A Posteriori Quantization of Progressive Matching Pursuit Streams

This paper proposes a rate-distortion optimal a posteriori quantization scheme for Matching Pursuit coefficients. The a posteriori quantization applies to a Matching Pursuit expansion that has been generated off-line, and cannot benefit of any feedback loop to the encoder in order to compensate for the quantization noise. The redundancy of the Matching Pursuit dictionary provides an indicator of the relative importance of coefficients and atom indices, and subsequently on the quantization error. It is used to define a universal upper-bound on the decay of the coefficients, sorted in decreasing order of magnitude. A new quantization scheme is then derived, where this bound is used as an Oracle for the design of an optimal a posteriori quantizer. The latter turns the exponentially distributed coefficient entropy-constrained quantization problem into a simple uniform quantization problem. Using simulations with random dictionaries, we show that the proposed exponentially upper-bounded quantization (EUQ) clearly outperforms classical schemes. Stepping on the ideal Oracle-based approach, a sub-optimal adaptive scheme is then designed that approximates the EUQ but still outperforms competing quantization methods in terms of rate-distortion characteristics. Finally, the proposed quantization method is studied in the context of image coding. It performs similarly to state-of-the-art coding methods (and even better at low rates), while interestingly providing a progressive stream, very easy to transcode and adapt to changing rate constraints

A two-stage video coding framework with both self-adaptive redundant dictionary and adaptively orthonormalized DCT basis

In this work, we propose a two-stage video coding framework, as an extension of our previous one-stage framework in [1]. The two-stage frameworks consists two different dictionaries. Specifically, the first stage directly finds the sparse representation of a block with a self-adaptive dictionary consisting of all possible inter-prediction candidates by solving an L0-norm minimization problem using an improved orthogonal matching pursuit with embedded orthonormalization (eOMP) algorithm, and the second stage codes the residual using DCT dictionary adaptively orthonormalized to the subspace spanned by the first stage atoms. The transition of the first stage and the second stage is determined based on both stages' quantization stepsizes and a threshold. We further propose a complete context adaptive entropy coder to efficiently code the locations and the coefficients of chosen first stage atoms. Simulation results show that the proposed coder significantly improves the RD performance over our previous one-stage coder. More importantly, the two-stage coder, using a fixed block size and inter-prediction only, outperforms the H.264 coder (x264) and is competitive with the HEVC reference coder (HM) over a large rate range

Analysis-by-Synthesis-based Quantization of Compressed Sensing Measurements

We consider a resource-constrained scenario where a compressed sensing- (CS) based sensor has a low number of measurements which are quantized at a low rate followed by transmission or storage. Applying this scenario, we develop a new quantizer design which aims to attain a high-quality reconstruction performance of a sparse source signal based on analysis-by-synthesis framework. Through simulations, we compare the performance of the proposed quantization algorithm vis-a-vis existing quantization methods.Comment: 5 pages, Published in ICASSP 201

On Sparse Coding as an Alternate Transform in Video Coding

In video compression, specifically in the prediction process, a residual signal is calculated by subtracting the predicted from the original signal, which represents the error of this process. This residual signal is usually transformed by a discrete cosine transform (DCT) from the pixel, into the frequency domain. It is then quantized, which filters more or less high frequencies (depending on a quality parameter). The quantized signal is then entropy encoded usually by a context-adaptive binary arithmetic coding engine (CABAC), and written into a bitstream. In the decoding phase the process is reversed. DCT and quantization in combination are efficient tools, but they are not performing well at lower bitrates and creates distortion and side effect. The proposed method uses sparse coding as an alternate transform which compresses well at lower bitrates, but not well at high bitrates. The decision which transform is used is based on a rate-distortion optimization (RDO) cost calculation to get both transforms in their optimal performance range. The proposed method is implemented in high efficient video coding (HEVC) test model HM-16.18 and high efficient video coding for screen content coding (HEVC-SCC) for test model HM-16.18+SCM-8.7, with a Bjontegaard rate difference (BD-rate) saving, which archives up to 5.5%, compared to the standard

