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1

Simulation of the Operation of a Single Pixel Camera with Compressive Sensing in the Long-Wave Infrared

Szajewska Anna

Pomiary Automatyka Robotyka

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2021

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R. 25, nr 2

53--60

EN

Imaging with the use of a single pixel camera and based on compressed sensing (CS) is a new and promising technology. The use of CS allows reconstruction of images in various spectrum ranges depending on the spectrum sensibility of the used detector. During the study image reconstruction was performed in the LWIR range based on a thermogram from a simulated single pixel camera. For needs of reconstruction CS was used. A case analysis showed that the CS method may be used for construction of infrared-based observation single pixel cameras. This solution may also be applied in measuring cameras. Yet the execution of a measurement of radiation temperature requires calibration of results obtained by CS reconstruction. In the study a calibration method of the infrared observation camera was proposed and studies were carried out of the impact exerted by the number of measurements made on the quality of reconstruction. Reconstructed thermograms were compared with reference images of infrared radiation. It has been ascertained that the reduction of the reconstruction error is not directly in proportion to the number of collected samples being collected. Based on a review of individual cases it has been ascertained that apart from the number of collected samples, an important factor that affects the reconstruction fidelity is the structure of the image as such. It has been proven that estimation of the error for reconstructed thermograms may not be based solely on the quantity of executed measurements.

PL

Obrazowanie kamerą jednopikselową z użyciem CS (compressed sensing) jest nową i obiecującą technologią. Za pomocą CS można rekonstruować obrazy w różnych zakresach widmowych zależnie od czułości spektralnej użytego detektora. W pracy wykonano rekonstrukcję obrazu w zakresie LWIR (Long-Wave Infrared) na podstawie termogramu z zasymulowanej kamery jednopikselowej. Do rekonstrukcji użyto CS. Na podstawie analizy przypadków stwierdzono, że metodę CS można wykorzystać do budowania kamer obserwacyjnych jednopikselowych na podczerwień. Możliwe jest również zastosowanie tego rozwiązania w kamerach pomiarowych. Aby wykonać pomiar temperatury radiacyjnej należy dokonać kalibracji wyników uzyskanych na drodze rekonstrukcji CS. W badaniu zaproponowano sposób kalibracji kamery pomiarowej na podczerwień oraz zbadano wpływ liczby pomiarów na jakość rekonstrukcji. Zrekonstruowane termogramy porównano z referencyjnymi obrazami promieniowania podczerwonego. Stwierdzono, że redukcja błędu rekonstrukcji nie jest wprost proporcjonalna do zwiększanej liczby pobieranych próbek. Na podstawie analizy przypadków zaobserwowano, że poza liczbą pobieranych próbek, istotnym czynnikiem mającym wpływającym na wierność rekonstrukcji jest struktura samego obrazu. Dowiedziono, że szacowanie błędu dla zrekonstruowanych termogramów nie może być oparte tylko na liczbie wykonywanych pomiarów.

2

Linear and Planar Array Pattern Nulling via Compressed Sensing

Mohammed Jafar Ramadhan, Thaher Raad H., Abdulqader Ahmed Jameel

Journal of Telecommunications and Information Technology

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2021

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nr 3

50--55

EN

An optimization method based on compressed sensing is proposed for uniformly excited linear or planar antenna arrays to perturb excitation of the minimum number of array elements in such a way that the required number of nulls is obtained. First, the spares theory is relied upon to formulate the problem and then the convex optimization approach is adopted to find the optimum solution. The optimization process is further developed by using iterative re-weighted l1- norm minimization, helping select the least number of the sparse elements and impose the required constraints on the array radiation pattern. Furthermore, the nulls generated are wide enough to cancel a whole specific sidelobe. Simulation results demonstrate the effectiveness of the proposed method and the required nulls are placed with a minimum number of perturbed elements. Thus, in practical implementations of the proposed method, a highly limited number of attenuators and phase shifters is required compared to other, conventional methods.

