Motion‐Compensated Transform Coding

Interframe Hybrid Transform/dpcm Coders Encode Television Signals by Taking a Spatial Transform of a Block of Picture Elements in a Frame and Predictively Coding the Resulting Coefficients using the Corresponding Coefficients of the Spatial Block at the Same Location in the Previous Frame. These Coders Can Be Made More Efficient for Scenes Containing Objects in Translational Motion by First Estimating the Translational Displacement of Objects and Then using Coefficients of a Spatially Displaced Block in the Previous Frame for Prediction. This Paper Presents Simulation Results for Such Motion‐compensated Transform Coders using Two Algorithms for Estimating Displacements. the First Algorithm, Which is Developed in a Companion Paper, Recursively Estimates the Displacements from the Previously Transmitted Transform Coefficients, Thereby Eliminating the Need to Transmit the Displacement Estimates. the Second Algorithm, Due to Limb and Murphy, Estimates Displacements by Taking Ratios of Accumulated Frame Difference and Spatial Difference Signals in a Block. in This Scheme, the Displacement Estimates Are Transmitted to the Receiver. Computer Simulations on Two Typical Real‐life Sequences of Frames Show that Motion‐compensated Coefficient Prediction Results in Coder Bit Rates that Are 20 to 40 Percent Lower Than Conventional Interframe Transform Coders using Frame Difference of Coefficients. Comparisons of Bit Rates for Approximately the Same Picture Quality Show that the Two Methods of Displacement Estimation Are Quite Similar in Performance with a Slight Preference for the Scheme with Recursive Displacement Estimation. © 1979 the Bell System Technical Journa

Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell

Transform Domain Motion Estimation

This Paper Introduces an Algorithm for Estimating the Displacement of Moving Objects in a Television Scene from Spatial Transform Coefficients of Successive Frames. the Algorithm Works Recursively in Such a Way that the Displacement Estimates Are Updated from Coefficient to Coefficient. a Promising Application of This Algorithm is in Motion‐compensated Interframe Hybrid Transform‐dpcm Image Coding. We Give a Statistical Analysis of the Transform Domain Displacement Estimation Algorithm and Prove its Convergence under Certain Realistic Conditions. an Analytical Derivation is Presented that Gives Sufficient Conditions for the Rate of Convergence of the Algorithm to Be Independent of the Transform Type. This Result is Supported by a Number of Simulation Examples using Hadamard, Haar, and Slant Transforms. We Also Describe an Extension of the Algorithm that Adaptively Updates Displacement Estimation According to the Local Features of the Moving Objects. Simulation Results Demonstrate that the Adaptive Displacement Estimation Algorithm Has Good Convergence Properties in Estimating Displacement Even for Very Noisy Images. © 1979 the Bell System Technical Journa