Hanying Feng

On the rate-distortion performance and computational efficiency of the Karhunen-Loeve transform for lossy data compression

We examine the rate-distortion performance and computational complexity of linear transforms for lossy data compression. The goal is to better understand the performance/complexity tradeoffs associated with using the Karhunen-Loeve transform (KLT) and its fast approximations. Since the optimal transform for transform coding is unknown in general, we investigate the performance penalties associated with using the KLT by examining cases where the KLT fails, developing a new transform that corrects the KLTs failures in those examples, and then empirically testing the performance difference between this new transform and the KLT. Experiments demonstrate that while the worst KLT can yield transform coding performance at least 3 dB worse than that of alternative block transforms, the performance penalty associated with using the KLT on real data sets seems to be significantly smaller, giving at most 0.5 dB difference in our experiments. The KLT and its fast variations studied here range in complexity requirements from O(n(2)) to O(n log n) in coding vectors of dimension n. We empirically investigate the rate-distortion performance tradeoffs associated with traversing this range of options. For example, an algorithm with complexity O(n(3/2)) and memory O(n) gives 0.4 dB performance loss relative to the full KLT in our image compression experiments.

On the achievable region for multiple description source codes on Gaussian sources

We demonstrate inconsistencies in prior results on the achievable region for multiple description (MD) source codes on i.i.d. Gaussian sources with the squared error distortion measure. We then describe the complete region.

Improved bounds for the rate loss of multi-resolution source codes

We present new bounds for the rate loss of multiresolution source codes (MRSCs). Considering an M-resolution code, the rate loss at the ith resolution with distortion D/sub i/ is defined as L/sub i/=R/sub i/-R(D/sub i/), where R/sub i/ is the rate achievable by the MRSC at stage i. This rate loss describes the performance degradation of the MRSC compared to the best single-resolution code with the same distortion. For two-resolution source codes, there are three scenarios of particular interest: (i) when both resolutions are equally important; (ii) when the rate loss at the first resolution is 0 (L/sub 1/=0); (iii) when the rate loss at the second resolution is 0 (L/sub 2/=0). The work of Lastras and Berger (see ibid., vol.47, p.918-26, Mar. 2001) gives constant upper bounds for the rate loss of an arbitrary memoryless source in scenarios (i) and (ii) and an asymptotic bound for scenario (iii) as D/sub 2/ approaches 0. We focus on the squared error distortion measure and (a) prove that for scenario (iii) L/sub 1/<1.1610 for all D/sub 2/<D/sub 1/; (b) tighten the Lastras-Berger bound for scenario (ii) from L/sub 2//spl les/1 to L/sub 2/<0.7250; (c) tighten the Lastras-Berger bound for scenario (i) from L/sub i//spl les/1/2 to L/sub i/<0.3802, i/spl isin/{1,2}; and (d) generalize the bounds for scenarios (ii) and (iii) to M-resolution codes with M/spl ges/2. We also present upper bounds for the rate losses of additive MRSCs (AMRSCs). An AMRSC is a special MRSC where each resolution describes an incremental reproduction and the kth-resolution reconstruction equals the sum of the first k incremental reproductions. We obtain two bounds on the rate loss of AMRSCs: one primarily good for low-rate coding and another which depends on the source entropy.

Network source coding using entropy constrained dithered quantization

Summary form only given. Assuming the squared error distortion measure, the performance achieved is bounded by using scalar entropy constrained dithered quantization (SECDQ) to build multi-resolution (MR), multiple access (MA) and broadcast system (BS) source codes. The resulting performances for arbitrary source distribution are discussed.

Multiresolution source coding using entropy constrained dithered scalar quantization

In this paper, we build multiresolution source codes using entropy constrained dithered scalar quantizers. We demonstrate that for n-dimensional random vectors, dithering followed by uniform scalar quantization and then by entropy coding achieves performance close to the n-dimensional optimum for a multiresolution source code. Based on this result, we propose a practical code design algorithm and compare its performance with that of the set partitioning in hierarchical trees (SPIHT) algorithm on natural images.

On the Rate Loss of Multiterminal Source Codes

In this paper, we study the rate loss and achievable region of the multiterminal source code (MTSC), which is the code designed for a system comprising two independent encoders and joint decoder: encoders 1 and 2 describe sources X and Y using rates R₁ and R₂, respectively, and the joint decoder reconstructs X with distortion D₁ and reconstructs Y with distortion D₂. The rate loss of an MTSC is defined as L₁ = R ₁

On the rate loss of multiresolution source codes in the Wyner-Ziv setting

R_X|Y(D₁), L₂ = R₂ - R_X|Y(D₂), and L₀ = R₁ + R₂ - R_XY(D₁, D₂), where R_XY(D₁, D₂) is the joint rate-distortion function of (X,Y), and R_X|Y(D₁) and R_Y|X(D₂) are two conditional rate-distortion functions. We first show that for general real-valued memoryless sources and mean squared error distortion measure, the rate loss has an intrinsic connection with K₁ = R_XY(D₁, D₂)

Separable Karhunen Loeve transforms for the weighted universal transform coding algorithm

R_Y(D₂) - R_X|Y(D₁) and K₂ = R_XY(D₁, D₂) - R_X(D₁) - R_Y|X(D₂). We then study two common types of sources, jointly Gaussian sources and remote sources, in more details and bound K₁ and K₂ from above by small universal constants, which leads to small universal upper bounds on the rate loss and therefore good approximations of the achievable region

Near separability of optimal multiple description source codes

In this paper, we present upper bounds on the rate loss of the multiresolution source code in the Wyner-Ziv setting (WZ-MRSC). We define two types of rate loss, the side-information rate loss and the multiresolution rate loss, to measure the nonsuccessive refinability. The former compares the rates achievable by a given WZ-MRSC to the corresponding minimal rates achievable by single-resolution Wyner-Ziv codes, and the latter refers to the difference between the rates achievable by a given WZ-MRSC and the minimal achievable rates by any WZ-MRSC at the same resolution. We bound these two types of rate loss from above and show that the side-information rate loss and corresponding successive refinability largely depend on the side information, while there exist small universal constant upper bounds on the multiresolution rate loss that are generally independent of the side information

On the rate loss of multiple description source codes and additive successive refinement codes

The weighted universal transform code (WUTC) is a two-stage transform code that replaces JPEGs single, non-optimal transform code with a jointly designed collection of transform codes to achieve good performance across a broader class of possible sources. Unfortunately, the performance gains of WUTC are achieved at the expense of significant increases in computational complexity and larger codes. We here present a faster, more space-efficient WUTC algorithm. The new algorithm uses separable coding instead of direct KLT. While separable coding gives performance comparable to that of WUTC, it uses only 1/8 of the floating-point multiplications and 1/32 of storage of direct KLT. Experimental results included in this work compare the performance of new separable WUTC with both the WUTC and other fast variations of that algorithm.