3

High-resolution Direction of Arrival Estimation Method Based on Sparse Arrays with Minimum Number of Elements

Mohammed Jafar Ramadhan

Journal of Telecommunications and Information Technology

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2021

|

nr 1

8--14

EN

Regular fully filled antenna arrays have been widely used in direction of arrival (DOA) estimation. However, practical implementation of these arrays is rather complex and their resolutions are limited to the beamwidth of the array pattern. Therefore, higher resolution and simpler methods are desirable. In this paper, the compressed sensing method is first applied to an initial fully filled array to randomly select the most prominent and effective elements which are used to form the sparse array. To keep the dimension of the sparse array equal to that of the fully filled array, the first and the last elements were excluded from the sparseness process. In addition, some constraints on the sparse spectrum are applied to increase estimation accuracy. The optimization problem is then solved iteratively using the iterative reweighted l1 norm. Finally, a simple searching algorithm is used to detect peaks in the spectrum solution that correspond to the directions of the arriving signals. Compared with the existing scanned beam methods, such as the minimum variance distortionless response (MVDR) technique, and with subspace approaches, such as multiple signal classification (MUSIC) and ESPIRT algorithms, the proposed sparse array method offers better performance even with a lower number of array elements and in severely noisy environments. Effectiveness of the proposed sparse array method is verified via computer simulations.

4

An unscented transformation approach to stochastic analysis of measurement uncertainty in magnet resonance imaging with applications in engineering

Rauh Andreas, John Kristine, Wüstenhagen Carolin, Bruschewski Martin, Grundmann Sven

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 1

73--83

EN

In the frame of stochastic filtering for nonlinear (discrete-time) dynamic systems, the unscented transformation plays a vital role in predicting state information from one time step to another and correcting a priori knowledge of uncertain state estimates by available measured data corrupted by random noise. In contrast to linearization-based techniques, such as the extended Kalman filter, the use of an unscented transformation not only allows an approximation of a nonlinear process or measurement model in terms of a first-order Taylor series expansion at a single operating point, but it also leads to an enhanced quantification of the first two moments of a stochastic probability distribution by a large signal-like sampling of the state space at the so-called sigma points which are chosen in a deterministic manner. In this paper, a novel application of the unscented transformation technique is presented for the stochastic analysis of measurement uncertainty in magnet resonance imaging (MRI). A representative benchmark scenario from the field of velocimetry for engineering applications which is based on measured data gathered at an MRI scanner concludes this contribution.

5

Damped Zero-Pseudorandom Noise OFDM Systems

Esmaiel H.

International Journal of Electronics and Telecommunications

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2018

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Vol. 64, No. 4

433--438

EN

This paper proposed a new OFDM scheme called damped zero-pseudorandom noise orthogonal frequency division multiplexing (DZPN-OFDM) scheme. In the proposed scheme, ZPN-OFDM non-zero part is damped to reduce its energy, thus the mutual interference power in-between the data and training blocks with conservative the pseudo-noise conventional properties required for channel estimation or synchronization. The motivation of this paper is the OFDM long guard interval working in wide dispersion channels, whereas a significant energy is wasted when the conventional ZPN-OFDM is used as well as the BER performance is also degraded. Moreover, the proposed scheme doesn’t duplicate the guard interval to solve the ZPN-OFDM spectrum efficiency loss problem. Both detailed performance analysis and simulation results show that the proposed DZPNOFDM scheme can, indeed, offer significant bit error rate, spectrum efficiency and energy efficiency improvement.

6

Compressed sensing in MRI : mathematical preliminaries and basic examples

Błaszczyk Ł.

