SUMMARY Spatial patterns of functional organization, resolved by microelectrode mapping, comprise a core principle of sensory cortices. In auditory cortex, however, recent two-photon Ca2+ imaging challenges this precept, as the traditional tonotopic arrangement appears weakly organized at the level of individual neurons. To resolve this fundamental ambiguity about the organization of auditory cortex, we developed multiscale optical Ca2+ imaging of unanesthetized GCaMP transgenic mice. Single-neuron activity monitored by two-photon imaging was precisely registered to large-scale cortical maps provided by transcranial wide field imaging. Neurons in the primary field responded well to tones, neighboring neurons were appreciably co-tuned, and preferred frequencies adhered tightly to a tonotopic axis. By contrast, nearby secondary-field neurons exhibited heterogeneous tuning. The multiscale imaging approach also readily localized vocalization regions and neurons. Altogether, these findings cohere electrode and two-photon perspectives, resolve new features of auditory cortex, and offer a promising approach generalizable to any cortical area.

Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it challenging to apply them to large scale datasets. Moreover, in many applications the data can display structures beyond simply being low-rank, e.g., images and videos present complex spatio-temporal structures that are largely ignored by standard low-rank methods. In this paper we study a matrix factorization technique that is suitable for large datasets and captures additional structure in the factors by using a particular form of regularization that includes well-known regularizers such as total variation and the nuclear norm as particular cases. Although the resulting optimization problem is non-convex, we show that if the size of the factors is large enough, under certain conditions, any local minimizer for the factors yields a global minimizer. A few practical algorithms are also provided to solve the matrix factorization problem, and bounds on the distance from a given approximate solution of the optimization problem to the global optimum are derived. Examples in neural calcium imaging video segmentation and hyperspectral compressed recovery show the advantages of our approach on high-dimensional datasets.

No abstract

Functional organization is a key feature of the neocortex that often guides studies of sensory processing, development, and plasticity. Tonotopy, which arises from the transduction properties of the cochlea, is the most widely studied organizational feature in auditory cortex; however, in order to process complex sounds, cortical regions are likely specialized for higher order features. Here, motivated by the prevalence of frequency modulations in mouse ultrasonic vocalizations and aided by the use of a multiscale imaging approach, we uncover a functional organization across the extent of auditory cortex for the rate of frequency modulated (FM) sweeps. In particular, using two-photon Ca2+ imaging of layer 2/3 neurons, we identify a tone-insensitive region at the border of AI and AAF. This central sweep region behaves fundamentally differently from nearby neurons in AI and AII, responding preferentially to fast FM sweeps but not to tones or bandlimited noise. Together these findings define a second dimension of organization in the mouse auditory cortex for sweep rate complementary to that of tone frequency.