A practical projection-based postprocessing of block-coded images with fast convergence rate

A smoothness constraint set based on local statistics of BDCT coefficients for image postprocessing

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.

It is well known that low bit rate block-based discrete cosine transform coded image exhibits visually annoying coding artifacts. In this paper, we proposed a projection onto convex sets (PCOS)-based deblocking algorithm using a novel region smoothness constraint set for graphic images containing objects with smooth regions. The smoothness constraint set is obtained by an explicit modeling of smooth regions in the image using a spatially adaptive thin-plate spline. In contrast to most deblocking algorithms which enforce smoothness just around the 8/spl times/8 block boundaries, our algorithm enforces smoothness in regions which could possibly span several blocks. We showed that convergence of our algorithm could be reached within one iteration. The performance of the proposed algorithm is evaluated visually and quantitatively in term of peak signal-to-noise ratios and the mean squared difference of slope metric, which measures the impact of the blocking effects, for several graphic images. The results show that our algorithm can effectively suppress blockiness in smooth regions while still preserving the sharpness of object edges.

Generating artifacts is a major problem with compressed images coded by the block discrete cosine transform (BDCT). An iterative deblocking method based on projection onto convex sets (POCS) is presented in this paper. The method considers pixel-wise local adaptability. The adjustment of a pixel is determined by local properties of the pixel. A coded image is iteratively projected onto two locally adaptive smoothness constraint sets, a locally adaptive quantization constraint set and an intensity constraint set to obtain an improved image where artifacts are reduced. The proposed method is tested on JPEG encoded images with excellent results.

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 addresses a simple, and yet effective approach to the design of block adaptive beamformers via parallel projection method (PPM), which is an extension of the classic projection onto convex set (POCS) method to inconsistent sets scenarios. The proposed approach begins with the construction of the convex constraint sets which the weight vector of the adaptive beamformer lies in. The convex sets are judiciously chosen to force the weights to possess some desirable properties or to meet some prescribed rules. Based on the minimum variance criterion and a fixed gain at the look direction, two constraint sets including the minimum variance constraint set and the gain constraint set are considered. For every input block of data, the weights of the proposed beamformer can then be determined by iteratively projecting the weight vector onto these convex sets until it converges. Furnished simulations show that the proposed beamformer provides superior performance compared with previous works in various scenarios but yet in general with lower computational overhead.

The projection onto convex sets (POCS) is a powerful iterative approach for the solution of inverse problems. One can easily incorporate into this approach a variety of useful constraints for image restoration which would otherwise be difficult to implement using the traditional image restoration techniques. We present the application of POCS for restoration of 3D real images. The underlying principle of the method is discussed in detail, and optical microscopy images restored by this method are presented and analysed. It will be shown that POCS is a versatile image restoration method and can produce high quality 1estored images if an appropriate set of constraints are used.

CCTV forensics is a very challenging task as video files seized from a CCTV DVR can be in a detrimental state with bad lighting ambience, noise, blurring due to optical settings and motion, compression artifacts, interlaces and low-resolved frame size to name a few. This always results in the difficulties in analyzing subjects in the video which are subjected to investigation. We present a multiple-frames Super-Resolution technique by combining a sequence of video frames of a subject in order to create a super-resolved frame of the subject with increased resolution and clarities. For that purpose, we used Projection onto Convex Sets (POCS) method for the super-resolution. For estimating the shift and rotational parameters of frames for the POCS we used Keren for that purpose. This process is tested with real footage of CCTV video which we did simulation on a crime scene. From the experiments we conducted, the results found are far exceeding in quality than conventional image resampling methods.

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

The theory of projection onto convex sets (POCS) is applied to reduce blocking artifacts in compressed images coded by the block discrete cosine transform (BDCT). An image before compression is simulated by a triangular mesh, which is the basis of a proposed smoothness constraint set. The mesh is constructed by dividing each block into a set of triangles. The proposed method outperforms four existing methods subjectively and objectively.

In this paper, we propose a method that recovers a smooth high-resolution image from several blurred and roughly quantized low-resolution images. For compensation of the quantization effect we introduce measurements of smoothness, Huber function that is originally used for suppression of block noises in a JPEG compressed image [Schultz & Stevenson '94] and a smoothed version of total variation. With a simple operator that approximates the convex projection onto constraint set defined for each quantized image [Hasegawa et al. '05], we propose a method that minimizes these cost functions, which are smooth convex functions, over the intersection of all constraint sets, i.e. the set of all images satisfying all quantization constraints simultaneously, by using hybrid steepest descent method [Yamada & Ogura '04]. Finally in the numerical example we compare images derived by the proposed method, Projections Onto Convex Sets (POCS) based conventinal method, and generalized proposed method minimizing energy of output of Laplacian.

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.