Nukleonika

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2016

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Vol. 61, No. 1

41--43

EN

In magnetic resonance imaging (MRI), k-space sampling, due to physical restrictions, is very time- -consuming. It cannot be much improved using classical Nyquist-based sampling theory. Recent developments utilize the fact that MR images are sparse in some representations (i.e. wavelet coeffi cients). This new theory, created by Candès and Romberg, called compressed sensing (CS), shows that images with sparse representations can be recovered from randomly undersampled k-space data, by using nonlinear reconstruction algorithms (i.e. l1-norm minimization). Throughout this paper, mathematical preliminaries of CS are outlined, in the form introduced by Candès. We describe the main conditions for measurement matrices and recovery algorithms and present a basic example, showing that while the method really works (reducing the time of MR examination), there are some major problems that need to be taken into consideration.

7

Application of the compress sensing theory for improvement of the TOF resolution in a novel J-PET instrument

Raczyński L., Moskal P., Kowalski P., Wiślicki W., Bednarski T., Białas P., Czerwiński E., Gajos A., Kapłon Ł., Kochanowski A., Korcyl G., Kowal J., Kozik T., Krzemień W., Kubicz E., Niedźwiecki S., Pałka M., Rudy Z., Salabura P., Gupta-Sharma N., Silarski M., Słomski A., Smyrski J., Strzelecki A., Wieczorek A., Zieliński M., Zoń N.

Nukleonika

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2016

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Vol. 61, No. 1

35--39

EN

Nowadays, in positron emission tomography (PET) systems, a time of fl ight (TOF) information is used to improve the image reconstruction process. In TOF-PET, fast detectors are able to measure the difference in the arrival time of the two gamma rays, with the precision enabling to shorten signifi cantly a range along the line-of-response (LOR) where the annihilation occurred. In the new concept, called J-PET scanner, gamma rays are detected in plastic scintillators. In a single strip of J-PET system, time values are obtained by probing signals in the amplitude domain. Owing to compressive sensing (CS) theory, information about the shape and amplitude of the signals is recovered. In this paper, we demonstrate that based on the acquired signals parameters, a better signal normalization may be provided in order to improve the TOF resolution. The procedure was tested using large sample of data registered by a dedicated detection setup enabling sampling of signals with 50-ps intervals. Experimental setup provided irradiation of a chosen position in the plastic scintillator strip with annihilation gamma quanta.

8

Semi-PROPELLER Compressed Sensing Image Reconstruction with Enhanced Resolution in MRI

Malczewski K.

International Journal of Electronics and Telecommunications

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2015

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Vol. 61, No. 2

211–217

EN

Magnetic Resonance Imaging (MRI) reconstruction algorithm using semi-PROPELLER compressed sensing is presented in this paper. It is exhibited that introduced algorithm for estimating data shifts is feasible when super- resolution is applied. The offered approach utilizes compressively sensed MRI PROPELLER sequences and improves MR images spatial resolution in circumstances when highly undersampled k-space trajectories are applied. Compressed sensing (CS) aims at signal and images reconstructing from significantly fewer measurements than were traditionally thought necessary. It is shown that the presented approach improves MR spatial resolution in cases when Compressed Sensing (CS) sequences are used. The application of CS in medical modalities has the potential for significant scan time reductions, with visible benefits for patients and health care economics. These methods emphasize on maximizing image sparsity on known sparse transform domain and minimizing fidelity. This diagnostic modality struggles with an inherently slow data acquisition process. The use of CS to MRI leads to substantial scan time reductions [7] and visible benefits for patients and economic factors. In this report the objective is to combine Super-Resolution image enhancement algorithm with both PROPELLER sequence and CS framework. The motion estimation algorithm being a part of super resolution reconstruction (SRR) estimates shifts for all blades jointly, utilizing blade-pair correlations that are both strong and more robust to noise.

9

Wpływ rozmieszczenia mierzonych przekrojów na dokładność wyznaczenia odchyłki walcowości

Gorycki Ł.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Nauki Techniczne

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2014

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Z. 18

44--50

PL

W niniejszym artykule zamieszczona jest analiza wpływu liczby losowo wybranych przekrojów na odchyłkę walcowości. Jest to podstawa do określenia metody „ślepej”, pozwalającej na określenie właściwej liczby przekrojów w celu wykonania szybkich i dokładnych pomiarów dowolnego elementu walcowego.

