A new multistage lattice vector quantization with adaptive subband thresholding for image compression

Lattice vector quantization (LVQ) reduces coding complexity and computation due to its regular structure. A new multistage LVQ (MLVQ) using an adaptive subband thresholding technique is presented and applied to image compression. The technique concentrates on reducing the quantization error of the quantized vectors by "blowing out" the residual quantization errors with an LVQ scale factor. The significant coefficients of each subband are identified using an optimum adaptive thresholding scheme for each subband. A variable length coding procedure using Golomb codes is used to compress the codebook index which produces a very efficient and fast technique for entropy coding. Experimental results using the MLVQ are shown to be significantly better than JPEG 2000 and the recent VQ techniques for various test images

A new multistage lattice vector quantization with adaptive subband thresholding for image compression

Lattice vector quantization (LVQ) reduces coding complexity and computation due to its regular structure. A new multistage LVQ (MLVQ) using an adaptive subband thresholding technique is presented and applied to image compression. The technique concentrates on reducing the quantization error of the quantized vectors by "blowing out" the residual quantization errors with an LVQ scale factor. The significant coefficients of each subband are identified using an optimum adaptive thresholding scheme for each subband. A variable length coding procedure using Golomb codes is used to compress the codebook index which produces a very efficient and fast technique for entropy coding. Experimental results using the MLVQ are shown to be significantly better than JPEG 2000 and the recent VQ techniques for various test images

Piecewise uniform switched vector quantization of the memoryless two-dimensional Laplace source

A simple and complete asymptotical analysis of an optimal piecewise uniform quantization of two-dimensional memoryless Laplacian source with the respect to distortion (D) i.e. the mean-square error (MSE) is presented. Piecewise uniform quantization consists of L different uniform vector quan-tizers. Uniform quantizer optimality conditions and all main equations for optimal number of output points and levels for each partition are presented (using rectangular cells). The optimal granular distortion (i) for each partition in a closed form is derived. Switched quantization is used in order to give higher quality by increasing signal-to-quantization noise ratio (SQNR) in a wide range of signal volumes (variances) or to decrease necessary sample rate

Piecewise uniform switched vector quantization of the memoryless two-dimensional Laplacian source

A simple and complete asymptotical analysis of an optimal piecewise uniform quantization of two-dimensional memoryless Laplacian source with the respect to distortion (D) i.e. the mean-square error (MSE) is presented. Piecewise uniform quantization consists of L different uniform vector quantizers. Uniform quantizer optimality conditions and all main equations for optimal number of output points and levels for each partition are presented (using rectangular cells). The optimal granular distortion Doptg (i) for each partition in a closed form is derived. Switched quantization is used in order to give higher quality by increasing signal-to-quantization noise ratio (SQNR) in a wide range of signal volumes (variances) or to decrease necessary sample rate.Представлен простой и полный асимптотический анализ оптимального, кусочно-равномерного квантования двумерного лапласовского источника без запоминания относительно искажения (D), т.е. среднеквадратическая ошибка (СКО). Кусочно-равномерное квантование состоит из L различных векторных квантователей с равномерным шагом. Представлены с использованием прямоугольных элементов оптимальные условия для квантователей с равномерным шагом и все основные уравнения для оптимального количества выходных точек и уровней при каждом разделении. Получено оптимальное искажение, обусловленное зернистостью изображения Doptg (i), для каждого разделения в замкнутом виде. Квантование с переключением используется для достижения более высокого качества путем увеличения отношения сигнал/шум квантования (SQNR) в широком диапазоне уровней сигнала (колебаний) или уменьшения необходимой частоты выборки.Наведено простий і повний асимптотичний аналіз оптимального, кусково-рівномірного квантування двомірного лапласівського джерела без запам’ятовування відносно викривлення (D), тобто середньоквадратичної помилки (СКП). Кусково-рівномірне квантування складається з L різноманітних векторних квантувателів з рівномірним шагом. Наведено з використанням прямокутних елементів оптимальні умови для квантувателів із рівномірним шагом і всі основні рівняння для оптимальної кількості вихідних точок і рівнів для кожного розподілення. Отримано оптимальне викривлення, що обумовлене зернистістю зображення Doptg (i), для кожного розподілення у замкнутому вигляді. Квантування з перемиканням використовується для досягнення більш високої якості шляхом збільшення відношення сигнал/шум квантування (SQNR) у широкому діапазоні рівнів сигналу (коливань) або зменшення необхідної частоти вибірки

