However, such quantizer implements an added complexity nonlinear quantization function, which allows the encoder to more accurately manage the tradeoff between bitrate and image quality. Multiplechannel optimized quantizers for rayleigh fading. Optical encoders home nyu tandon school of engineering. The function i is called an encoder, and function c is called a decoder 7. Channel optimized quantizer decoders, in turn, depend on the source, the quantizer encoder, the channel, and the indexassignment. Lloydmax scalar quantizer also known as pdfoptimized quantizer given m, the optimal bi and yi that minimize mse satisfy. The quantizer is defined by an encoding function, cy, which maps quantizer inputs to discrete integer indices or encoder discrete indices into realvalued decoded outputs or recon i 1 j1 h. The first element of quantization codebook is the value for the interval between negative infinity and the first element of p. Point density functions depend on the quantizer decoders. Joint sourcechannel vector quantization for compressed sensing. It is shown that the nbc never induces empty cells in the quantizer encoder, whereas the cnc can.
This block processes each vector element independently. The location of the reconstruction levels may be optimized. Displacement, however, is obtained with respect to some reference point on the disk, as indicated by a reference pulse index pulse generated at that location on the disk. Encode each input value by associating it with index value of. Deep image compression with iterative nonuniform quantization jianrui cai and lei zhang dept. A pdfoptimized scalar quantizer is designed for each of the m2 dct coefficients of y according to the rate allocation discussed above. The condition of cell convexity is not restrictive in. Gaussian and laplacian distributions are assumed for dc and ac coef. The decision thresholds of the softdecision detectors are optimized to achieve minimum endtoend distortion.
The set of stage quantizers are equivalent to a single quantizer, which is referred to as the directsum vector. Overview of different variations of vector quantization. For a fourdimensional vector quantizer having a rate of 1 bitsample transmitted through a noisy channel, the softdecoding channeloptimized quantizer can achieve about 33. Optimality of the natural binary code for quantizers with channel optimized decoders1. Hence the simple inputindependent additive noise model is only an approximation to the noise in the pdf optimized quantizer. Optimality of the natural binary code for quantizers with. Gaussian and laplacian distributions are assumed for dc and ac coefficients, respectively finally, the vq codeword index from the encoder is generated by concatenating the binary codes from each of. Simulation results show that mcoqd provides more robust. At this point, we do not make any particular assumptions about the. A product quantizer can generate an exponentially large codebook at very low memorytime cost. The lower bound for performance of the new quantizer with complemented natural code cnc index assignment is given. Combined compression and denoising of images using vector. Uniform quantizer an overview sciencedirect topics. The scalar quantizer encoder block maps each input value to a quantization region by comparing the input value to the quantizer boundary points defined in the boundary points parameter.
The next theorem extends this result to decoder optimized uniform quantizers. A pdfoptimized scalar quantizer is designed for each of the m 2 dct coef. The quantizing encoder block quantizes the input signal according to the partition vector and encodes the input signal according to the codebook vector. Channeloptimized vector quantizer design for compressed.
The structure of the msvq encoder 27 consists of a cascade of vq stages as shown in fig. When the pdf of the analog sample is uniform, the decision intervals and output levels of the lloydmax quantizer can be computed analytically as shown below. Channeloptimized scalar quantizers with erasure correcting codes. Channel loses and decoding having described the predictive quantizer encoder. The idea now is to compute a new better quantized difference signal dqb n and use it for a better. Fast encoder optimization for multiresolution scalar quantizer design article pdf available in ieee transactions on information theory 573.
Rounding and truncation are typical examples of quantization processes. Variable rate image compression method with deadzone quantizer. Channel optimized quantizer decoders, in turn, depend on the source, the quantizer encoder, the channel, and the index assignment. This paper investigates the design of channeloptimized scalar quantizers with erasure correcting codes over binary symmetric channels bsc. Optimized compressive image sensing system over mobile. Dynamic memory model based optimization of scalar and vector. A pdf optimized scalar quantizer is designed for each of the m2 dct coefficients of y according to the rate allocation discussed above. The encoder function takes a 16bit twos complement speech sample and returns an 8. The reconstruction values yj of the optimum quantizer are identical to the linear.
The encoder fe and decoder fd are composed of convolutions and gdnigdn nonlinearities. Optimized product quantization 1 optimized product quantization. Quantizer design and distributed encoding algorithm for. Variable rate image compression method with deadzone. Optimized product quantization for approximate nearest. Optimized product quantization for approximate nearest neighbor search tiezheng ge1. Quantizers with uniform encoders and channel optimized. Joint design of a channeloptimized quantizer and multicarrier modulation article pdf available in ieee transactions on communications 4610.
Deep image compression with iterative nonuniform quantization. Dynamic memory model based optimization of scalar and. Using a dynamic memory model, the optimal computationmemory tradeoff is exploited to minimize the encoding time. For an stage msvq, an thstage quantizer, is associated with a stage codebook. Optimized product quantization 1 optimized product quantization tiezheng ge, kaiming hey, qifa ke, and jian sun abstractproduct quantization pq is an effective vector quantization method. Pdf joint design of a channeloptimized quantizer and. For uniform pdfx max x f x x 12x max want to uniformly quantize an rv x ux max,x max assume that desire m rls for r. A new scalar quantizer with uniform decoder and channeloptimized encoder aided by erasure correcting code is proposed. Ictus now con sider the transmission and decodingfestimation. As in the case of uniform quantizers, the pdf optimized nonuniform quantizers also have problems when the assumptions underlying their design are violated. Perceptually optimized bitallocation and associated. For uniform pdf x max x f x x 12x max want to uniformly quantize an rv x ux max,x max assume that desire m rls for r.