EN

In this article we analysis the influence of the number of randomly selected cross-sections on the cylindricity deviation. It is the basis for determineing the "blind" method of to assign the correct number of sections in order to make quick and accurate measurements of any of the cylindrical element.

10

Phase Transitions and Cosparse Tomographic Recovery of Compound Solid Bodies from Few Projections

Denitiu A., Petra S., Schnörr C., Schnörr Ch.

Fundamenta Informaticae

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2014

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Vol. 135, nr 1/2

73--102

EN

We study unique recovery of cosparse signals from limited-view tomographic measurements of two- and three-dimensional domains. Admissible signals belong to the union of subspaces defined by all cosupports of maximal cardinality l with respect to the discrete gradient operator. We relate l both to the number of measurements and to a nullspace condition with respect to the measurement matrix, so as to achieve unique recovery by linear programming. These results are supported by comprehensive numerical experiments that show a high correlation of performance in practice and theoretical predictions. Despite poor properties of the measurement matrix from the viewpoint of compressed sensing, the class of uniquely recoverable signals basically seems large enough to cover practical applications, like contactless quality inspection of compound solid bodies composed of few materials.

11

Study on Piecewise Smooth Signal Reconstruction Algorithms based on Compressed Sensing

Gao G. C., Zhang C., Zhao S. Y.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 1b

168--170

EN

In this paper, the unknown piecewise smooth signal was chosen as tested signal. After random matrix were chosen as measure matrix, we design the CS (Compressed Sensing) model for the unknown piecewise smooth signal. The signal was reconstructed using the OMP (Orthogonal Matching Pursuit) algorithm. The linear combination wavelet bases were proposed by the authors and were chosen as the sparse base in the CS model. The simulation results show that CS model by this paper can acquire the better approximation of the original signal.

PL

W artykule opisano metodę rekonstrukcji sygnału odcinkowo-gładkiego, z wykorzystaniem algorytmu OMP. Dane uzyskane z modelu próbkowania oszczędnego (ang. Compressed Sensing) sygnału, umieszczono w wygenerowanej losowo macierzy pomiarowej. W algorytmie próbkowania wykorzystano falkowe kombinacje liniowe. Wykazano, że zastosowany model próbkowania oszczędnego pozwala na lepszą aproksymację sygnału.

12

Recognition of the numbers in the Polish language

Plichta A., Gąciarz T., Krzywdziński T.

Journal of Telecommunications and Information Technology

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2013

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nr 4

70--78

EN

Automatic Speech Recognition is one of the hottest research and application problems in today’s ICT technologies. Huge progress in the development of the intelligent mobile systems needs an implementation of the new services, where users can communicate with devices by sending audio commands. Those systems must be additionally integrated with the highly distributed infrastructures such as computational and mobile clouds, Wireless Sensor Networks (WSNs), and many others. This paper presents the recent research results for the recognition of the separate words and words in short contexts (limited to the numbers) articulated in the Polish language. Compressed Sensing Theory (CST) is applied for the first time as a methodology of speech recognition. The effectiveness of the proposed methodology is justified in numerical tests for both separate words and short sentences.

13

Critical Parameter Values and Reconstruction Properties of Discrete Tomography : Application to Experimental Fluid Dynamics

Petra S., Schnörr C., Schröder A.