Quantization and erasures in frame representations

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 123-126).Frame representations, which correspond to overcomplete generalizations to basis expansions, are often used in signal processing to provide robustness to errors. In this thesis robustness is provided through the use of projections to compensate for errors in the representation coefficients, with specific focus on quantization and erasure errors. The projections are implemented by modifying the unaffected coefficients using an additive term, which is linear in the error. This low-complexity implementation only assumes linear reconstruction using a pre-determined synthesis frame, and makes no assumption on how the representation coefficients are generated. In the context of quantization, the limits of scalar quantization of frame representations are first examined, assuming the analysis is using inner products with the frame vectors. Bounds on the error and the bit-efficiency are derived, demonstrating that scalar quantization of the coefficients is suboptimal. As an alternative to scalar quantization, a generalization of Sigma-Delta noise shaping to arbitrary frame representations is developed by reformulating noise shaping as a sequence of compensations for the quantization error using projections.(cont.) The total error is quantified using both the additive noise model of quantization, and a deterministic upper bound based on the triangle inequality. It is thus shown that the average and the worst-case error is reduced compared to scalar quantization of the coefficients. The projection principle is also used to provide robustness to erasures. Specifically, the case of a transmitter that is aware of the erasure occurrence is considered, which compensates for the erasure error by projecting it to the subsequent frame vectors. It is further demonstrated that the transmitter can be split to a transmitter/receiver combination that performs the same compensation, but in which only the receiver is aware of the erasure occurrence. Furthermore, an algorithm to puncture dense representations in order to produce sparse approximate ones is introduced. In this algorithm the error due to the puncturing is also projected to the span of the remaining coefficients. The algorithm can be combined with quantization to produce quantized sparse representations approximating the original dense representation.by Petros T. Boufounos.Sc.D

Quadrature sigma-delta modulators for reconfigurable A/D interface and dynamic spectrum access: analysis, design principles and digital post-processing

In the course of development of wireless communications and its modern applications, such as cloud technologies and increased consumption and sharing of multimedia, the radio spectrum has become increasingly congested. However, temporarily and spatially underused spectrum exists at the same time. For increasing the efficiency of spectrum usage, the concept of dynamic spectrum access (DSA) has been proposed. Ultimately, the DSA principle should be exploited also in cognitive radio (CR) receivers. Herein, this paradigm is approached from the receiver architecture point-of-view, considering software-defined radio (SDR) as a platform for the future DSA and CR devices. Particularly, an analog-to-digital converter (ADC) architecture exploiting quadrature ΣΔ modulator (QΣΔM) is studied in detail and proposed as a solution for the A/D interface, being identified as a performance bottleneck in SDRs. By exploiting a complex valued noise transfer function (NTF) enabled by the QΣΔM, the quantization precision of the ADC can be efficiently and flexibly focused on the frequency channels and the signals to be received and detected. At the same time, with a traditional non-noise-shaping ADC, the precision is distributed equally for the whole digitized frequency band containing also noninteresting signals. With a single QΣΔM, it is also possible to design a multiband NTF, allowing reception of multiple noncontiguous frequency channels without parallel receiver chains. Furthermore, with the help of digital control, the QΣΔM response can be reconfigured during operation. These capabilities fit in especially well with the above mentioned DSA and CR schemes, where the temporarily and spatially available channels might be scattered in frequency. From the implementation point-of-view, the effects of inherent implementation inaccuracies in the QΣΔM design need to be thoroughly understood. In this thesis, novel closed-form matrix-algebraic expressions are presented for analyzing the transfer functions of a general multistage QΣΔM with arbitrary number of arbitrary-order stages. Altogether, the signal response of an I/Q mismatched QΣΔM has four components. These are the NTF, an image noise transfer function, a signal transfer function (STF) and an image signal transfer function. The image transfer functions are provoked by the I/Q mismatches and define the frequency profile of the generated mirror-frequency interference (MFI), potentially deteriorating the quality of the received signal. This contribution of the thesis increases the understanding of different QΣΔM structures and allows the designers to study the effects of the implementation inaccuracies in closed form. In order to mitigate the MFI and improve the signal reception, a mirror-frequency rejecting STF design is proposed herein. This design is found to be effective against I/Q mismatches taking place in the feedback branches of the QΣΔM. This is shown with help of the closed-form analysis and confirmed with computer simulations on realistic reception scenarios. When a mismatch location independent MFI suppression is the desired option, it is a logical choice to do this processing in a digital domain, after the whole analog receiver front-end. However, this sets demands for the information to be digitized, i.e., the source of the MFI should be available also in the digital domain. For this purpose, a novel multiband transfer function design is proposed herein. In addition, a QΣΔM specific digital MFI compensation algorithm is developed. The compensation performance is illustrated in practical single- and multiband reception scenarios, considering desired signal bandwidths up to 20 MHz. In the multiband scenario, allowing reception and detection of noncontiguous frequency channels with a single receiver chain, the digital compensation processing is done sub-bandwise, securing reliable functionality also under strongly frequency-selective interference. In the applied single- and multistage QΣΔM architectures, the I/Q mismatches are considered in all the QΣΔM branches as well as in the preceding receiver front-end, modeling the challenging and realistic scenario where the whole receiver chain includes cascaded in-phase/quadrature (I/Q) mismatch sources. As a whole, developing digital MFI compensation is a significant step towards practical receiver implementations with QΣΔM ADCs. In consequence, this allows the exploitation of the multiband and reconfigurability properties. The proposed design can be implemented without additional analog components and is straightforwardly reconfigurable in dynamic signal conditions typical for DSA and CR systems, e.g., in case of frequency hand-off because of a primary user appearance. In addition, the digital post-compensation of the MFI eases the strict demands for the matching of the analog circuits in SDRs