Joint sourcechannel vector quantization for compressed. I i i i i b b b b i i i f xdx xf xdx y e x x i y d 1 1 0 yi is the centroid of interval bi1, bi. Assuming that you know the pdf of the samples to be quantized design the quantizer s step so that it is optimal for that pdf. Our practical encoderdecoder designs consider channeloptimized vq for cs, coined covqcs, and channeloptimized msvq for. In order to design the optimized quantizer, the statistical properties of the encoded data are considered. Our practical encoder decoder designs consider channel optimized vq for cs, coined covqcs, and channel optimized msvq for cs, coined comsvqcs. Craig 3 by counting pulses or by timing the pulse width using a clock signal, both angular displacement and angular velocity can be determined. A low complexity quantization scheme using transform coding and bit allocation techniques which allows for easy mapping from observation to quantized value is. The second output signal from this block contains the quantization of the input signal based on the quantization indices and prescribed values.
To obtain the compressed representation of the input im. In this case, the decision intervals are all equal as well as the intervals between the output levels and the quantizer is called a uniform quantizer. To further improve its performance, the deadzone quantizer is introduced. The block outputs the zerobased index of the associated region. This object finds a zerobased index of the nearest codeword for each given input column vector.
Finally, the codeword index from the encoder is generated byconcatenatingthebinarycodes from each ofthe. Adaptive differential pulse code modulation using picmicro. Multiple description quantizer design using a channel optimized quantizer approach yugang zhou and waiyip chan department of electrical and computer engineering queens university, kingston, ontario, canada, k7l 3n6 email. Let a decoder optimized uniform quantizer denote a rate quantizer with a uniform encoder on and a channel optimized decoder i. Softdecoding vector quantizer using reliability information. This paper investigates the design of channel optimized scalar quantizers with erasure correcting codes over binary symmetric channels bsc. Pdf fast encoder optimization for multiresolution scalar. A new scalar quantizer with uniform decoder and channel optimized encoder aided by erasure correcting code is proposed. Initially, the quantizer step size index and the predicted sample s p are set to zero. Fast quantization method with simplified ratedistortion. Encode each input value by associating it with index value. Lloydmax quantizer optimum for fixedrate encoding, how can we. Each sensor processes its readings with a scalar quantizer. Assuming that you know the pdf of the samples to be quantized design the quantizers step so that it is optimal for that pdf.
Quantize signal using partition and codebook simulink. Vectorquantizerencoder returns a vector quantizer encoder system object, vqenc. The set of inputs and outputs of a quantizer can be scalars scalar quantizer. For this paper, we assume a uniform source on 0,1, a uniform quantizer encoder, a channel optimized quantizer decoder, and a binary symmetric channel with bit. Data input, specified as a column vector of size kby1 or a matrix of size kbym, where k is the length of each codeword in the codebook the number of rows in the data input, the length of the weights vector, and the length of the codeword vector must all be the same value. Note this definition of distortion applies to any quantizer, no matter what the encoder and decoder are. Note that for the optimum quantizer, the output signal variance is less than that of the input. Pdfoptimized scalar quantization with fixed length codes. Hence the simple inputindependent additive noise model is only an approximation to the noise in the pdfoptimized quantizer. Optimized product quantization 1 optimized product. The encoder and decoder of the quantizer are optimized iteratively. Multiple description quantizer design using a channel.
The quantizer makes the coding lossy, but it provides the major contribution in compression. Theorem 4 the natural binary code index assignment is optimal for a decoder optimized uniform quantizer. Deep convolutional autoencoderbased lossy image compression zhengxue cheng, heming sun, masaru takeuchi, and jiro katto. Quantizers with uniform encoders and channel optimized decoders. In summary, at high bit rates, one can conclude that the best quantization strategy is to use a uniform quantizer followed by an entropy encoder, which would result in a fairly simple lossy. In this paper, we present design and analysis of an automated algorithm optimizer for scalar and vector quantizer encoders. Deep convolutional autoencoderbased lossy image compression.
According to our experimental results, our method can achieve comparable rd performance with models optimized separately both in psnr and msssim. Given a codebook c, an encoder that minimizes the dis. Rate distortion optimized quantization rdoq is an efficient encoder optimization method that plays an important role in improving the ratedistortion rd performance of the high efficiency. An autoencoder with unbalanced structure as shown in figure 1 is used. Kaiming he2 qifa ke3 jian sun2 1university of science and technologyof china 2microsoft research asia 3microsoft research silicon valley abstract product quantization is an effective vector quantization approach to compactly encode highdimensional vectors. Observe the number of output values that falls in outer levels and inner levels if they match the assumed pdf.
1460 252 403 1269 198 1265 555 1422 1346 465 1265 609 1605 924 1456 1514 420 964 31 1043 1124 576 312 734 233 779 296 407 1198 1424 9 1110 947 405 812 826