Fundamenta Informaticae

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2013

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Vol. 125, nr 3/4

285--312

EN

We analyze representative ill-posed scenarios of tomographic PIV (particle image velocimetry) with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interest with small particles, the corresponding systems of linear projection equations are probabilistically analyzed in order to determine: (i) the ability of unique reconstruction in terms of the imaging geometry and the critical sparsity parameter, and (ii) sharpness of the transition to non-unique reconstruction with ghost particles when choosing the sparsity parameter improperly. The sparsity parameter directly relates to the seeding density used for PIV in experimental fluids dynamics that is chosen empirically to date. Our results provide a basic mathematical characterization of the PIV volume reconstruction problem that is an essential prerequisite for any algorithm used to actually compute the reconstruction. Moreover, we connect the sparse volume function reconstruction problem from few tomographic projections to major developments in compressed sensing.

14

Ograniczenie ilości danych przesyłanych w systemach elektronicznych z wykorzystaniem próbkowania nierównomiernego

Kazała R.

Elektronika : konstrukcje, technologie, zastosowania

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2013

|

Vol. 54, nr 11

32-35

PL

Praca przedstawia wykorzystanie próbkowania nierównomiernego do rejestracji sygnałów elektrycznych o niepełnym widmie częstotliwościowym. Opisuje różne typy sygnałów spotykanych w systemach elektronicznych wykorzystywanych w elektrotechnice i przedstawia możliwości ograniczenia ilości rejestrowanych danych, przy zachowaniu pełnej informacji o sygnale. Na specjalnie dobranych przykładach pokazuje wykorzystanie opisanych metod i wyniki rekonstrukcji mierzonego sygnału. Wyniki pracy mogą być wykorzystane do ograniczenia ilości danych przesyłanych w systemach elektronicznych.

EN

The paper presents the use of non-uniform sampling to record the electrical signals with sparse frequency spectrum. Describes the different types of signals met in electronic systems used in the electrotechnics and presents the potential for reducing amount of recorded data, with full information about the registered signal. The specially selected examples showing the use of these methods and results of the reconstruction of the measured signal. Our results can be used to reduce the amount of data transmitted in electronic systems.

15

Compressed Sensing applied to image reconstruction in a noise SAR

Misiurewicz J., Maślikowski Ł.

Elektronika : konstrukcje, technologie, zastosowania

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2012

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Vol. 53, nr 7

37-40

EN

The paper presents a practical application of Compressed Sensing for reconstruction of radar image from synthetic aperture measurements in a noise radar. When the spatial sampling frequency is limited by external constraints, the image constructed with classical approach would suffer from spatial aliasing. Nonuniform sampling in spatial (along-track) domain followed by Compressed Sensing reconstruction of SAR image leads to correct image reconstruction under the assumption of image sparsity. The described technique is applied to the real data from an experimental ground-based noise SAR built in Warsaw University of Technology. The imaged scene was not a specifically sparse one, however the Compressed Sensing approach proved to be effective even in this case - images of a sparse target recovered with Compressed Sensing do not exhibit aliasing even with significant thinning of the input data.

PL

W pracy przedstawiono praktyczne zastosowanie metody Compressed Sensing do rekonstrukcji obrazu radarowego z sygnału zarejestrowanego radarem szumowym z syntetyczną aperturą. W sytuacji, w której z powodów obiektywnych występują ograniczenia częstotliwości próbkowania w wymiarze przestrzennym poniżej częstotliwości Nyquista, obraz zrekonstruowany metodami klasycznymi wykazuje silne efekty aliasingu przestrzennego. Wykorzystanie nierównomiernego próbkowania i rekonstrukcji metodami Compressed Sensing pozwala na uzyskanie poprawnego obrazu przy założeniu, że obrazowana scena jest rzadka. Opisana technika została zastosowana do rzeczywistego sygnału zarejestrowanego przy pomocy eksperymentalnego radaru szumowego SAR skonstruowanego w Politechnice Warszawskiej. Obrazowana scena nie spełniała ściśle założenia o rzadkości, jednakże technika Compressed Sensing pozwoliła zrekonstruować obraz rzadkich obiektów bez aliasingu nawet przy znacznym podpróbkowaniu danych wejściowych.

16

Podstawowe idee próbkowania oszczędnego

Klamra M.