Open Loop Rate-Distortion Optimized Audio Coding

This paper addresses complexity reduced rate-distortion optimized audio coding under rate constraint. A technique where distor-tion minimizing coding templates, chosen from a set of templates, are jointly selected for a set of segments. This optimization re-quires knowledge of rate-distortion pairs for all segments, and for each coding template, which often are costly to obtain. The pro-posed framework exchanges true rate-distortion pairs with pre-dicted ones, thereby allowing for complexity reduction. The pre-diction is based on a property vector extracted for each segment, from which distortion predictions, using Gaussian mixture mod-els, are performed. Here, we evaluate the proposed framework in a sinusoidal coding context. The results show that the proposed framework can increase the distortion performance, compared to a fixed sinusoidal coding scheme. 1

A Posteriori Quantized Matching Pursuit

This paper studies quantization error in the context of Matching Pursuit coded streams and proposes a new coefficient quantization scheme taking benefit of the Matching Pursuit properties. The coefficients energy in Matching Pursuit indeed decreases with the iteration number, and the decay rate can be upper-bounded with an exponential curve driven by the redundancy of the dictionary. The redundancy factor is therefore used to design an optimal a posteriori quantization scheme for multi-resolution Matching Pursuit coding. Bits are optimally distributed between successive coefficients according to their relative contribution to the signal representation. The quantization range and the number of quantization steps are therefore reduced along the iteration number. Moreover, the quantization scheme selects the optimal number of Matching Pursuit iterations to be coded to satisfy rate constraints. Finally, the new exponentially upper-bounded quantization of Matching Pursuit coefficients clearly outperforms classical uniform quantization methods for both random dictionaries and Gabor dictionaries in the practical case of image coding

Sparse image approximation with application to flexible image coding

Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the direction of the edge, and irregularities on the perpendicular direction. Modeling edges with the minimum possible number of terms is of key importance for numerous applications, such as image coding, segmentation or denoising. Standard separable basis fail to provide sparse enough representation of contours, due to the fact that this kind of basis do not see the regularity of edges. In order to be able to detect this regularity, a new method based on (possibly redundant) sets of basis functions able to capture the geometry of images is needed. This thesis presents, in a first stage, a study about the features that basis functions should have in order to provide sparse representations of a piecewise-smooth image. This study emphasizes the need for edge-adapted basis functions, capable to accurately capture local orientation and anisotropic scaling of image structures. The need of different anisotropy degrees and orientations in the basis function set leads to the use of redundant dictionaries. However, redundant dictionaries have the inconvenience of giving no unique sparse image decompositions, and from all the possible decompositions of a signal in a redundant dictionary, just the sparsest is needed. There are several algorithms that allow to find sparse decompositions over redundant dictionaries, but most of these algorithms do not always guarantee that the optimal approximation has been recovered. To cope with this problem, a mathematical study about the properties of sparse approximations is performed. From this, a test to check whether a given sparse approximation is the sparsest is provided. The second part of this thesis presents a novel image approximation scheme, based on the use of a redundant dictionary. This scheme allows to have a good approximation of an image with a number of terms much smaller than the dimension of the signal. This novel approximation scheme is based on a dictionary formed by a combination of anisotropically refined and rotated wavelet-like mother functions and Gaussians. An efficient Full Search Matching Pursuit algorithm to perform the image decomposition in such a dictionary is designed. Finally, a geometric image coding scheme based on the image approximated over the anisotropic and rotated dictionary of basis functions is designed. The coding performances of this dictionary are studied. Coefficient quantization appears to be of crucial importance in the design of a Matching Pursuit based coding scheme. Thus, a quantization scheme for the MP coefficients has been designed, based on the theoretical energy upper bound of the MP algorithm and the empirical observations of the coefficient distribution and evolution. Thanks to this quantization, our image coder provides low to medium bit-rate image approximations, while it allows for on the fly resolution switching and several other affine image transformations to be performed directly in the transformed domain