional POCS based SR methods, the proposed approach imposes additional constraints to the solution. The experimental results on frontal face images show that the proposed approach gains a better performance both on noise suppression and reconstruction quality.

Recently, it has been shown that interior tomography problems in x-ray CT can be uniquely determined if tiny subregions inside of the region of interest are known. The solution can be obtained by the projection onto convex sets (POCS) combined with the backprojection filtration algorithm. However, it is well-known that the convergence speed of POCS is slow; hence, to overcome the limitation, this paper employs a parallel proximal algorithm (PPXA) to simultaneously consider multiple convex constraints rather than projecting on each of them sequentially as in POCS. Our simulation results show that the solution for the interior tomography problem can be accurately obtained using PPXA with a much smaller number of iterations than POCS.

This paper proposes a comparative study of various super resolution (SR) techniques: Spectral approach, Interpolation and fusion, Wiener filtering, Maximum A Posteriori (MAP), Eigenfaces reconstruction and Projection Onto Convex Sets (POCS). MAP, Eigenfaces, Wiener filtering and POCS have been implemented and experimented on gray level images. We compare the performances of the algorithms on standard test protocols. The POCS and MAP give similar results. Blind SR [4], hybrid methods POCS-MAP and also the improvement of algorithms so that they can operate in real time are future directions for research work.

To investigate limitations of partial Fourier acquisition in phase-contrast MRI of turbulent kinetic energy (TKE). To assess the validity of partial Fourier reconstruction of TKE and phase images, computational fluid dynamics data of mean and turbulent velocities in a stenotic U-bend phantom was used. Partial Fourier acquisition with 75% k-space coverage was simulated and TKE data were reconstructed using zero-filling, homodyne reconstruction, and the method of projections onto convex sets (POCS). Results were compared to data from fully sampled k-space and 75% symmetric sampling. In addition, compressed sensing (CS) reconstruction was compared for a standard variable density sampling pattern and a variable density sampling pattern combined with 75% partial Fourier. For illustration purposes, in vivo examples of velocity magnitude and TKE maps of aortic flow reconstructed with the different methods are provided. In accordance with theory, partial Fourier reconstruction of TKE maps from phase-contrast data results in artifacts relative to fully sampled data. It is demonstrated that neither homodyne reconstruction nor POCS can improve reconstruction of TKE data with respect to zero-filling reconstruction when compared to ground-truth (RMS error: 4.70%, 4.34%, and 2.45% for homodyne, POCS, and zero-filling reconstruction of in vivo data, respectively). CS reconstruction from data acquired with partial Fourier did not recover the resolution loss incurred by partial Fourier sampling. Partial Fourier reconstruction of TKE maps from phase-contrast data does not yield a benefit over zero-filling reconstruction. In consequence, symmetric sampling is preferred over partial Fourier acquisition for a given number of phase-encodes in phase-contrast MRI.