Czasopismo Techniczne. Nauki Podstawowe

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2012

|

R. 109, z. 1-NP

85--100

PL

Próbkowanie oszczędne jest nową metodą akwizycji danych. Typowe podejście do akwizycji danych polega na pomiarze sygnałów z częstością określoną przez twierdzenie o próbkowaniu. Tak uzyskane dane często są nadmiarowe. Niezbędna jest zatem ich późniejsza kompresja, przeważnie stratna (tutaj idealnym przykładem jest kompresja obrazów np. JPEG), w celu zmniejszenia ilości danych, jakie należy transportować lub składować. Działanie takie powoduje, że zaraz po dokonaniu pomiaru część danych odrzucamy. Próbkowanie oszczędne to protokół pomiaru, który w momencie pomiaru od razu minimalizuje ilość koniecznych pomiarów. Dąży do pomiaru jedynie istotnych składowych sygnału, dane nadmiarowe pomijając. Zastosowanie go jest możliwe przy spełnieniu dodatkowych warunków: rzadkości sygnału badanego oraz niekoherencji w procesie pomiaru.

EN

Compressed Sensing is new method of data acquisition. Typical data acquisition approach is based on the measurement of signals with a frequency determined by the sampling theorem. Data sampled in this way are often redundant. Therefore it is necessary to compress it, often in a loss manner (the perfect examples are image compression algorithms such as JPEG), in order to reduce the amount of data to be transported or stored. Doing so causes that immediately after the measurement, part of the data is rejected. Compressed Sensing is sensing protocol that minimizes the amount of required measurements during sensing. It is designed to measure only the essential components of the signal, omitting redundant information. It is possible to apply such protocol when additional conditions are fulfilled: sparseness of the signal as well as incoherence during sensing.

17

On the application of compressive sampling techniques to high throughput data in computational genomics

Hernández-Lemus H.

Theoretical and Applied Informatics

|

2011

|

Vol. 23, No. 3-4

177-192

EN

With the advent of high throughput experiments in genomics and proteomics, the researcher in computational data analysis is faced with new challenges, both with regards to the computational capacities and also in the probabilistic/statistical methodology fields; in order to handle such massive amounts of data in a systematic coherent way. In this paper we describe the basic aspects of the mathematical theory and the computational implications of a recently developed technique called Compressive Sampling, as well as some possible applications within the scope of Computational Genomics, and Computational Biology in general. The central idea behind this work is that most of the information sampled from the experiments turns out to be discarded (for being non-useful) in the final stages of biological analysis, hence it would be better if we could find an algorithm to remove selectively such information in order to get rid of the computational burden associated with processing and analyzing such huge amounts of data. Here we show that a possible algorithm for doing so it is precisely Compressive Sampling. As a working example, we will consider the data-analysis of whole-genome microarray gene expression for 1191 individuals within a breast cancer project.

18

Efficient coding of LSP parameters using Compressed Sensing on Approximate KLT Domain

Xiao Q., Chen L., Zhu T., Wang Y.

Przegląd Elektrotechniczny

|

2011

|

R. 87, nr 7

230-234

EN

An efficient LSP parameters quantization scheme is proposed using the compressed sensing (CS). The LSP parameters extracted from consecutive speech frames are compressed by CS on the approximate KLT domain to produce a measurement vector, which is quantized using the split vector quantizer. Then, from the quantized measurements, the original LSP parameters are reconstructed by the orthogonal matching pursuit method. Experiments show that the scheme can obtain "transparent quality" at 5 bits/frame with drastic bits reduction compared to other methods.

PL

Zaproponowano kwantyzację parametru LSP (Linear prediction coefficient) przy użyciu metody compressed sensing CS. Oryginalna wartośc LSP może być zrekonstruowana przy zastosowaniu metody ortogonalnego dopasowania. Uzyskano dobrą jakość ramki 5 bitów/ramka ze znacząca redukcją bitów w porównaniu z innymi metodami.